Institute for Economic Studies, Keio University
Keio-IES Discussion Paper Series

第三者間における罰則規範遂行に関する考察：
二つの社会からの新しい実験事実
亀井 憲樹、Smriti Sharma、Matthew J. Walker
2023 年 8 月 21 日

DP2023-014
https://ies.keio.ac.jp/publications/22912/

Institute for Economic Studies, Keio University
2-15-45 Mita, Minato-ku, Tokyo 108-8345, Japan
ies-office@adst.keio.ac.jp
21 August, 2023
※ DP2023-010 の改訂版

第三者間における罰則規範遂行に関する考察：二つの社会からの新しい実験事実
亀井 憲樹、Smriti Sharma、Matthew J. Walker
IES Keio DP2023-014
2023 年 8 月 21 日
JEL Classification: C92, H41, D01, D91
キーワード: 実験、社会間比較、公共財、第 3 者罰則、高次罰則【要旨】
社会における協力規範の醸成には第三者による自発的罰則が有効である。一方で、複数の第三者が同時に規範逸脱に直面した時には、第三者は互いに相手の行動にただ乗りをする誘惑に駆られる。本論文では、囚人ジレンマゲーム実験を行い行動データを収集することで、（A）第三者罰
則に関する人々のただ乗り性向を分析するとともに、（B）第三者間での高度の罰則が果たす役割を考察した。人々の第三者としての罰則行動には血族関係の強さや文化が影響すると主張する
人類学・理論生物学・経済学の知見をもとに、その度合いが強いと知られる『インド』と、弱いと知られる『英国』の二地域を研究実施地に選び実験を行った。実験結果によると、どちらの社会でも、囚人ジレンマゲームで裏切りを選択しパートナーを搾取したものが強い罰則を受け、また、そのような罰則を科さなかった第三者は別の第三者から高次の罰則を受けた。一方で、地域間比較の分析からは、英国における第三者罰則がインドよりも強いという結果が得られた。この
行動パターンは、祖先からの血縁関係が弱い社会ほど第三者罰則性向が強いと主張する人類学・
理論生物学・経済学における主張と整合的である。一方で、同文献における主張や社会的選好理論とは異なり、「グループサイズ効果」に関するインドと英国での明確な違いも確認された。英国では、第三者は、他の第三者が複数いる環境では他の第三者にただ乗りをする性向を持つ（自身は罰則額を減らそうとする）一方で、インドでは、第三者は、他の第三者が周りにいることによって自身が罰則額を増やそうとする性向があった。
亀井 憲樹
慶應義塾大学経済学部〒108-8345 東京都港区三田2-15-45
kenju.kamei@keio.jp
Smriti SharmaBusiness School, Newcastle University
5 Barrack Road Newcastle upon Tyne NE1 4SE, United Kingdom
smriti.sharma@newcastle.ac.uk
Matthew J. Walker
Business School, Newcastle University
5 Barrack Road Newcastle upon Tyne NE1 4SE, United Kingdom
matt.walker@newcastle.ac.uk
謝辞：We thank Advaita Singh, Shivansh Wadhwa, Rohan Agarwal and Ragini Ramanujam for excellent
research assistance, and seminar participants in Newcastle, Louis Putterman and Simon Siegenthaler for
useful comments. Financial support by the Murata Science Foundation and Newcastle University Business
School is gratefully acknowledged. The experiments in this study received ethical approval from the
Newcastle University Ethics Committee ref. 15678/2021.

Collective Sanction Enforcement: New Experimental
Evidence from Two Societies

This version: August, 2023
Kenju Kamei1, Smriti Sharma2, Matthew J. Walker3
1

Faculty of Economics, Keio University, 2-15-45, Mita, Minato-ku, Tokyo 108-8345, Japan. Email:kenju.kamei@keio.jp.

2

Business School, Newcastle University, 5 Barrack Road Newcastle upon Tyne NE1 4SE, United
Kingdom. Email: smriti.sharma@newcastle.ac.uk.

3

Business School, Newcastle University, 5 Barrack Road Newcastle upon Tyne NE1 4SE, United
Kingdom. Email: matt.walker@newcastle.ac.uk.

Abstract: Sanction enforcement offers the potential to mitigate free riding on punishment among
multiple third parties. Cross-societal differences in the effectiveness of sanction enforcement may be
explained by factors rooted in cultural evolution. This paper provides the first experiment to study thirdparty enforcement of punishment norms with and without opportunities for higher-order punishment byselecting two different societies in terms of the degree of ancestral kinship ties: India and the United
Kingdom. In both societies, third parties strongly inflict punishment when they encounter a norm
violation, and a third party’s failure to punish the norm violator invites higher-order punishment fromtheir fellow third parties. These behavioral patterns are consistent with a model of social preferences andliterature from anthropology and theoretical biology. On the other hand, two clear cross-societal variation
emerges. First, third-party enforcement is stronger in the UK than in India. Parallel to this behavioral
pattern, a supplementary survey also validates the conjecture that people in a society with looser ancestral
kinship ties (the UK) are relatively more willing to engage in pro-social punishment. Second, intriguingly,
the group size effect varies across the two societies: whereas third parties free ride on others’ punitive actsin the UK, they punish more when in the presence of other third parties in India.
JEL codes: C92, H41, D01, D91
Keywords: Experiment; Cross-societal variation; Public Goods; Third-party punishment; Higher-orderAcknowledgements: We thank Advaita Singh, Shivansh Wadhwa, Rohan Agarwal and Ragini
Ramanujam for excellent research assistance, and seminar participants in Newcastle, Louis Putterman andSimon Siegenthaler for useful comments. Financial support by the Murata Science Foundation and
Newcastle University Business School is gratefully acknowledged. The experiments in this study received
ethical approval from the Newcastle University Ethics Committee ref. 15678/2021.
Declarations of interest: None1

1. Introduction
How to achieve cooperation in society remains an enduring question in the social sciences. Societal
cooperation and self-governance can be achieved without a centralized governing body if the threat ofpunishment is strong enough (Ostrom, 1990). Informal punishment inflicted by independent parties
helped in promoting cooperation and trust before the emergence of states, such as in medieval Iceland andEurope, gold rush California (e.g., Hadfield and Weingast, 2013), and agency relations between Maghribi
traders in the eleventh century (e.g., Grief, 1993). More recently, decentralized punishment underpinned
trading agreements among nonstate firms in Vietnam at the end of the twentieth century (McMillan andWoodruff, 1999a, b), and substituted for formal institutions during warfare among nomadic societies in
East Africa (Mathew and Boyd, 2011). Voluntary altruistic sanctions to enforce social norms are alsoprevalent on social media platforms.1 Due to its importance, recent theoretical research has studied how
costly (third-party) norm enforcement may sustain cooperative behaviors in societies or organizations(e.g., Acemoglu and Wolitzky, 2020, 2021; Dixit, 2003; Levine and Modica, 2016; Acemoglu andJackson, 2017). However, there is little empirical work on the coordination of decentralized collective
punishment, i.e., punishment where there is no direct material gain to the norm enforcer.
Norm enforcement by uninvolved parties is a second-order public good, typical for a collective
action problem (Olson, 1965; Ostrom, 1990). As free-riding problems can arise in third parties’sanctioning behaviors, to ensure efficient punishment, it is necessary to establish institutions that assist
them in coordinating punitive acts. Existing theory thus emphasizes the role of second-order punishment:
punishment of the failure to sanction a norm violator (e.g., Acemoglu and Wolitzky, 2020, 2021; Axelrod,
1986; Hadfield and Weingast, 2013; Hechter, 1987; Henrich, 2004; Henrich and Boyd, 2001) orpunishment for committing an unjustified punishment act (e.g., Kamei and Putterman, 2015). However,
it is a priori unclear how serious free riding among multiple third parties would be and how second-order
norm enforcement among third parties mitigates free riding or deters anti-social punishment of acooperator.2
To address this question in a setting with high internal validity, a novel laboratory experiment was
conducted to study higher-order sanction enforcement among uninvolved individuals in anonymousinteractions. In addition to providing the first empirical evidence on this issue, the paper contributes to thewider literature on norm enforcement in social dilemmas by carefully implementing a cross-societal
design. Prior research by social scientists has found that human altruistic tendencies differ markedly
across societies and reflect the emergence of variable norms and institutions over time (e.g., Herrmann etal., 2008; Henrich et al., 2006; Marlowe et al., 2008; Henrich et al., 2010). Further, recent research has
1

Consider online content moderation and information sharing, which is often conducted voluntarily by a subset ofcommunity members with no direct benefit to the act of enforcement for any one individual. The prevailing norms
and the quality of information on digital platforms rely on sanction enforcement, another public good.
2
While there is a rich research agenda on higher-order punishment in the context of direct (peer-to-peer)
punishment, i.e., norm enforcement by involved parties, which has been shown to either drastically undermine oreffectively boost cooperation norms (e.g., Denant-Boemont et al., 2007; Nikiforakis, 2008; Hopfensitz and Reuben,
2009; Kamei and Putterman, 2015), surprisingly there is no experimental research on higher-order enforcement
among third parties.

1

revealed systematic variation in the perceived restrictiveness (“tightness”) of social norms in different
societies (e.g., Gelfand et al., 2011; Harrington and Gelfand, 2014).3 The evidence suggests thatdifferences in the historical tightness of kin-based institutions across countries persist till the present day(Schulz et al., 2019). In a breakthrough study, Enke (2019) linked cross-cultural data sets and informationin the Ethnographic Atlas to argue that contemporary societies with loose ancestral kinship ties may
display a greater willingness to engage in third-party punishment than those societies with historicallytight kinship ties. Building on these observations, the present study provides new evidence on crosssocietal variation by selecting two societies at opposite ends of the tight-loose kinship spectrum (Enke,2019): India, a country with relatively tight ancestral kinship ties, and the United Kingdom (UK), a
country with relatively loose ancestral kinship ties.
In the experiment, groups of two players engaged in a cooperation dilemma in the presence of eithera single third party or multiple third parties. The distinctive feature of the design is that it varies acrosstreatments the number of third parties confronted with a norm violation and the opportunities available tothird parties to punish each other after observing their peers’ norm enforcement acts (i.e., the availabilityof higher-order norm enforcement). The experimental results reveal three intriguing cross-societal
differences in punishment.
First, third parties punish a norm violator in the cooperation dilemma significantly more frequently
and strongly in the UK than in India, and this behavioral pattern is correctly anticipated by people in eachsociety. Second, different group size effects are detected across the two societies. In the UK, a third-party
punishment of a norm violator is significantly less frequent and less strong when there are other thirdparty peers confronting the norm violation. Thus, consistent with the theoretical research, the availabilityof higher-order punishment opportunities plays a crucial role in resolving the free-riding dilemma among
third parties. On the other hand, in India, the opposite group size effect emerges in that having fellow
third parties present encourages a third party to punish a norm violator significantly more frequently andmore strongly. Having higher-order sanction enforcement opportunities does not alter this pattern. Third,“efficient” higher-order enforcement, i.e., punishment of a third party’s failure to punish a norm violator
or of their “mis-directed” punishment in the primary cooperation dilemma, is more prevalent in the UK
than in India.
The cross-societal differences in the relative strength of pro-social first-order punishment andefficient higher-order enforcement quantitatively support Enke’s (2019) conjecture that people in acontemporary society with loose ancestral kinship ties (the UK) display a greater willingness to engage in
pro-social (first-order) and efficient (higher-order) altruistic punishment acts relative to those in acontemporary society with tight ancestral kinship ties (India). There is evidence to suggest that the crosssocietal difference in the group size effect can be explained by cooperation/trust. A survey conducted as apart of the experiment project indicates that generalized trust underpins productive economic interactions

In his book, “The WEIRDest People in the World,” Henrich (2020) discussed the evolutionary approaches to
explaining this variation, such as the kin-based morality versus universalist morality theme.
32

in loose kinship societies, but not in tight kinship societies; however, the relationship in the former isfragile when third-party peers are present, due to free-riding tendencies.
The findings of this study significantly advance our understanding of the conditions under which
decentralized collective punishment is likely to be effective at promoting cooperative behaviors when
there is no direct material gain to the enforcer and provide useful policy implications. Under these
conditions, in a society with loose ancestral kinship ties, free riding on punishment may arise among third
parties. Thus, appropriate higher-order institutions should be in place to deter free riding. While in theexperiment the higher-order institution was implemented as a costly punishment action, in practice thehigher-order institution may also constitute social rewards (e.g., “Likes” on social media platforms).
Under this interpretation, the threat of second-order peer punishment - or the anticipation of peer rewards- may sustain social norm enforcement in large groups; the relative strength of each remains an open
empirical question.
The cross-societal component of this study, however, suggests caution in generalizing about freeriding tendencies and desirable policies across diverse populations: although punishment is a secondorder public good, the results presented here suggest that in a society with tight ancestral kinship ties,
introducing multiple third parties may even reduce free-riding on punishment, which could be driven by
the baseline level of norm enforcement. In such cases, introducing a mechanism to increase the number of
independent third parties – perhaps through increased visibility of transactions – may improvecooperative behavior. This finding has broader implications for the study of cooperation, sanction
enforcement, and social norms: researchers should more carefully consider the effects of culture andhistorical backgrounds in determining contemporary patterns of sanction enforcement and designingdesirable policies to promote pro-social norms.
A central challenge for policymakers and researchers is to design institutions that can successfully
coordinate the actions of diverse actors to enforce cooperative behaviors (Ostrom, 2010). Previous
experimental work in the public goods literature has considered the coordination of direct punishment by
involved individuals to improve cooperation and deter anti-social punishment. A coordination mechanismthat has to date been found quite effective in repeated interaction settings is a democratic commitment toa particular punishment rule (e.g., Ertan et al., 2009; Kosfeld et al., 2009; Sutter et al., 2010; Dal Bó etal., 2010; Putterman et al., 2011; Andreoni and Gee, 2012; Markussen et al., 2014, Kamei et al., 2015;
Ambrus and Greiner, 2019; Nicklisch et al., 2016; Fehr and Williams, 2018). However, voting
institutions may be less effective in coordinating punishment to sustain cooperation when there areheterogeneous actors (Noussair and Tan, 2011) or in one-shot settings (see Van Miltenburg et al., 2014).
Moreover, such democratic institutions may not be available for coordination among uninvolved parties.
The present study is the first to study an alternative higher-order punishment mechanism to coordinate
decentralized collective punishment among multiple uninvolved individuals in anonymous one-shot
interactions, such as online, where alternative sanctioning mechanisms may not be feasible to implement
and where there is no fear of retaliation (for example, because anonymity precludes reputation building).
The experiment data demonstrate that such a coordination mechanism can be effective in certain contexts,
without relying on formal institutions.
3

The rest of the paper proceeds as follows: Section 2 briefly explains the related literature, andSection 3 summarizes the experimental design and implementation. Section 4 formulates hypotheses
based on theoretical analyses and related literature (the details of the theoretical analyses can be found in
Appendix B). Section 5 reports the results, and Section 6 concludes.

2. Related LiteratureThis study speaks to and builds upon two branches of the literature: (a) third-party enforcement ofsocial norms, and (b) direct (peer-to-peer) punishment.
Third-party Enforcement of Social Norms. Most research uses a prisoner’s dilemma game to examine
norm enforcement. In their seminal study, Fehr and Fischbacher (2004) found that third parties are willingto incur a private cost to punish a defector who exploited a cooperator. Several subsequent experiments
confirmed the robustness of human third-party punishment tendencies by varying the experimental
environment. First, third-party punishment tendencies have been seen to be stronger for in-group than outgroup settings (e.g., Bernhard et al., 2006; Lieberman and Linke, 2007) and when their acts are observed
rather than anonymous (e.g., Kurzban et al., 2007; Kamei, 2018). Second, while Fehr and Fischbacher(2004) demonstrated that third-party punishment is driven by outcome-based preferences, such as
inequity aversion (Fehr and Schmidt, 1999), it is also driven by emotions, such as anger (Nelissen andZeelenberg, 2009). Third, while most experiments were held for adults, the willingness of others to takecostly action to enforce cooperation norms is also widespread among children (e.g., Lergetporer et al.,2014; McAuliffe et al., 2015). Fourth, a third party inflicts stronger punishment on a norm violator whens/he is democratically elected than otherwise (e.g., Marcin et al., 2019). Fifth, while third-party
punishment is ubiquitous, its tendencies differ by society (e.g., Henrich et al., 2006; Marlowe et al., 2008;
Henrich et al., 2010). Sixth, two recent papers, Martin et al. (2019) and Krügel and Maaser (2020),
examined how the punishment decision of a third party is judged and is punished by an uninvolved
bystander (“fourth party”), both finding that failure to punish the respective norm violation is punished bya fourth party.
Although there are many experiments on third-party punishment, all except Kamei (2020) wereconducted by letting a single third-party player face a norm violation. In contrast, Kamei (2020) studied
third-party punishment when multiple third parties are faced with a norm violation in a small-scale
experiment. Third-party punishment was still observed in such environments. The present experiment
explores for the first time the tendency of higher-order punishment among third parties, such that higherorder punishment acts are also subject to free riding. This study is novel as the experiment is conducted
at two different societies in terms of the degree of ancestral kinship ties, considering that Enke (2019)
proposes that societies with loose ancestral kinship ties display a greater willingness to engage in thirdparty rather than peer-to-peer punishment. To the best of the authors’ knowledge, no study has previously
compared third parties’ free-riding and higher-order sanction enforcement tendencies across societies.
Direct (Peer-to-peer) Punishment. Although higher-order enforcement among third parties is to dateunderstudied, higher-order punishment has been examined in the context of direct (peer-to-peer)
punishment. A typical experimental design in this area adopts a repeated public goods game setup that4

includes additional punishment opportunities among peers immediately after a direct punishment stage(Fehr and Gächter 2000, 2002). Higher-order punishment has two opposing effects. On the one hand,human motives for revenge may lead to counter-punishment, thereby worsening group atmospheres andcooperation norms (e.g., Denant-Boemont et al., 2007; Nikiforakis, 2008; Bolle et al., 2014; Nikiforakis
and Engelmann, 2011). On the other hand, efficient higher-order punishment acts, i.e., punishment of
those who failed to punish a norm violation, and punishment of those who committed “mis-directed”
punishment (e.g., punishing a cooperator), or the mere visibility of punishment acts, may help discipline
punishment activities and promote cooperation norms (e.g., Denant-Boèmont et al., 2007; Kamei and
Putterman, 2015; Fu et al., 2017). Revenge is not applicable to the context of higher-order punishment
among third parties, as the third parties are not the victims of a norm violation in the primary cooperation
problem. The efficient form of higher-order punishment act described above, however, remain relevant if
the punitive phenomenon is driven by humans’ other regarding preferences (see, e.g, Fehr and Schmidt[2006] and Sobel [2005] for a survey). Thus, similar positive effects of sanction enforcement may emerge
in the context of third-party punishment when higher-order punishment is allowed.

3. Experimental Design and Implementation
The experiment is designed based on a prisoner’s dilemma game with third-party punishment(Fehr and Fischbacher, 2004; Kamei, 2020). Three treatments are designed by changing the number ofthird parties per group and the possibility of higher-order punishment among third parties. The threetreatments are named as the “Baseline”, “Trio”, and “Higher-Order” treatments. Groups in the Baseline
treatment have three subjects each, while groups in the Trio and Higher-Order treatments have fivesubjects each. Two subjects in each group are randomly assigned to play a prisoner’s dilemma game – thePD players hereafter, and the rest (either one or three depending on the treatment) are assigned the role ofa third-party player.4 The experiment begins with a stage in which the PD players decide whether tocooperate (Section 3.1). This is the same for all treatments, after which third parties make punishment
decisions. The punishment stage differs by the treatment (Section 3.2).

3.1. Prisoner’s Dilemma Game
Two PD players are endowed with 40 points each (5 points = £1), and then simultaneously decide
whether to send 16 points to one another. Amounts sent will be tripled and become the payoff of therecipient. This is the only decision to make for the PD players. The possible payoffs of the two PD
players can be summarized in the form of payoff matrix in Figure 1. This framing of the prisoner’s
dilemma game is frequently adopted in the experimental research on third-party punishment (e.g., Fehrand Fischbacher, 2004; Kamei, 2020).
The PD player who sent (did not send) 16 points is called a “cooperator” (“defector”) hereafter.
The third-party players have no decision to make in this stage. They are instead asked to submit theirbelief, in increments of 10 percentage points, about the percentage of cooperators in the groups that they4

The PD player is called Player A, while the third-party player is called Player B in experiment instructions.

5

do not belong to.5,6 They can earn one point if the difference between their guess and the actual
percentage is less than or equal to five percentage points.

Figure 1: Payoff Matrix in the Prisoner’s Dilemma Game
Player 2

Send (cooperate)
Player 1
Not send (defect)

Send

Not send(a)72, 72(b)88, 24(c)24, 88(d)40, 40This stage is called “Stage 1” in the experiment instructions. Once PD players make sending
decisions and third-party players submit their beliefs, Stage 2 begins. The PD players’ decisions to sendremain anonymous throughout. In Stage 2, third-party players make punishment decisions utilizing astrategy method (Section 3.2).

3.2. Third Parties’ Decisions
Third-party players are each endowed with 60 points in the experiment. In Stage 2, they decide
how many punishment points they wish to assign to each of the two PD players in their own group undereach contingency (in the Trio and Higher-Order treatments, three third parties in each groupsimultaneously and independently make the punishment decisions). Specifically, they make fourdecisions as there are four possible interaction outcomes in Stage 1 regarding
the following:7,8(a) how many punishment points to impose on a cooperator (a PD player who sent 16 points) while theother PD player is also a cooperator.
(b) how many punishment points to impose on a defector (a PD player who did not send 16 points) while
the other PD player is a cooperator.
(c) how many punishment points to impose on a cooperator while the other PD player is a defector.
(d) how many punishment points to impose on a defector while the other PD player is also a defector.
A third-party player can assign up to ten punishment points (in increments of 2s) to a PD playerin each scenario. For each punishment point assigned, the punisher needs to pay one point, but the payoffof the recipient (PD player) is then reduced by three points. The cost ratio of 1:3 is commonly used in

5

The inclusion of the task helps make subjects equally busy in the experiment, thereby retaining high anonymity.
The two PD players’ decisions in their own group are excluded from the reference group to avoid hedging.
7
Third-party punishment decisions are known to be robust to using the strategy method (e.g., Jordan et al., 2016).
8
The four questions are randomly ordered on a computer screen that a third-party player sees, to control for the
possibility of spill-over effects between scenarios.
66

third-party punishment experiments (e.g., Fischbacher and Fehr, 2004; Kamei, 2020). Scenarios (a), (b),(c) and (d) are referred to as “mutual cooperation”, “betrayal”, “victim”, and “mutual defection,”
respectively. Punishment of a PD player in the “betrayal” or “mutual defection” scenario is called “prosocial,” while third-party punishment in the “mutual cooperation” or “victim” scenario is called “antisocial”.9 There are no decisions for PD players to make in Stage 2. They are instead asked to submit theirbelief about the average number of punishment points assigned by third parties in each of the four
scenarios, in the groups they do not belong to.10
Decisions in two of the four scenarios will be applied based on the two PD players’ actual
sending decisions in their own group. For example, if (cooperate, defect) is the realized outcome, thethird-party player’s decision in “victim” and “betrayal” will be applied. The third-party players (PDplayers) will not be informed of which scenarios are realized (how they are punished) until the decisionmaking portion of the experiment ends. The decision-making experiment is over once Stage 2 ends in the
Baseline and Trio treatments. In contrast, there is an additional stage (Stage 3) for higher-orderpunishment among third parties in the Higher-Order treatment.
In Stage 3 of the Higher-Order treatment, each third-party player will be presented with 30
possible scenarios from Stages 1 and 2 in sequence; and they will then decide how to reduce the payoffs
of the other two third-party players in their own group based on their punishment decisions in Stage 2(see Appendix A.4 for a screen image of one scenario). The punishment technology is the same as inStage 2: the punishment points to another third-party player is from {0, 2, 4, 6, 8, 10} and the cost ratio is
1:3. 30 scenarios include (a) 29 randomly constructed hypothetical scenarios by the computer and (b) one
real one, in which third parties’ Stage 3 punishment decisions will be applied to determine the final
payoffs of the three third parties in their group.11
Considering the literature on direct punishment (Section 2), it can be assumed that both higherorder punishment of those who failed to punish a norm violation, and of those who committed “misdirected” punishment, i.e., punishing a cooperator, may undermine the establishment of first-order
punitive norms that encourage socially optimal PD interactions. For this reason, higher-order punishmentfrom i to j when j pro-socially punished a defector less than i in “betrayal” or “mutual defection,” or when
j anti-socially punished a cooperator more than i in “mutual cooperation” and “victim” are called“efficient” higher-order punishment. In all other cases, higher-order punishment is referred to here as“inefficient.”
There are no decisions for PD players to make in Stage 3. To retain high levels of anonymity, andalso to collect the data on prevailing norms, they are instead presented with 30 possible scenarios from
Stage 1 and 2 that third-party players in other groups were presented. They are then asked to submit their
9

In the experimental literature on punishment, the anti-social/pro-social classification is usually made by taking thepunisher’s own contribution into account (e.g., Herrmann et al., 2007). This paper simply defines that punishing any
cooperator in a one-shot PD is anti-social and punishing any defector is pro-social without considering a third
party’s payoff, because the third party is not materially affected by the PD interactions.
10
The presence of the task makes subjects equally occupied in Stage 2. See footnote 7 also.
11
For “mutual cooperation” and “mutual defection”, the scenario is applied twice, once for each of the PD players;for “betrayal” and “victim”, there are two real scenarios, each of which is applied once.

7

beliefs regarding how the third-party players will inflict punishment in Stage 3. Four out of 30 scenarios
will be randomly selected for payment based on the accuracy of the guesses.12

3.3. Payoffs
The payoff of a PD player depends on their own sending decision, their partner’s sending
decision and first-order punishments given by third-party player(s) in their own groups. If the payoff isnegative, it is set at zero. The payoff of PD player i  {1,2} is therefore expressed by:
𝜋𝑖 = max⁡{𝜋1,𝑖 − 3𝑝𝑖 , 0},(1)where 𝜋1,𝑖 = 72, 88, 24, or 40 (Stage 1 payoff), 𝑝𝑖 is punishment points received by i, and 𝑝𝑖 = ∑𝑛𝑗=3 𝑝𝑗→𝑖 ,where 𝑝𝑗→𝑖 is punishment from third-party player j  {3,4,5} to PD player i and n is the group size, i.e., n= 3 for the Baseline treatment (n = 5 for the Trio and Higher-Order treatments).
By contrast, the payoff of third-party player j depends on their punishment activities, and isexpressed as follows:
𝜋𝑗 = 60 − ∑𝑖 𝑝𝑗→𝑖 for the Baseline and Trio Treatments; and𝜋𝑗 = max⁡{60 − ∑𝑖 𝑝𝑗→𝑖 − ∑𝑘 𝑝𝑝𝑗→𝑘 − 3 ∑𝑘 𝑝𝑝𝑘→𝑗 , 0} for the Higher-Order treatment,(2)

where 𝑝𝑝𝑗→𝑘 is second-order punishment from third-party player j to k.
As shown in Equations (1) and (2), the payoff is set at zero if their payoff is negative due topunishment activities.13 As explained in Section 3.2, both PD players and third-party players can earn
additional points from the questions about beliefs.

3.4. Additional Data Collection
This experiment consists of three parts. In Part 1, all subjects take a short intelligence test
consisting of 12 questions –see Appendix A.1 for the instructions. The questions are taken from Raven’s
progressive matrices (see Raven, 2000). A total of 40 seconds is allocated to complete each question. The
subjects can earn one point for every correct answer, while they are not penalized for wrong answers. Part
2 begins after everyone finishes the intelligence test; this part is the decision-making experimentsummarized in Sections 3.1 to 3.3. Part 3 is a post-experiment questionnaire, which includes a battery ofquestions from contemporary surveys that measure moral variables –see Appendix A.5 for details of thequestionnaire.

12

Each scenario askes two guessing questions as there are two targets for each third-party player. If the difference
between guess about average punishment points and the peers’ actual punishment points is less than or equal to one
point, they will receive one point. Since four scenarios will be used for payments, they can earn up to eight points.
13
It is commonly set that an experimenter does not take money from a subject even if the subject receives a negative
payoff in experiments on decentralized punishment in general —see, e.g., Fehr and Gächter (2000, 2002) for direct
punishment, and Fehr and Fischbacher (2004) and Kamei (2020) for third-party punishment.

8

3.5. Experimentation
3.5.1. Selection of the Two Societies
Prior research suggests that the extent to which people in pre-industrial societies were embedded
in extended and interconnected family networks is positively related to societal patterns of cooperationand trust for in-groups, and inversely related to the willingness of people to engage in productive
economic interactions with strangers (see, e.g., Alesina and Giuliano, 2013). The present research uses a
conventional lab experiment and targets two theoretically relevant subject pools to measure punitive
tendencies. This approach has an advantage that enables us to achieve the highest internal validity of alaboratory setup.
Selection of the two societies (India and the UK, see Figure 2) for the present experiment was
based on the observation that these differences in the organization of economic activities across societies
may have engendered different moral systems to regulate behavior. Building on ethnographic datasets(Murdock, 1967; Giuliano and Nunn, 2018), Enke (2019) constructed a normalized index of historicalkinship tightness (scale from zero to one) and mapped the index to contemporary country-level population
distributions. Historical kinship tightness is found to be a strong predictor of variation in contemporary
cross-country moral behaviors. People in societies with loose ancestral kinship ties (index score < 0.25)
are relatively more willing to engage in third-party punishment relative to direct (peer-to-peer)
punishment.
To explore cross-societal differences in sanction enforcement further, two countries classified as“loose” or “tight” based on Enke’s (2019) kinship tightness index were selected for the present study: theUK (index score of 0.023) and India (index score of 0.776). There were two practical reasons for selecting
these societies in which to implement the experiments: (a) strong English language abilities in India,14 and(b) the access to an established behavioral economics laboratory that ensures high internal validity in eachresearch site. To check whether the subjects in these two locations have different tendencies consistent
with the literature, as shown in Table 1, z-scores of stated willingness to engage in third-party relative todirect punishment for the selected societies were calculated based on responses to survey questions fromthe GPS, implemented in the post-experiment questionnaire (Part 3 of the experiment). It shows that,consistent with the observation in Enke (2019), respondents in the UK report a greater willingness toengage in third-party punishment relative to direct punishment. This suggests that subjects in the two
research sites exhibit the expected cross-country differences in attitudes towards sanction enforcement.

14

India is the largest member state of the Commonwealth, an association of countries which are connected throughtheir use of the English language and shared democratic values. Maintaining some similarities on these dimensions
is desirable to explore the relationship between historical kinship tightness and punitive behaviors.

9(a) Contains OS data © Crown copyright and database right (2023); (b) Made with Natural Earth.

(a) UK (Newcastle)(b) India (Sonipat)

Figure 2: Selection of the Two Societies
Table 1: Kinship Tightness and Stated Punishment Preferences in the Experiment Sample
UK (Newcastle)

India (Sonipat)

a. Kinship tightness index (Enke 2018)

0.023

0.776

b. Third-party vs. direct punishment (Experiment sample)

0.086-0.078Society

Difference-0.164**

Notes: Row a is computed based on the country-level score published in Enke (2018). Row b is a z-scoreconstructed based on subjects’ responses to post-experiment survey questions from the GPS in the present
experiment (see Appendix A.5 for details on construction of this variable). The Diff column is the coefficientof a linear regression of society on the variable for our experiment sample (N=501). Stars indicate whether thisdifference is significant. ** two-sided p <0.05.

3.5.2. Implementation
The experiment sessions were conducted face to face at the Experimental and Behavioural
Economics Laboratory, Newcastle University in Newcastle upon Tyne, the UK, from December 2021 toJune 2022, and at the Behavioural Laboratory, Ashoka University in Sonipat, India from April to October
2022. Subjects voluntarily registered for and participated in the experiment sessions.15 No subject
participated in more than one session. The experimental procedures were identical at the two research

15

Invitations were sent using hroot (Bock et al., 2014) in Newcastle, and via campus advertisements in Sonipat.

10sites. The number of subjects in Newcastle is 254, and that in Sonipat is 262 (Table 2).16 To check
whether key demographic information is balanced between the two subject pools, the information ongender and academic major was collected from the subjects. The percentages of female subjects nor
economics majors are significantly different between India (Sonipat) and UK (Newcastle).17 Further, thetwo universities are highly selective in their admissions processes. The average score of Raven’s
progressive matrix supports this assumption: the average score in Newcastle was 5.34, insignificantly
different at two-sided p = 0.646 (Mann-Whitney test) from that in Sonipat, 5.17 – see Appendix Figure
C.1. This implies that cognitive ability is also balanced between the two research sites.
The experiment was computerized based on oTree (Chen et al., 2016). As explained, there arethree parts (Part 1, Part 2 and Part 3) in the experiment. At the onset of each part, subjects were given
instructions for that part only; and were given instructions for the next part only after the current part wasover.18 The experiment sessions lasted around 60 minutes on average. The average per-subject payments
were £14.93 pounds sterling in Newcastle and INR 1022 Indian Rupees (approx. £10.20 at the prevailingexchange rate) in Sonipat, respectively.19

Table 2: Treatment and Number of Subjects
Treatment# of third parties per group

Higher-order punishment# of subjects# of groups

A. United Kingdom (Newcastle)
Baseline

1

No

69

23

Trio

3

No

90

18

Higher-Order

3

Yes

95

19

Total

---

---

254

60

Baseline

1

No

57

19

Trio

3

No

105

21

Higher-Order

3

Yes

100

20

Total

---

---

262

60

Total

---

---

516

120

B. India (Sonipat)

16

Sessions were conducted with an aim to collect around 20 independent observations per treatment in each subject
pool. One session of 15 subjects for the Higher-Order treatment in Newcastle experienced a server outage at the endof the 27th scenario in Stage 3. For this reason, data for the final three scenarios and for the post-experimentquestionnaire are missing for these subjects.
17
The percentage of female subjects in Newcastle was 48.9%, which is not significantly different at two-sided p =0.209 (Fisher exact test) from that in Sonipat, 43.3%. The percentages of economics majors are 30.4% and 29.5% in
the two samples, respectively; these two percentages are not significantly different according to two-sided p = 0.845(Fisher exact test).
18
This kind of gradual learning is often used in an experimental design with many components or with complex
decisions to avoid cognitive overload (e.g., Ertan et al., 2009; Kamei et al., 2015).
19
The payment size in each subject pool was decided following the laboratory norm in each research site. The
minimum daily wage for skilled labour in Haryana state (in which Sonipat is located) at the time of experiment was
INR 503 (https://storage.hrylabour.gov.in/uploads/labour_laws/Y2022/Oct/W2/D14/1665746988.pdf, last accessed
April 2023).

11

4. Hypotheses
Standard theoretical predictions based on players’ self-interest and common knowledge of theself-interested preferences are straightforward in this experiment as third-party punishment is costly andnon-enforceable. The logic of backward induction can be applied to all the three treatments. First, in the
Baseline treatment, a third-party player inflicts no punishment on a PD player in the second stage (final
stage) as punishment activities cost the punisher. Knowing this, it is privately optimal for the PD player todefect. Second, this prediction of the Baseline treatment does not change when there are three third parties
per group, as again no third parties punish their PD players due to the costliness of punishment acts. Thus,in the Trio treatment, defection continues to be the strictly dominant strategy for the PD players. Lastly,
the possibility of third parties’ higher-order punishments does not change anything, as it is costly for athird party to higher-order punish another third party. The Higher-Order treatment is essentially the sameas the Trio treatment for self-interested players, due to the no higher-order punishment activities.
Hypothesis 1 (Self-interested preferences): (a) Every PD player chooses to defect (i.e., not to send 16
points to each other) in the first stage. (b) Third parties neither first-order punish PD players nor higherorder punish their fellow third parties in the punishment stages.
As summarized in Section 2, experiments over the past 20 years have consistently documented
that third parties do inflict altruistic punishment, thereby enforcing cooperation norms effectively undercertain conditions (e.g., Fehr and Fischbacher, 2004). This is inconsistent with Hypothesis 1. Although
there are several social preference theories in the behavioral literature (for surveys, see Sobel, 2005; Fehrand Schmidt, 2006), inequality-averse preferences are known to explain such punishment behaviors
effectively (e.g., Fehr and Fischbacher, 2004; Kamei, 2020). Online Appendix B summarizes theoreticalanalyses conducted to obtain insights for subjects’ behaviors in the present experimental framework,
using the inequity-averse preference model by Fehr and Schmidt (1999):20
𝑈𝑖 (𝑥) = 𝜋𝑖 −𝛼𝑖
𝛽∑ max{𝜋𝑗 − 𝜋𝑖 , 0} − 𝑖 ∑𝑗≠𝑖 max{𝜋𝑖 − 𝜋𝑗 , 0},𝑛−1 𝑗≠𝑖𝑛−1(3)where n is the number of players per group (= 3 or 5), x is the list of the n players’ payoffs, 𝛼𝑖 indicatesplayer i’s aversion to disadvantageous inequality, while 𝛽𝑖 indicates player i’s aversion to advantageous
inequality, satisfying 𝛽𝑖 ≤ 𝛼𝑖 and 0 ≤ 𝛽𝑖 < 1. An analysis focused on symmetric equilibria provides four
useful lessons.
First, unlike Hypothesis 1, some PD players choose to cooperate with their paired PD players,
driven by their inequality concern or by the threat of punishment. Second, third parties only inflictpunishment on their PD players in the “mutual cooperation,” “victim” and “mutual defection” scenarios
under very stringent conditions.21 On the other hand, they are more likely to inflict punishment on a PD
The theoretical analyses extend the approach of Kamei (2018). In Appendix B, the four scenarios in the prisoner’s
dilemma game, “mutual cooperation,” “victim,” “betrayal,” and “mutual defection,” are denoted as, respectively,
scenarios CC, CD, DC, and DD, for consistency with the mathematical expressions.
21
More precisely, it predicts that a third party never punishes a PD player in the “victim” and “mutual defection”
scenario in all three treatments. In contrast, the third party is predicted to punish a PD player in the “mutual
cooperation” scenario if and only if 𝛼𝑖 > 2 in the Baseline treatment, and 𝛼𝑖 /2 + 𝛽𝑖 > 2 in the Trio and Higher20

12

player in the “betrayal” scenario if they are sufficiently averse to inequality in each treatment condition.22
The behavioral patterns just described fit quite well with prior related experiments on third-party
punishment with a single third-party player (e.g., Fehr and Fischbacher, 2004) as well as with multiple
third-party players (Kamei, 2020). Third, punishment of a “betrayal” defector per third-party player isweaker in the Trio and Higher-Order treatments than in the Baseline treatment. This tendency is the socalled “group size effect” similar to Olson (1965): having multiple third parties triggers incentives among
third parties to free ride on the peers’ punishment acts. Fourth, a comparison between the Trio andHigher-Order treatments suggests that higher-order punishment opportunities do not affect any predictedbehaviors in the Trio treatment. Notice that, in any symmetric equilibrium of the Trio treatment, using
higher-order punishment opportunities worsens inequality, as higher-order punishment activities reduce
the payoffs of the punisher and the punished, thus making a deviation from the no punishment situation
unbeneficial.
Hypothesis 2 (Social preferences): (a) Some PD players choose to cooperate (i.e., send 16 points to theirpaired PD players) in the first stage in each treatment. (b) Third parties are more likely to punish a
defector in the “betrayal” scenario than in any other scenario. (c) The punishment of a defector isweaker in the Trio and Higher-Order treatments than in the Baseline treatment.
The assumption of inequality-averse preferences does not postulate the higher-order punishment
opportunities to alter or improve (first-order) punitive norms among third parties in groups as a symmetricequilibrium outcome. However, higher-order punishment behaviors can also be predicted under theassumption of social preferences, once deviating from the symmetry in behaviors (see Appendix B for thedetailed mathematical analyses).23
First, under the assumption of inequality aversion, a third party’s failure to (first-order) punish a
defector invites higher-order punishments from their peers. Notice that when first-order punishments of adefector are heterogeneous in the “betrayal” scenario, a third party that punished less (informally, “nonpunisher,” hereafter) has an advantage in terms of interim payoff levels. Thus, the peers’ higher-orderpunishment of the non-punisher mitigates inequality by decreasing the non-punisher’s payoff advantage.
Likewise, a non-punisher in the “mutual defection” scenario invites higher-order punishments from theirpeers due to receiving the highest interim payoff in the group after the first punishment stage. Higherorder punishment of the non-punisher thus again reduces inequality among the group members. Second, athird party’s punishment of a cooperator in the “victim” scenario also invites higher-order punishments,

Order treatments – see Appendix B. The two conditions, 𝛼𝑖 > 2 and 𝛼𝑖 /2 + 𝛽𝑖 > 2, are restrictive, however. Almost
all people do not satisfy the conditions if using the distribution of 𝛼𝑖 and 𝛽𝑖 calibrated by Fehr and Schmidt (2010).
22
A third party is predicted to punish a defector in the “betrayal” scenario if 𝛼𝑖 + 𝛽𝑖 /⁡2 > 1 in the Baseline
treatment, and 𝛼𝑖 /2 + 3𝛽𝑖 /4 > 1 in the Trio and Higher-Order treatments. These conditions are less restrictive thanthe ones reported in footnote 23.
23
These predictions on higher-order punishments are formally derived by examining how the average higher-orderpunishment amount in a given scenario (Figure B.4 for the “mutual cooperation” scenario, Figure B.6 for the“betrayal” and “victim” scenarios, and Figure B.8 for the “mutual defection” scenario) depends on their fellow third
parties’ punishment amounts in the second stage – see Remarks 1 to 4 in Appendix B.3.

13

because doing so reduces inequality between the cooperator (a person who receives a very low payoff)and the third parties.
These off-equilibrium predictions complement a substantial literature in theoretical biology andanthropology in which scholars argue for the emergence of free-riding problems in third parties’sanctioning behaviors when there are multiple third-party peers in a group. Existing theoretical work inthis area emphasizes the role of efficient higher-order punishment among third parties to enforce prosocial first-order punitive norms. Such punishment takes a form of punishment of the failure to sanction anorm violator (e.g., Hadfield and Weingast, 2013; Axelrod, 1986; Henrich, 2004; Henrich and Boyd,
2001) or punishment for commission, i.e., inflicting unjustified sanctions (e.g., Kamei and Putterman,2015). Axelrod (1986) used the term “meta-norm” to refer to the punishment of non-punishers, andHenrich and Boyd (2001) and Henrich (2004) argue that such punishments effectively stabilize
cooperation. Higher-order punishment for commission is also crucial to maintain cooperation norms, as
anti-social punishment is widespread in our societies (e.g., Herrmann et al., 2007; Cinyabuguma et al.,2006).
The theoretical analysis and these discussions on higher-order punishment can be summarized as
Hypothesis 3 below:
Hypothesis 3 (Social preferences and arguments in theoretical biology and anthropology): (a) A third
party’s failure to punish a defector invites higher-order punishment from their fellow third parties. (b) A
third party’s punishment of a cooperator invites higher-order punishment from the peers.24
How do the third parties’ punitive tendencies differ by society? As discussed in Section 3.5.1, thepresent experiment carefully selected two countries, India and the UK, with an aim to investigate crosssocietal differences in people’s punitive behaviors. The final hypothesis of the present experiment follows
from the literature discussed therein.
Hypothesis 4: (a) Subjects in the loose kinship society (the UK) display a greater willingness to engage
in pro-social (first-order) and efficient (higher-order) third-party punishment acts relative to subjects inthe tight kinship society (India). (b) Anticipating these variable punitive norms, PD players in the UK
exhibit a higher inclination to cooperate than those in India.

24

A theoretical analysis using the social preference model does not always provide a reasonable prediction. As
shown in Appendix B, it predicts perverse reactions among inequality-averse third parties in the “mutual
cooperation” scenario, which is at odds with Hypothesis 3. Specifically, it states that a failure to inefficiently punish
a cooperator in the second stage attracts more higher-order punishment from the peers. The mechanism is that in the“mutual cooperation” scenario, some third parties may wish to punish cooperators if they are strongly averse toinequality, as a cooperator receives the highest payoff after the first stage (72 > 60). However, the third parties thencare about inequality between themselves and the non-punisher in the third stage. The predicted perverse reactions
among third parties are at odds with well-known behavioral patterns and motives for punishment in the literature(e.g., Fehr and Gächter 2000, 2002, Denant-Boemont et al. 2007, Kamei and Putterman 2015).

14

5. Results
5.1. Cooperation and first-order punishment
A first view of the cross-societal differences in cooperation and first-order punishment issummarized in Panel A of Figure 3. The numbers reported in this figure were calculated by using datafrom all three treatments so that the general patterns can be seen with the full dataset. An across-scenario
comparison suggests two clear patterns that support the predictions from social preferences. First,
consistent with Hypothesis 2.a (not Hypothesis 1.a), many PD players selected cooperation. The
cooperation rates were more than 50%, which are significantly positive at two-sided p < 0.001 for boththe subject pools.25 Second, third-party punishment of a defector in “betrayal” is much more frequent andis stronger than in any other scenario for both the subject pools. The higher frequency and stronger
punishment intensity in “betrayal” are both significant at the 1% level compared with any other scenarios
for each subject pool – see Part A of Appendix Table C.1. This pattern is consistent with Hypothesis 2.b(not Hypothesis 1.b).
Two interesting cross-societal differences also emerge – see again Figure 3.A and also Appendix
Table C.2. First, third parties’ punishment of a defector in “betrayal” is more frequent and stronger in the
UK (Newcastle) than in India (Sonipat). The differences are significant at the 1% level for both thepunishment frequency and the per-third-party strength. In addition, punishment of a defector in “mutual
defection” is significantly more frequent in the UK than in India at the 5% level. In sharp contrast, thirdparty punishment of a cooperator (whether in “mutual cooperation” or “victim”) is slightly stronger in the
UK than in India; the difference is not significant. Second, PD players’ cooperation rate is larger in the
UK (Newcastle) than in India (Sonipat) by more than 15 percentage points. The difference is significant
at the 1% level. These cross-societal differences in cooperation and first-order punishment are in line with
Hypothesis 4 that underlines the role of kinship tightness in affecting human altruistic punishment.
As explained in Section 3, third parties answered about their beliefs of PD players’ decisions tocooperate in the first stage; and PD players answered their beliefs on third parties’ punitive behavior in
the second round. This provides a measure of empirical expectations about punishment norms in our
experiment. Panel B of Figure 3 summarizes the average beliefs in the two stages. While the punishment
anticipated was stronger than the actual decision in each scenario (Panel B.ii), qualitatively similartendencies hold for beliefs (also see Part Bs of Appendix Tables C.1 and C.2). First, PD players in bothresearch sites believed that third parties inflict punishment in “betrayal” significantly more frequently andsignificantly more strongly than in any other scenario. Second, PD players in the UK (Newcastle)
anticipated significantly more frequent and significantly stronger third-party punishment in “betrayal”
than those in India (Sonipat). Third, third parties in the UK anticipated significantly higher cooperation
rates among PD players than those in India.

25

The null hypothesis of no cooperation is rejected at two-sided p < 0.001 according to a two-sided z test based on
the marginal effects from a Probit regression with no constant in each subject pool.

15

Figure 3: Cooperation and the First-Order Punishment by Society
100%

5.0

90%

4.5

80%

UK

4.0

India

70%

3.5

60%

3.0

50%

2.5

40%

2.0

30%

1.5

20%

1.0

10%

0.5

0%

UK

India

0.0
Cooperation
Mutualrate
cooperation
stage 1

VictimBetrayal

Mutualdefection

Mutualcooperation

Stage 2 - 1st order punishment

VictimBetrayal

Mutualdefection

Stage 2 - 1st order punishment(i) Frequency(ii) Average punishment given

A. Actual Decisions
100%

5.0

90%

4.5

80%

UK

4.0

India

70%

3.5

60%

3.0

50%

2.5

40%

2.0

30%

1.5

20%

1.0

10%

0.5

UK

India

0.0

0%
Cooperation
Mutualrate
cooperation
stage 1

VictimBetrayal

Mutualdefection

Mutualcooperation

VictimBetrayal

Mutualdefection

Stage 2 - 1st order punishment

Stage 2 - 1st order punishment(i) Frequency(ii) Average punishment given

B. Beliefs
Notes: Each Panel i reports the cooperation rates of PD players, and the percentages of third-party players that
inflicted punishment. Each Panel ii reports average punishment points given per third-party player. See Appendix
Tables C.1 and C.2 for testing of the cross-societal and across-scenario differences.

Figure 4 reports the first-order punishment patterns by treatment. The figures are drawn
separately for the UK (Newcastle) and India (Sonipat). The decision data (Panel Is) reveals first that thirdparty punishment of a defector in “betrayal” or “mutual defection” is more frequent and stronger than thatof a cooperator in “mutual cooperation” or “victim” for all three treatment conditions, whether in the UK(Newcastle) or India (Sonipat). The differences in the per-third-party punishment strength are significant
at least at the 5% level for almost all comparisons in the three treatments, in both the research sites (see16

Table 3).26 In addition, the difference in the punishment frequency is also large and significant for almost
all comparisons in the UK (Newcastle).27 Second, third-party punishment of defector is significantly more
frequent and significantly stronger in “betrayal” than in “mutual defection” for both the research sites(again see Table 3). These results are robust to including demographic controls (Appendix Table C.3).
The behavioral patterns detected resonate with the idea (from social preferences) that when punishing anorm violator, third parties are concerned about the welfare of his/her opponent.
The observed first-order punitive tendencies are again in line with the prevailing norms in thesocieties. Panels A.II and B.II of Figure 4 indicate almost similar belief patterns to the decision data, i.e.,
anticipated stronger third-party punishment of a defector, especially in “betrayal,” in all three treatments,
and these are supported by panel regression models as shown in Table 3 and Appendix Table C.3.
Result 1: (i) Whether in India (Sonipat) or in the UK (Newcastle), consistent with Hypothesis 2.b (notHypothesis 1.b), third parties’ first-order punishment is significantly more frequent and stronger in“betrayal” than in any other scenario in all three treatments. (ii) Consistent with Hypothesis 4.a, thethird-party punishment in “betrayal” is significantly more frequent and stronger in the UK than in India.
(iii) The behavioral patterns in (i) and (ii) were correctly anticipated by the subjects in each society.

5.2. Group Size EffectA close look at the treatment difference in first-order punishment decisions (Panel A.I and B.I of
Figure 4, Table 4) uncovers three intriguing cross-societal differences. First, a clear group size effectparallel to the theoretical analysis result was detected in the UK (Newcastle). The punishment frequency
and the per-third-party punishment strength in the “betrayal” scenario are both much lower in the Triothan in the Baseline treatment (Figures 3.A.I). As shown in column II of Table 4.A, and column II of
Table 4.B, the negative group size effect is significant at least at the 5% level. This is consistent with
Hypothesis 2.c.
Second, however, having fellow third parties in the Trio treatment increases a third-party player’s
punishment in “betrayal” in India (Sonipat). The opposite group size effect was seen both for the data of
the punishment frequency and strength (Figures 3.B.I), and the effect is significant at least at the 5% level(column II in Tables 5.A and 5.B). Further, the opposite group size effect was also observed in theHigher-Order treatment (see again Figure 4.B.I). These patterns in the Trio and Higher-Order treatments
are inconsistent with Hypothesis 2.c.

26

The punishment strengths are significantly different at least at the 5% level for all comparisons except three cases.
The two cases are the differences between “victim” and “mutual defection” in the UK’s Trio treatment, and in the
India’s Higher-Order treatment; These differences are significant at the 10% level. The third case is the difference
between “victim” and “mutual defection” in the UK’s Baseline treatment; and the difference is not significant.
27
The punishment frequencies are significantly different at least at the 5% level for all but two comparisons. The
exception is a comparison between “victim” and “mutual defection” in the Trio treatment (significantly different at
the 10% level) and in the Baseline treatment (insignificantly different).

17

Figure 4: (First-Order) Third-Party Punishment by Treatment
100%

5.0

100%

5.0

90%

4.5

90%

4.5

80%

4.0

80%

4.0

70%

3.5

70%

3.5

60%

3.0

60%

3.0

50%

2.5

50%

2.5

40%

2.0

40%

Baseline

Trio

Higher-Order

Baseline

Trio

Higher-Order

1.5

30%

2.0
Baseline

30%

Baseline

1.5

Trio

Trio
20%

1.0

20%

10%

0.5

10%

0.0

0%
Mutualcooperation

VictimBetrayal

Mutualcooperation

Mutualdefection

VictimBetrayal

Higher-Order

0.0
Mutualcooperation

ii. Avg. per-third-party punishment
points given

i. Frequency

Higher-Order

0.5

0%

Mutualdefection

1.0

VictimBetrayal

Mutualcooperation

Mutualdefection

VictimBetrayal

Mutualdefection

ii. Avg. per-third-party punishment
points given

i. Frequency

I. Actual Decisions

II. Beliefs

A. UK (Newcastle)
100%

5.0

100%
Baseline

Trio

Higher-Order

Baseline

Trio

5.0
Baseline

Higher-Order

Trio

Higher-Order

Baseline

90%

4.5

90%

4.5

80%

4.0

80%

4.0

70%

3.5

70%

3.5

60%

3.0

60%

3.0

50%

2.5

50%

2.5

40%

2.0

40%

2.0

30%

1.5

30%

1.5

20%

1.0

20%

1.0

0.5

10%

0.5

10%
0%

0%

0.0
Mutualcooperation

VictimBetrayali. Frequency

Mutualdefection

Mutualcooperation

VictimBetrayal

VictimBetrayal

Mutualdefection

Mutualcooperation

I. Actual Decisions

II. Beliefs

B. India (Sonipat)

VictimBetrayal

Mutualdefection

ii. Avg. per-third-party punishment
points given

i. Frequency

ii. Avg. per-third-party punishment
points given

18

Higher-Order

0.0
Mutualcooperation

Mutualdefection

TrioTable 3: Across-Scenario Difference in First-Order Punishment by Treatment(A) Frequency of first-order punishment given to PD players
Dependent variable:
Independent Variable:
India (Sonipat)
Betrayal
Mutual defection
VictimSonipat  Betrayal
Sonipat  Mutual defection

Baseline#1
Decisions
Beliefs
(1)
(2)

Trio
Decisions
Beliefs(3)(4)

Higher-Order
Decisions
Beliefs(5)(6)-0.979*(0.561)1.720***(0.374)0.727***(0.267)0.140(0.426)-0.296(0.602)0.031(0.591)-0.781***(0.296)-0.132(0.277)1.233***(0.252)0.781***(0.248)-0.164(0.197)-0.202(0.347)-0.583*(0.303)0.097(0.298)-0.000(0.186)0.061(0.293)
1.221***(0.241)0.748***(0.254)0.363(0.238)-0.334(0.323)-0.246(0.330)-0.363(0.342)-1.128***(0.217)-0.050(0.287)1.663***(0.359)0.834***(0.298)0.070(0.232)-0.752*(0.429)-0.284(0.353)-0.010(0.282)-0.070(0.210)-0.040(0.255)1.322***(0.207)0.578***(0.195)-0.057(0.206)-0.678**(0.268)-0.375(0.252)0.162(0.275)-0.688***(0.182)0.136(0.287)1.611***(0.318)1.099***(0.243)-0.000(0.235)-0.614(0.394)-0.361(0.314)-0.063(0.288)-0.199(0.206)149-76.500.206

336-199.70.113

468-254.10.0810312-183.2
0.108

468
-280
0.0885312-176.6
0.138

Sonipat  Victim
Constant
Observations
Loglikelihood
Pseudo R2

H0: Betrayal = Mutual defection(Do third parties punish defectors differently between “betrayal” and “mutual defection in the UK?)
Chi-squared-stat.
10.424
3.806
9.422
6.903
17.2342.792
p-value (2-sided)0.001***
0.051*
0.002***
0.009***
0.000***
0.095*
H0: Sonipat = Sonipat + Betrayal + Sonipat  Betrayal(Do third parties punish more strongly in “betrayal” than in the reference “mutual cooperation” in India?)Chi-squared-stat.
4.899
18.71517.15715.01914.41718.473p-value (2-sided)
0.027**
0.000***
0.000***
0.000***
0.000***
0.000***
H0: Betrayal + Sonipat  Betrayal = Mutual defection + Sonipat  Mutual defection(Do third parties punish defectors differently between “betrayal” and “mutual defection in India?)Chi-squared-stat.
4.774
13.992
8.115
2.897
9.334
p-value (2-sided)
0.029**
0.000***
0.004***
0.089*
0.002***

3.238
0.072*

Notes: Probit regressions with robust standard errors in parentheses clustered by subject ID. The dependent variable
is an indicator variable for a third-party player i’s decision (or a PD player’s beliefs about a third-party player i’s
decision) to first-order punish. The results are qualitatively the same when demographic variables are added – seeAppendix Table C.3 for the detail. #1 The interaction Sonipat  Victim is omitted because Sonipat  Mutual cooperation
is empty (Figure 4). *** p<0.01, ** p<0.05, * p<0.1

19

(B) Punishment strength (punishment points given) per third-party player
Baseline
Dependent variable: Decisions
Beliefs
Independent Variable:(1)(2)
India (Sonipat)-19.378***-0.478(2.357)(0.894)
Betrayal
7.171***
4.501***(1.850)(0.645)
Mutual defection
3.230***
1.970***(1.013)(0.603)
Victim
0.939-0.068(1.819)(0.675)14.397***-1.150
Sonipat  Betrayal(2.213)(0.947)-1.047
Sonipat  Mutual defection 15.346***(2.830)(0.832)15.666***-0.034
Sonipat  Victim(3.367)(0.967)
Constant-3.422**0.014(1.538)(0.609)Trio
Decisions
Beliefs
(3)
(4)
0.585
0.024
(1.965)(1.175)8.096***
4.348***(1.782)(0.861)4.615***
2.389**(1.623)(1.079)2.245-0.107(1.531)(0.839)-1.533-1.686(2.117)(1.073)-0.274-1.313(2.239)(1.172)-1.8030.219(2.331)(0.985)-8.011***0.142(1.920)(0.866)Higher-Order
Decisions
Beliefs(5)(6)-0.053
1.155(1.227)(1.038)5.655***
4.675***(0.803)(0.662)2.348***
2.563***(0.873)(0.591)-0.318-0.136(1.012)(0.803)-2.756**-1.942**(1.077)(0.962)-1.266-1.164(1.189)(0.861)0.275-0.650(1.308)(1.025)-3.049***-0.348(0.920)(0.725)Observations# left-censored obs.
# right-censored obs.
Loglikelihood
Pseudo R2

468
338
16
-549.80.0405468297
7-655.50.0422

168
116
3
-188
0.138

336
132
8
-633
0.0518312115
12-625.40.0301312114
6-608.80.0478

H0: Betrayal = Mutual defection(Do third parties punish defectors differently between “betrayal” and “mutual defection” in the UK?)
F-stat.
8.361
25.59413.36910.30729.98524.327p-value (2-sided)
0.004***
0.000***
0.000***
0.001***
0.000***
0.000***
H0: Sonipat = Sonipat + Betrayal + Sonipat  Betrayal(Do third parties punish more strongly in “betrayal” than in the reference “mutual cooperation” in India?)
F-stat.
54.28722.62714.37315.601
13.61316.421p-value (2-sided)
0.000***
0.000***
0.000***
0.000***
0.000***
0.000***
H0: Betrayal + Sonipat  Betrayal = Mutual defection + Sonipat  Mutual defection(Do third parties punish defectors differently between “betrayal” and “mutual defection in India?)
F-stat.
6.553
10.058
7.511
8.185
7.824
16.558p-value (2-sided)
0.011***
0.002***
0.006***
0.005***
0.005***
0.000***
Notes: Tobit regressions with robust standard errors in parentheses clustered by subject ID. The dependent variable isa third-party player i’s punishment points (or a PD player’s beliefs about a third-party player i’s punishment points)
given to a PD player. The results are qualitatively the same even when demographic variables are added – seeAppendix Table C.3 for the detail. *** p<0.01, ** p<0.05, * p<0.1

20

Table 4: Across-Treatment, and Cross-societal Difference in First-Order Punishment(A) Frequency of cooperation and first-order punishment given to PD players
Dependent var.

PD players’
decision tocooperate

Third parties’ decision to first-order punish(1)-0.517*(0.280)0.411(0.308)-0.115(0.283)-0.225(0.417)0.370(0.402)0.451**(0.192)(2)-0.484(0.299)0.360(0.320)0.099(0.328)-0.250(0.435)0.131(0.448)-0.191(0.596)

Scenario
I. “mutual
II. “betrayal”
III. “victim”
cooperation”
(3)#1
(4)#1
(5)
(6)
(7)
(8)#1
-0.040-0.078 -1.275*** -1.611*** -0.979*
0.072(0.255) (0.306) (0.426)(0.479)(0.555) (0.294)-0.347-0.624 -0.846** -1.125*** -0.124-0.404(0.365) (0.395) (0.353)(0.394)(0.340) (0.371)
0.093-0.012-0.305-0.327-0.105-0.286(0.345) (0.376) (0.357)(0.410)(0.337) (0.370)
0.100
0.365
1.002** 1.463*** 0.676-0.236(0.388) (0.438) (0.486)(0.532)(0.618) (0.409)
0.558
0.678
1.101*(0.490)(0.549)(0.610)-0.781*** -1.121 0.939***1.394-0.641**0.548(0.293) (1.130) (0.308)(0.970)(0.282) (1.106)

240
No-154.30.0344

217
Yes-132.40.0728257
No-123.10.0170IV. “mutual
defection”(9)(10)-0.949** -1.328***(0.435) (0.505)-0.326 -0.537(0.315) (0.330)-0.056 -0.200(0.310) (0.331)
0.763 1.271**(0.498) (0.556)
0.534
0.948*(0.496) (0.563)-0.055 -1.267(0.262) (0.928)
276
No-172.90.0271242
Yes-146.40.0667

H0: Trio + Sonipat  Trio = Sonipat (Do the behaviors differ between the Trio and Baseline treatments in India?)Chi-squared-stat.
2.05
1.27
0.11
0.07
4.39
6.67
2.28
1.10
3.31
p-value (2-sided)
0.15
0.26
0.74
0.80
0.04**
0.01***
0.13
0.29
0.07*

5.23
0.02**

Independent Var.
India (Sonipat)
Trio
Higher-Order
Sonipat  Trio
Sonipat  HO
Constant

Observations
Control
Loglikelihood
Pseudo R2

224
Yes-101.90.0447276
No-177.70.0640242
Yes-149.50.0990276
No-137
0.0257

224
Yes-109.40.0381

H0: Higher-Order + Sonipat  Higher-Order = Sonipat (Do the behaviors differ between the Higher-Order and Baseline
treatments in India?)Chi-squared-stat.
2.45
1.82
0.07
0.01
4.99
6.82
3.82
0.41
3.51
5.37
p-value (2-sided)
0.12
0.18
0.79
0.91
0.03**
0.01***
0.05**
0.52
0.06*
0.02**
H0: Sonipat + Sonipat  Trio = Trio (Do the behaviors differ between the UK and India in the Trio treatment?)
Chi-squared-stat.
4.35
3.69
0.53
2.13
1.38
3.35
0.12
0.18
0.09
p-value (2-sided)
0.04**
0.05**
0.47
0.14
0.24
0.07*
0.73
0.67
0.76

0.94
0.33

H0: Sonipat + Sonipat  Higher-Order= Higher-Order (Do the behaviors differ between the UK and India in the Higher-Order
treatment?)
Chi-squared-stat.
0.00
0.58
0.07
0.01
0.68
1.03
0.21
0.41
0.62
0.12
p-value (2-sided)
0.95
0.45
0.79
0.91
0.41
0.31
0.65
0.52
0.43
0.72

Notes: Probit regressions with robust standard errors in parentheses. The control variables in the even-numberedcolumns include a dummy for female, age, number of siblings, income rank and the Raven’s test score. #1 The
interaction Sonipat  Higher-Order is omitted due to collinearity in columns (3), (4) and (8). *** p<0.01, ** p<0.05,* p<0.1

21

(B) Punishment strength per third-party player
A third-party player’s punishment points given to a PD player

Dependent var.

Scenario
I. “mutual cooperation”
Independent Var.
India (Sonipat)
Trio
Higher-Order

(1)

(2)

II. “betrayal”

III. “victim”

(3)

(5)

(6)#1

(7)

(8)

-4.867-27.555***-4.963**-6.202**(4)-25.718*** -25.159*** -5.573*** -6.110***

IV. “mutual defection”(2.497)(2.887)(1.716)(1.836)(3.271)(3.558)(2.178)(2.488)-1.507-2.821-2.925**-3.423**-0.712-1.523-1.517-2.178(1.928)(1.976)(1.306)(1.379)(1.811)(1.959)(1.422)(1.432)

0.956

0.440

-1.188-1.020-0.523-1.018-0.275-0.653(1.816)(1.893)(1.189)(1.251)(1.806)(1.965)(1.365)(1.370)

Sonipat  Trio

26.238***26.863***4.850**

6.123***

3.899

26.988***5.348**

7.366**(3.105)(3.439)(2.098)(2.214)(3.710)(4.334)(2.624)(2.865)

Sonipat  HO

25.623***24.643***

2.628

3.065

5.171

27.417***3.409

4.941*(2.737)(2.842)(1.949)(2.068)(3.504)(3.765)(2.494)(2.770)Constant-4.953***-4.7673.709***

1.104-3.789**2.848-0.927-7.021*(1.724)(5.715)(1.006)(3.670)(1.661)(5.268)(1.215)(4.216)

Observations

276

242

276

242

276

245

276

242

Control

No

Yes

No

Yes

No

Yes

No

Yes

# left-censored obs.

227

201

124

106

219

199

181

157

# right-censored obs.
Loglikelihood
Pseudo R2

1-229.10.0255

1-188.90.037517-526.80.017717-464.40.02562-259.70.008562-209.10.03196-386.40.008566-338.50.0216

H0: Trio + Sonipat  Trio = Sonipat (Do the behaviors differ between the Trio and Baseline treatments in India?)
F-stat.
120.63
81.92
6.08
7.07
1.68
56.00
4.62
5.69
p-value (2-sided)
0.00***
0.00***
0.01***
0.01**
0.20
0.00***
0.03**
0.03**
H0: Higher-Order + Sonipat  Higher-Order = Sonipat (Do the behaviors differ between the Higher-Order and Baseline
treatments in India?)
F-stat.
128.73
89.67
5.52
6.44
2.48
69.16
4.06
5.03
p-value (2-sided)
0.00***
0.00***
0.02**
0.01***
0.12
0.00***
0.04**
0.03**
H0: Sonipat + Sonipat  Trio = Trio (Do the behaviors differ between the UK and India in the Trio treatment?)
F-stat.
0.43
1.91
1.08
2.37
0.01
0.10
0.66
p-value (2-sided)
0.51
0.17
0.30
0.12
0.93
0.75
0.42

2.03
0.16

H0: Sonipat + Sonipat  Higher-Order= Higher-Order (Do the behaviors differ between the UK and India in the HigherOrder treatment?)
F-stat.
0.15
0.10
1.01
1.04
0.10
0.09
0.36
0.07
p-value (2-sided)
0.70
0.75
0.32
0.31
0.75
0.77
0.55
0.79

Notes: Tobit regressions with robust standard errors in parentheses. The control variables in the even-numberedcolumns include a dummy for female, age, number of siblings (except for column 6 due to collinearity), income rank
and the Raven’s test score. *** p<0.01, ** p<0.05, * p<0.1.

22

Third, higher-order punishment opportunities mitigate the negative group size effect in the UK.
Figure 4.A.I shows that a third-party player inflicts punishment more strongly in the Higher-Order than in
the Trio treatment; and the former frequency is close to the Baseline treatment. A two-sided z test
indicates that the punishment frequency is not significantly different between the Higher-Order andBaseline treatment (column II of Table 4.A). As there are three third parties per group in the HigherOrder treatment, this means that a PD player will be punished far more frequently in the Higher-Orderthan in the Baseline treatment. Figure 4.B.I also indicates that higher-order punishment opportunities
almost resolve third parties’ free riding on peers’ first-order punishing in terms of strength; and the effectis significant (column II of Table 4.B), parallel to the results of the punishment frequency.
Figure 4 and Table 4 also indicate that, in India (Sonipat), having fellow third parties in a groupcan even increase anti-social punishment in “mutual cooperation” and “victim.”28
Result 2: (i) In the UK (Newcastle), a third party inflicts punishment on a defector in “betrayal”
significantly less frequently and less strongly when having multiple third parties in the Trio treatment
than in the Baseline treatment, consistent with Hypothesis 2.c. Having higher-order punishment
opportunities in the Higher-Order treatment overcomes the negative group size effect. (ii) In India(Sonipat), the opposite group size effect emerges in that having multiple third parties in the Triotreatment encourages a third party to inflict punishment in “betrayal” significantly more frequently andmore strongly, relative to the Baseline treatment, at odds with Hypothesis 2.c. (c) In India, having
multiple third parties can exacerbate anti-social punishment among third parties.
Panels A.II and B.II of Figure 4 report subjects’ beliefs on cooperation and punishment in each of
the three treatments. It again indicates that subjects’ beliefs are larger than actual cooperation andpunishment observed in the experiment. This behavioral pattern is not surprising, however, because whilepeople are conditionally cooperative, they are known to be imperfect conditional cooperators on averagein choosing a contribution level (e.g., Fischbacher et al., 2001; Fischbacher and Gächter, 2010); andlikewise, they tend to punish conditionally upon their peers’ punitive activities, but somewhat less thanthe peers’ punishment amounts (e.g., Kamei, 2014; Kamei, 2020). In addition, theoretically, third parties
can free ride on peers’ punishment acts when there are other third parties in their group, thus having
further incentives to reduce altruistic punishments in comparison with their beliefs in the Trio and HigherOrder treatments.
Unlike in Result 1.iii, there is a discrepancy between prevailing beliefs and third parties’
behaviors for the group size effect. The first-order punishment frequencies and strengths are both similar
for the three treatments; and, respectively, negative and positive group size effects appear to be absent inIndia (Sonipat) and the UK (Newcastle) regarding beliefs–see again Panels A.II and B.II of Figure 4. Thisis also statistically supported. Appendix Table C.4 reports a regression analysis whose specifications are

Third-party punishment in “victim” is significantly more frequent in the Higher-Order than in the Baseline
treatment (Table 4.B). The per-third-party punishment strength is significantly stronger in the Trio and Higher-Order
treatments than in the Baseline (Table 4.B).
28

23

the same as Table 4 but using beliefs as the dependent variables. The results indicate almost no group size
effect for beliefs in all four scenarios, in both the UK and India.
However, a calculation of observed punishment frequencies and strengths as the percentages ofbeliefs formed by the PD players (“punishment-belief ratio” hereafter) reinforces Result 2. Table 5summarizes the calculations. There, while the punishment-belief ratios are always below (in most cases
far below) 1, large cross-societal differences are evident. First, the punishment-belief ratios in the
Baseline treatment can be thought of as reflecting subjects’ conditional preferences, without having theeffects of multiple third parties. In this treatment, third parties punished a defector in “betrayal” almost
similarly to the prevailing beliefs in the UK (Newcastle). In clear contrast, the punishment-belief ratio
under “betrayal” is only 45.8% and 34.4% for the frequency and strength, respectively, in India (Sonipat).
This suggests that, consistent with Hypothesis 4, conditional preferences (the slopes of conditional
punishment preferences in relation to the prevailing beliefs) are weaker in India than in the UK.29 Second,
parallel to Result 2.i (the negative group size effect in the UK), the punishment-belief ratios are in generallower in the Trio than in the Baseline treatment, but these are similar for the Baseline and Higher-Order
treatments. On the other hand, the positive group size effect was detected in India; the punishment-belief
ratios are larger in the Trio than in the Baseline treatment.
Result 3: Consistent with Hypothesis 4, the punishment-belief ratios in the Baseline treatments are
smaller in India (Sonipat) than in the UK (Newcastle).

Table 5: First-order Punishment as the Percentage of Belief
A. UK (Newcastle)
Punishment Frequency

Avg Per-Third-Party Punishment Points Given

Treatment

mutual coop.

victimbetrayalmutual defect. mutual coop.

Baseline

44.0%

60.8%

94.9%

62.8%

Trio

26.4%

44.0%

56.8%

45.0%

Higher-Order

63.2%

55.2%

80.1%

55.2%

victimbetrayalmutual defect.

34.6%

62.8%

89.2%

66.9%

23.2%

41.3%

51.7%

39.7%

71.1%

67.4%

78.8%

62.6%

B. India (Sonipat)
Treatment
mutual coop.
Baseline
0.0%
Trio
31.0%
Higher-Order
47.3%

Punishment Frequency
victimbetrayal
12.0%
45.8%
28.4%
53.4%
59.8%
56.9%

mutual defect.
30.6%
41.3%
39.6%

Avg Per-Third-Party Punishment Points Givenmutual coop.
victimbetrayalmutual defect.
0.0%
23.9%
34.4%
21.9%
35.9%
35.7%
68.8%
72.6%
41.2%
43.8%
49.1%
48.4%

5.3. Discussion – Possible Drivers behind the Cross-Societal Differences in First-Order Punishment
What mechanism drives the interesting contrast in group size effect between India (Sonipat) andthe UK (Newcastle)? One possible explanation is that third parties’ punitive inclinations differ markedly
between the two research sites. As shown in Panel A.I and B.I of Figure 4 and Table 5, while punishment
Conditional willingness to punish can be interpreted as the strength of people’s normative influence in driving
compliance as discussed in Bicchieri (2017).
29

24

frequency and per-third-party strength are much lower in India than in the UK in the Baseline treatment
where third-party peers are absent, the levels of punishment are similar for the two locations in the Triotreatment where multiple third parties decide.
In addition to differences in the punitive inclinations, Enke (2019, Table I) discussed five further
domains of moral beliefs that characterize societies in terms of kinship tightness: cooperation/trust,
religion, moral values, moral emotions and emotion/value. A regression analysis was conducted to
explore how these five domains affected third parties’ first-order punishment decisions of defectors in the
Baseline and Trio treatments. The present experiment included a post-experiment questionnaire toconstruct proxy variables following his paper. Cooperation/trust is measured using the following question
from the World Values Survey: “Generally speaking, would you say that most people can be trusted orthat you need to be very careful in dealing with people?”. Religious beliefs are measured using thefollowing question from the World Values Survey: “How important is God in your life?”. Moral values
are measured as the relative importance of universal over communal moral values based on responses tothe Moral Foundations Questionnaire. Moral emotions are measured based on reactions designed to elicit
guilt in the Test of Self-Conscious Affect. Finally, emotion/value is measured as the moral relevance ofpurity and disgust based on responses to the Moral Foundations Questionnaire.
Table 6 reports the regression results. Results from religious beliefs, moral values, moral
emotions and emotion/value provide some, but weak predicted relation between these variables and third
parties’ punitive inclinations. First, there is mixed evidence that religious beliefs are positively associatedwith third parties’ inclinations to punish. In the UK, religious beliefs are a positive predictor ofpunishment frequency and strength in the Trio treatment (significant at the 5% level); no relationship isobserved in the Baseline treatment. In India, the findings are qualitatively similar but statistically weaker.
Second, there is no systematic statistical relationship between the importance subjects place on universal
over communal moral values and punishment frequency or strength in either society. Third, there is weakevidence (significant at the 10% level) that stronger moral emotions of internalized guilt drive higher
punishment frequencies and strength in the Baseline treatment in the UK. This relationship disappears even reverses for punishment strength - in the Trio treatment. No relationship between internalized guilt
and punishment behaviors is observed in India. Finally, there is some evidence that the emotion/value ofmoral purity and disgust is a positive predictor of punishment frequency (significant at the 10% level) andpunishment strength (significant at the 5% level) in the Trio treatment in the UK. No such relationship isobserved in the Baseline treatment in this society, or in either treatment in India.
The findings on cooperation/trust provide interesting nuance to Results 2 and 3. In the UK, higher
generalized trust is a strong positive predictor of punishment frequency and strength in the Baseline
treatment, significant at the 5% level. However, this relationship disappears (reverses for punishment
strength) in the Trio treatment. Generalized trust has no significant effect on punishment strength or
frequency in either treatment in India. Historically, generalized trust underpins productive economic
interactions in loose kinship societies, such as the UK, which may require third-party punishment systems
to regulate (Alesina and Giuliano, 2013). The finding suggests that this relationship may be more fragile
when multiple third parties decide independently in a group due to free-riding tendencies.
25

Table 6: Determinants of Cross-societal Difference in First-Order Punishment of Defectors between
the Baseline and Trio treatments: Moral beliefs.
Dependent var.:
Treatment:
DomainIndia (Sonipat)
Cooperation/trust
Sonipat × Cooperation/trust
Religious beliefs
Sonipat × Religious beliefs
Moral values
Sonipat × Moral values
Moral emotions
Sonipat × Moral emotions
Emotion/value
Sonipat × Emotion/value
Constant
Observations# left-censored obs.
# right-censored obs.
Loglikelihood
Pseudo R2

Third parties’ decision to first-orderpunishBaseline
Trio
(1)
(2)
-8.524-1.227(13.698)(1.847)0.375**-0.094(0.174)(0.073)-0.1320.032(0.433)(0.098)-0.0230.141**(0.049)(0.056)0.139-0.046(0.087)(0.076)-0.056*-0.009(0.030)(0.022)0.151**
0.024(0.068)(0.030)0.128*-0.046(0.071)(0.030)0.031
0.019(0.176)(0.040)-0.0020.075*(0.052)(0.042)0.381-0.039(0.303)(0.066)-6.886**
1.237(3.317)(1.399)82234-40.170.291-141.6
0.0994A third-party player’s punishment
points given to a PD player
Baseline
Trio
(3)
(4)
-22.415-7.460(27.543)(10.373)
1.339**-0.592*(0.602)(0.352)-0.8650.473(1.215)(0.639)0.008
0.813**(0.154)(0.315)0.402-0.336(0.336)(0.468)-0.1270.008(0.115)(0.104)
0.398**
0.070(0.193)(0.170)0.352*-0.355**(0.208)(0.159)0.111
0.122(0.377)(0.241)0.050
0.472**(0.172)(0.235)0.969-0.111(0.646)(0.412)-21.348*9.277(10.734)(6.750)
82
234
44
141
3
14
-124.2-356.50.117
0.0368

H0: Domain + Sonipat × Domain = 0 (Does the domain have a significant effect in India?)
Cooperation/trust (p-values, two-sided)
Religious beliefs
Moral values
Moral emotions
Emotion/value

0.540
0.108
0.121
0.321
0.204

0.347
0.065*
0.445
0.302
0.468

0.657
0.167
0.081*
0.146
0.117

0.823
0.171
0.564
0.211
0.293

Notes: Columns (1) and (2) are Probit regressions with robust standard errors in parentheses clustered by subject ID.
The dependent variable is an indicator for a third-party player i’s decision to first-order punish. Columns (3) and (4)are Tobit regressions with robust standard errors in parentheses clustered by subject ID. The dependent variable is athird-party player i’s punishment points given to a PD player. The independent variables proxy for five domains ofmoral beliefs as defined in Enke (2019, Table I). Cooperation/trust is measured using the following question from theWorld Values Survey: “Generally speaking, would you say that most people can be trusted or that you need to be very
careful in dealing with people?”. Religious beliefs are measured using the following question from the World Values
Survey: “How important is God in your life?”. Moral values are measured as the relative importance of universal overcommunal moral values based on responses to the Moral Foundations Questionnaire. Moral emotions are measured
based on reactions designed to elicit guilt in the Test of Self-Conscious Affect. Emotion/value is measured as themoral relevance of purity and disgust based on responses to the Moral Foundations Questionnaire. For more details
on the post-experiment questionnaire, see Appendix A.5.

26

5.4. Higher-Order Punishment
As discussed in Section 4, higher-order punishment, i.e., punishment of the failure to sanction anorm violator and punishment for committing an unjustified punishment act (Hypothesis 3), has a vitalrole in enforcing pro-social first-order punitive norms in societies. Recall that, theoretically, while
punishment of a defector in “betrayal” may deter an opportunistic PD player from violating a norm
through reducing material gains of defection, the first-order punishment is subject to second-order freeriding in a group setting unless higher-order punishment is credible. Panels A.I and B.I of Figure 5 report
the frequency and the per-third-party strength of higher-order punishment by scenario in the Higher-Order
treatment. The data reveal that, whether in India (Sonipat) or in the UK (Newcastle), efficient forms ofhigher-order punishment are more frequent, and stronger, than inefficient forms in all stage-two scenarios,
in support of Hypothesis 3. Efficient higher-order punishment in “betrayal,” i.e., higher-order punishmentof failure to punish a defector who exploited a cooperator, is the strongest among the four scenarios. In“betrayal,” the corresponding frequency and per-third-party strength are both significantly different fromthose of inefficient higher-order punishment for each of the two research sites (column II in each panel ofTable 7). Thus, Hypothesis 3.a is statistically supported for the “betrayal” scenario, and it underscores theubiquitous role of humans’ social preferences in reinforcing punitive norms, regardless of the degree ofkinship tightness.
Scholars in anthropology and theoretical biology have argued that the emergence of punishment
norms may depend on the ability of individuals to engage in collective higher-order punishment of those
who do not sanction free-riding behavior in the first instance (e.g., Hechter, 1987). If the costs of being
punished are sufficiently large to act as a deterrent, then moralistic strategies enforced by punishment of
those who fail to punish free riders can be evolutionary stable (Boyd and Richerson, 1992). The social
interactions introduced by the availability of punishment mechanisms increase the likelihood of multiple
stable equilibria (Boyd and Richerson, 2010). Thus, it is plausible that different societies converge on
different equilibria, which are underpinned by variable social environments and norms (Boyd andRicherson, 2009).
In our experiment data, efficient higher-order punishment norms are stronger in the UK(Newcastle) than in India (Sonipat), in support of the cross-societal difference predicted in Hypothesis 4 –see again Table 7. First, under “mutual defection,” higher-order punishment of failure to punish a defector
is significantly more frequent and stronger than the inefficient one in the UK (Newcastle), but not in India(Sonipat). Second, in “mutual cooperation” and “victim,” consistent with Hypothesis 3.b, efficient higherorder punishment, i.e., higher-order punishment of a first-order anti-social punisher, is significantly
different from inefficient punishment for subjects in the UK, but not for subjects in India.
It should be remarked that, as was the case for the cooperation and first-order punishment
decisions, third parties’ actual higher-order punishments were lower than their beliefs. This is again
consistent with the idea that people are imperfect conditional punishers (e.g., Fischbacher et al., 2001;
Fischbacher and Gächter, 2010; Kamei, 2014 and 2020). Nevertheless, the overall patterns in the beliefs
are qualitatively similar to those in the decisions: i.e., anticipated stronger efficient punishment thaninefficient ones (Panels A.II and B.II of Figure 5, Appendix Table C.5).
27

Figure 5: Efficient versus Inefficient Higher-order Punishment in the Higher-Order treatment
4.5

100%

Efficient

Efficient

Inefficient

90%

4.0

80%

3.5

70%

4.5

100%

Inefficient

Efficient

90%

Inefficient

4.0

80%

3.5

70%

3.0

Efficient

Inefficient

3.0

60%

60%

2.5

2.5
50%

50%
2.0

2.0

40%

40%

1.5
1.0

20%

Mutualcooperation

VictimBetrayali. Frequency

0.0

0%Mutualcooperation

Mutual defection

0.5

10%

0.0

0%

1.0

20%

0.5

10%

1.5

30%

30%

VictimBetrayal

Mutual defection

Mutualcooperation

VictimBetrayal

Mutualcooperation

Mutual defection

ii. Avg. per-third-party punishment
points given

VictimBetrayal

Mutual defection

ii. Avg. per-third-party punishment
points given

i. Frequency

I. Actual Decisions

II. Beliefs

A. India (Sonipat)
100%

Efficient

4.5

Inefficient90%

Efficient

100%

Inefficient

4.5

Inefficient

90%

4.0

80%

Efficient

80%

3.5

Inefficient

3.5

70%

70%

Efficient

4.0

3.0

3.0
60%

60%

2.5

2.5
50%

50%

2.0

2.0
40%

40%

1.5

1.5

30%

30%

1.0

20%

0.5

10%

Mutualcooperation

VictimBetrayali. Frequency

Mutual defection

0.5

10%

0.0

0%

1.0

20%

0.0

0%
Mutualcooperation

VictimBetrayal

Mutual defection

Mutualcooperation

VictimBetrayal

Mutual defection

Mutualcooperation

I. Actual Decisions

Betrayal

Mutual defection

ii. Avg. per-third-party punishment
points given

i. Frequency

ii. Avg. per-third-party punishment
points given

VictimII. Beliefs

B. India (Sonipat)
Note: Higher-order punishment from i to j when j pro-socially punished a defector less than i in “betrayal” or “mutual defection,” or when j anti-socially punished a cooperator
more than i in “mutual cooperation” and “victim” are called “efficient” higher-order punishment. In all other cases, higher-order punishment is referred to as “inefficient.”

28

Table 7: Cross-societal Difference in Efficient and Inefficient Higher-Order Punishment(A) Frequency of higher-order punishment given to other third parties
Third parties’ decision to higher-order punish
Scenario*
I. “mutual cooperation”
II. “betrayal”
III. “victim”
Independent Variable
(1)
(2)
(3)
(4)
(5)
(6)
India (Sonipat)
0.038
0.090
-0.146-0.098-0.144-0.039(0.262)(0.312)(0.212)(0.240)(0.270)(0.328)
Efficient
0.724*** 0.749*** 0.980*** 1.073***
0.472*
0.602**(0.170)(0.200)(0.192)(0.210)(0.245)(0.274)-0.649**-0.548*0.288
0.208-0.262-0.364
Sonipat  Efficient(0.275)(0.307)(0.304)(0.343)(0.299)(0.333)
Constant-0.766***-0.336-0.843***0.031-0.597***-0.050(0.158)(1.089)(0.154)(1.062)(0.210)(1.069)Dependent var.

Observations
Control
Loglikelihood
Pseudo R2

1,682
No
-1017
0.0462

1,372
Yes-823.5
0.06191,794
No-922.9
0.113

1,462
Yes
-719.1
0.156

1,736
No
-1084
0.0250

1,434
Yes
-862
0.0557

IV. “mutual defection”(7)(8)-0.1020.019(0.209)(0.236)
0.621***
0.549*(0.240)(0.295)0.042
0.048(0.414)(0.476)-0.695***-1.399(0.139)(1.108)1,754
No-972.70.0250

1,432
Yes
-762
0.0563

H0: Sonipat + Constant = 0 (Is the frequency of inefficient higher-order punishment behavior significant in India?)Chi-squared-stat.
12.09
0.06
45.65
0.00
18.84
0.01
26.06
p-value (two-sided)
0.00***
0.81
0.00***
0.95
0.00***
0.93
0.00***

1.62
0.20

H0: Sonipat = Efficient + Sonipat  Efficient (Is efficient higher-order punishment more frequent than inefficientpunishment in India?)Chi-squared-stat.
0.01
0.05
14.13
10.11
0.91
0.43
2.79
p-value (two-sided)
0.93
0.82
0.00***
0.00***
0.34
0.51
0.09*

1.32
0.25

Notes: Probit regressions with robust standard errors in parentheses clustered by subject ID. The control variables in theeven-numbered columns include a dummy for female, age, number of siblings, income rank and the Raven’s test score.
Higher-order punishment from i to j when j pro-socially punished a defector less than i in “betrayal” or “mutual defection,”or when j anti-socially punished a cooperator more than i in “mutual cooperation” and “victim” are called “efficient” higherorder punishment. In all other cases, higher-order punishment is referred to as “inefficient.” *** p<0.01, ** p<0.05, * p<0.1(B) Punishment strength per third-party player
A third-party player’s punishment points given to another third-party player

Dependent var.

Scenario
I. “mutual cooperation”
Independent Variable
India (Sonipat)
Efficient
Sonipat  Efficient
Constant
Observations(1)-0.082(1.467)3.534***(0.919)-2.704*(1.479)-4.147***(1.078)
1,682(2)

II. “betrayal”

III. “victim”

(3)

(4)

(5)

(6)

(7)

(8)

-0.297(1.266)5.433***(1.134)1.120(1.921)-3.501(5.620)-1.022(1.496)
1.987*(1.182)-0.611(1.532)-3.044***(1.157)-0.315(1.702)2.656**(1.316)-1.194(1.652)-1.818(5.202)-0.515(1.202)
3.877**(1.783)0.859(3.085)-4.283***(1.037)0.313(1.325)
3.634*(1.868)0.936(3.281)-10.164(6.308)

1,462

1,736

1,434

1,754

1,432

0.236
-0.870(1.641)(1.217)3.525*** 5.234***(1.052)(1.072)-2.0611.488(1.516)(1.734)-3.569 -4.685***(6.357)(1.037)
1,372

1,794

29

IV. “mutual defection”

Control# left-censored obs.
# right-censored obs.
Loglikelihood
Pseudo R2

No
1128
43
-2248
0.0177

Yes
908
35
-1849
0.0248

No
1316
28
-2004
0.0554

Yes
1068
24
-1604
0.0781

No
1147
43
-2383
0.00852

Yes
956
33
-1908
0.0228

No
1305
32
-1950
0.0173

Yes
1072
28
-1535
0.0379H0: Sonipat + Constant = 0 (Are inefficient punishment behaviors significant in India?)
F-stat.
9.65
0.30
28.90
0.47
13.89
0.19
p-value (two-sided)
0.00***
0.58
0.00***
0.49
0.00***
0.67

17.20
0.00***

2.50
0.11

H0: Sonipat = Efficient + Sonipat  Efficient (Is efficient punishment stronger than inefficient punishment in India?)
F-stat.
0.14
0.23
10.87
7.64
1.32
0.59
2.53
1.45
p-value (two-sided)
0.71
0.63
0.00***
0.01**
0.25
0.44
0.11
0.23
Notes: Tobit regressions with robust standard errors in parentheses clustered by subject ID. The control variables in theeven-numbered columns include a dummy for female, age, number of siblings, income rank and the Raven’s test score.
Higher-order punishment from i to j when j pro-socially punished a defector less than i in “betrayal” or “mutual defection,”or when j anti-socially punished a cooperator more than i in “mutual cooperation” and “victim” are called “efficient” higherorder punishment. In all other cases, higher-order punishment is referred to as “inefficient.” *** p<0.01, ** p<0.05, * p<0.1

In addition, a calculation of the punishment-belief ratios finds that the ratios are the strongest for
the efficient punishment under “betrayal” than in any other scenario in both research sites: the former
ratios were, respectively, 62.9% (76.5%) and 77.3% (79.6%), in the punishment frequency and per-thirdparty strength in the UK (India). Hence, it follows that third parties recognize the role of punishment of
failure to punish a defector in enforcing pro-social punitive norms as first-order punishment in “betrayal”
is a key to deter PD players’ opportunism in the group.
Result 4: (i) Failure to punish a defector who exploited a cooperator in “betrayal” attracted significantly
more frequent and stronger higher-order punishment than in any other scenario irrespective of theresearch site, consistent with Hypothesis 3.a. (ii) Efficient higher-order punishment is significantly more
frequent and stronger than inefficient higher-order punishment in each of the other three scenarios in the
UK (Newcastle), but not in India (Sonipat), consistent with Hypothesis 4.

6. Conclusions
Situations in which multiple (uninvolved) third parties encounter a norm violation are ubiquitousin contemporary societies. Prior theoretical research argues that punishment inflicted informally bymultiple independent third parties helped advance human societies by enforcing social norms, not only
before the emergence of states (Grief, 1993; Hadfield and Weingast, 2013), but also in more recent times(McMillan and Woodruff, 1999a, b; Mathew and Boyd 2011). Although free-riding problems may
conceptually arise in the third parties’ sanctioning activities, existing theory in law and theoretical biology
emphasizes the role of second-order punishment in disciplining first-order punishment: i.e., punishmentof the failure to sanction a norm violator (e.g., Hadfield and Weingast, 2012; Axelrod, 1986; Henrich,
2004; Henrich and Boyd, 2001) or punishment for committing an unjustified punishment act (e.g., Kamei
and Putterman, 2015). Surprisingly, however, to date there is minimal experimental research into third
parties’ free riding tendencies when there are multiple third parties per group. Further, to the authors’

30

knowledge, there is no previous research that experimentally studies third parties’ higher-orderpunishment activities.
The present paper reports on a novel set of experiments conducted in both India (Sonipat) and the
UK (Newcastle). The study aimed not only to investigate the free-riding tendencies of third parties andthe potential impact of higher-order punishments when multiple third parties are present but also tocompare the enforcement of sanctions across the two societies. To achieve this aim, the two societies
were purposely selected based on Enke’s (2019) kinship tightness index: the UK with a low scoreindicating loose kinship ties and India scoring highly.
The experiment results first uncovered punishment patterns of third parties that are consistent
with earlier experiments (e.g., Fehr and Fischbacher, 2004): third parties punished a defector who
exploited his/her matched cooperator in “betrayal” more frequently and strongly than in any otherscenario. However, notable cross-societal differences were observed for the first-order punishment
behaviors. Specifically, the frequency and strength of third-party punishment in response to “betrayal”
was higher in the UK than in India, and this behavior was correctly anticipated by the subjects in eachsociety. This finding supports previous research suggesting that individuals in contemporary societies
with loose ancestral kinship ties, such as the UK, are more likely to engage in pro-social first-order thirdparty punishment than those in contemporary societies with tight ancestral kinship ties, such as India.
Second, and equally important, there was a clear contrast in the group size effect between the twosocieties. Although third-party punishment of a defector in “betrayal” was less frequent and weaker when
having multiple third parties per group than a single third party in the UK, the opposite effect wasobserved in India. While third parties’ free riding can be rationalized by a model of social preferencessuch as inequity aversion, the latter effect cannot. Subjects’ survey responses administered in theexperiment provide some tentative evidence that this contrast in the group size effect could be driven by
the different impact of generalized trust by society.
Further, the treatments with higher-order punishment opportunities revealed that third parties’
failure to sanction a defector in “betrayal” did attract more frequent and stronger higher-order punishment
than in any other first-order punishment scenario, irrespective of the research site. This pattern resonateswith arguments in anthropology and theoretical biology. However, such efficient higher-order punishment
is more salient in the UK than in India. In particular, efficient higher-order punishment was significantly
more frequent and stronger than inefficient higher-order punishment in every first-order punishment
scenario in the UK (Newcastle). Hence, the cross-societal difference in the higher-order punishment isagain consistent with the conjecture that people in a society with relatively looser ancestral kinship ties
are more willing to engage in costly punishment acts to regulate cooperation behaviors.
It can therefore be concluded that, in the study of human third-party punishment activities,
researchers may wish to consider the effects of culture and historical backgrounds in determining
contemporary patterns of sanction enforcement. The present study provides new experimental evidence inthis domain of moral systems and on how this relates to third parties’ free riding tendencies and their
inclinations to higher-order punish when there are multiple third parties. Further research is needed toestablish the generalizability of these findings in other contexts.
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35

Supplementary material: NOT FOR PUBLICATION
Appendix A: Experiment Instructions
A.1. General Instructions and Part 1[At the onset of the experiment, the following instructions were read aloud, while the participants werealso given printed copies of the instructions. The instructions at this stage were the same for all threetreatments:]

Experimental Instructions
Welcome. You are now taking part in a decision-making experiment. You were randomly selectedfrom the Experimental and Behavioural Economics Laboratory’s pool of subjects to be invited toparticipate in this session. There will be several pauses for you to ask questions. During such a pause,
please raise your hand if you want to ask a question. Apart from asking questions in this way, youmust not communicate with anybody in this room or make any noise.
Depending on your decisions and the decisions of other participants, you will be able to earn money inaddition to the £3 [INR 200 for the experiment sessions in India] guaranteed for your participation.
During the experiment, your earnings will be calculated in points. At the end of the experiment yourpoints will be converted to pounds sterling [Indian Rupees] at the following rate:
5 points = £1 [INR 70](or each point will be exchanged for 20 pence [INR 14] of real money). At the end of the experiment
your total earnings obtained in the experiment and the £3 [INR 200] participation fee will be paid toyou in cash [electronic payment]. Your payment will be rounded up to the nearest 10 pence [Rupees](e.g., £9.40 if it is £9.33 [INR 550 if it is INR 544]). In case that your total earnings from theexperiment are negative, you will receive the £3 [INR 200] participation fee.
The session is made up of 3 parts. In the first part you will complete the task described below.
I will describe the second part of the session after you have completed the first part.
The third part of the session is a questionnaire (your responses to the questionnaire will not affect yourearnings in the experiment). At the end of today’s session, you will be informed of the outcome ofyour decisions and your total cash payment.
[Pause for questions]1Instructions for Part I
I will now describe the task which makes up the first part of the session. The task is made up of 12questions. For every question, there is a pattern with a piece missing and a number of pieces below thepattern. You must choose which of the pieces below is the right one to complete the pattern, bothalong the rows and down the columns, but NOT the diagonals. You will see 8 pieces that mightcomplete the pattern. In every case, one and only one of these pieces is the right one to complete thepattern.
For example (see pattern and pieces below):

The correct answer for this example is piece number 7.
For each question, please choose the piece that best fits the pattern. You will score 1 point for every
correct answer. You will not be penalized for wrong answers. You will have 40 seconds to complete
each question. The top of the screen will display the time remaining (in seconds).
[Pause for questions][Subjects complete Part I]2

A.2. Instructions for Part 2[Instructions for Part 2 differ by treatment. Once Part 1 is over, the following instructions were read
aloud, while the participants were also given printed copies of the instructions:](a) Baseline Treatment:
Instructions for Part II
A. The Nature of Interactions
In this part of the session, you will be randomly assigned to a group of 3 persons. In each group, two
persons will be randomly assigned the role of player A, and the third person will be assigned the role ofplayer B. This part consists of two stages. During this part, you will NOT communicate with anyother player when making your decisions.

Stage 1:
Two player As will interact with each other in their group. Specifically, each player A will be given an
endowment of 40 points, and then simultaneously decides whether or not to send 16 points to theother player A. We will refer to the two player As in a group as “Player A1” and “Player A2.” If Player
A1 sends 16 points to Player A2, the 16 points will be tripled and becomes earnings of Player A2.
Likewise, if Player A2 sends 16 points to Player A1, the 16 points will be tripled and becomes theearnings of Player A1. The possible payoffs from stage 1 are presented in the following decision matrix:

Player A2

Send
Player A1
Not send

Send

Not send(a)72, 72(b)88, 24(c)24, 88(d)40, 40Note: The first number in each cell is Player A1’s payoff, and thesecond number in each cell is Player A2’s payoff.
Suppose that you are Player A1. There are 4 possible situations:(a) Both you and Player A2 send 16 points to each other. In this situation, each player obtains 40– 16 + (3 × 16) = 72 points.

(b) Player A2 sends 16 points to you, but you do not send 16 points to Player A2. In this situation,
your earnings are 88 points. Player A2’s earnings are 24 points.

(c) You send 16 points to Player A2, but Player A2 does not send 16 points to you. In this situation,
your earnings are 24 points. Player A2’s earnings are 88 points.
3

(d) Neither you nor Player A2 sends 16 points to each other. In this situation, you and Player A2 eachobtain earnings of 40 points.
As indicated in the calculations above, your own earnings will be maximized when you do not send 16
points but Player A2 sends 16 points. However, if both players send 16 points to each other, the total
earnings of the 2 players will be maximized and will be 72 × 2 points = 144 points; and each player
obtains 72 points as earnings. Your earnings will be minimized if you send 16 points to Player A2 but
Player A2 does not send 16 points to you.
[Pause for questions]Stage 2:In this stage, player Bs will be asked to decide how many points they want to reduce from the earningsof the two player As in their group.
Each player B will be given an endowment of 60 points. Each reduction point player B allocates toreduce a player A’s earnings reduces the player B’s earnings by 1 point and reduces the player A’s
earnings by 3 points. The reduction points targeted at each player A must be a multiple of 2, between
zero and 10. If the Player B chooses zero as reduction points to a player A, the player A’s earnings
remain unchanged from Stage 1.
Specifically, each player B will be asked to make decisions for the following four scenarios:(a) how many reduction points he or she would like to assign to a Player A1 who sent 16 points toPlayer A2 when Player A2 also sent 16 points to Player A1.

(b) how many reduction points he or she would like to assign to a Player A1 who did not send 16
points to Player A2 when Player A2 sent 16 points to Player A1.

(c) how many reduction points he or she would like to assign to a Player A1 who sent 16 points toPlayer A2 when Player A2 did not send 16 points to Player A1.

(d) how many reduction points he or she would like to assign to a Player A1 who did not send 16
points to Player A2 when Player A2 also did not send 16 points to Player A1.
Two of the four scenarios will be applied based on the two player As’ actual sending decisions. For
example, suppose that Player A1 did not send 16 points while Player A2 did. In this case, player Bs’
decisions in (b) and (c) would be applied. Alternatively, suppose that both Player A1 and Player A2
did not send 16 points. In this case, player Bs’ decisions in (d) would be applied twice, i.e., to both
Player As.

Note:
Some further questions will appear on your screen during this part of the session when your role(either player A or player B) does not have a decision to make. In some cases, you will have an
opportunity to add to your payoff based on the accuracy of your answers. Instruction for these will be
4

provided to you on the computer screen.
[Pause for questions]

B. Your Earnings
If you are assigned the role of player A, your earnings for this part will be calculated as:Your earnings in Stage 1 (= 24, 40, 72 or 88)
minus
total reduction amounts you received from player B
Total reduction amounts you received from player B are sum of reduction points from the player B inyour group times 3. If the net amount becomes negative, then the payoff will be 0.
In addition, player As may receive points from stage 2 based on the accuracy of their answers to somequestions that appear on the computer screen in this stage.
If you are assigned the role of player B, your earnings for this part will be calculated as:Your endowment from Stage 2 (= 60)minus
the sum of reduction points you assigned to player As
For instance, if a player B assigns 4 reduction points to Player A1 and 10 reduction points to the Player
A2, then the player B obtains a payoff after stage 2 of 46 points (= 60 – 4 – 10).
In addition, player Bs may receive points from stage 1 based on the accuracy of their answers to somequestions that appear on the computer screen in this stage.
Any questions? We will now move on to the comprehension quiz, which will appear on your computer
screen. Once everyone has successfully completed this, Stage 1 will begin. During the quiz, please raise
your hand if you are stuck on any question.
[Subjects complete the comprehension question – see Section A.3 of the Appendix][Subjects complete Part II][Instructions for Part III on screen]5(b) Trio Treatment:
Instructions for Part II
A. The Nature of Interactions
In this part of the session, you will be randomly assigned to a group of 5 persons. In each group, two
persons will be randomly assigned the role of player A, and the rest of persons will be assigned the roleof player B. Thus, the number of persons who will be assigned the role of player B is three. This partconsists of two stages. During this part, you will NOT communicate with any other player when
making your decisions.

Stage 1:
Two player As will interact with each other in their group. Specifically, each player A will be given an
endowment of 40 points, and then simultaneously decides whether or not to send 16 points to theother player A. We will refer to the two player As in a group as “Player A1” and “Player A2.” If Player
A1 sends 16 points to Player A2, the 16 points will be tripled and becomes earnings of Player A2.
Likewise, if Player A2 sends 16 points to Player A1, the 16 points will be tripled and becomes theearnings of Player A1. The possible payoffs from stage 1 are presented in the following decision matrix:

Player A2

Send
Player A1
Not send

Send

Not send(a)72, 72(b)88, 24(c)24, 88(d)40, 40Note: The first number in each cell is Player A1’s payoff, and thesecond number in each cell is Player A2’s payoff
Suppose that you are Player A1. There are 4 possible situations:(a) Both you and Player A2 send 16 points to each other. In this situation, each player obtains 40 –16 + (3 × 16) = 72 points.
(b) Player A2 sends 16 points to you, but you do not send 16 points to Player A2. In this situation,
your earnings are 88 points. Player A2’s earnings are 24 points.
(c) You send 16 points to Player A2, but Player A2 does not send 16 points to you. In thissituation, your earnings are 24 points. Player A2’s earnings are 88 points.
(d) Neither you nor Player A2 sends 16 points to each other. In this situation, you and Player A2each obtain earnings of 40 points.
6

As indicated in the calculations above, your own earnings will be maximized when you do not send 16
points but Player A2 sends 16 points. However, if both players send 16 points to each other, the total
earnings of the 2 players will be maximized and will be 72 × 2 points = 144 points; and each player
obtains 72 points as earnings. Your earnings will be minimized if you send 16 points to Player A2 but
Player A2 does not send 16 points to you.
[Pause for questions]Stage 2:In this stage, player Bs will be asked to decide how many points they want to reduce from the earningsof the two player As in their group. The number of player Bs in a group is 3 and player Bs
simultaneously make such reduction decisions.
Each player B will be given an endowment of 60 points. Each reduction point player B allocates toreduce a player A’s earnings reduces the player B’s earnings by 1 point and reduces the player A’s
earnings by 3 points. The reduction points targeted at each player A must be a multiple of 2, between
zero and 10. If all three player Bs choose zero as reduction points to a player A, the player A’s earnings
remain unchanged from Stage 1.
Specifically, each player B will be asked to make decisions for the following four scenarios:(a) how many reduction points he or she would like to assign to a Player A1 who sent 16 points toPlayer A2 when Player A2 also sent 16 points to Player A1.

(b) how many reduction points he or she would like to assign to a Player A1 who did not send 16
points to Player A2 when Player A2 sent 16 points to Player A1.

(c) how many reduction points he or she would like to assign to a Player A1 who sent 16 points toPlayer A2 when Player A2 did not send 16 points to Player A1.

(d) how many reduction points he or she would like to assign to a Player A1 who did not send 16
points to Player A2 when Player A2 also did not send 16 points to Player A1.
Two of the four scenarios will be applied based on the two player As’ actual sending decisions. For
example, suppose that Player A1 did not send 16 points while Player A2 did. In this case, player Bs’
decisions in (b) and (c) would be applied. Alternatively, suppose that both Player A1 and Player A2
did not send 16 points. In this case, player Bs’ decisions in (d) would be applied twice, i.e., to both
Player As.

Note:
Some further questions will appear on your screen during this part of the session when your role(either player A or player B) does not have a decision to make. In some cases, you will have an
opportunity to add to your payoff based on the accuracy of your answers. Instruction for these will be
provided to you on the computer screen.

7

[Pause for questions]

B. Your Earnings
If you are assigned the role of player A, your earnings for this part will be calculated as:Your earnings in Stage 1 (= 24, 40, 72 or 88)
minus
total reduction amounts you received from player Bs
Total reduction amounts you received from player Bs are sum of reduction points from all threeplayer Bs in your group times 3. If the net amount becomes negative, then the payoff will be 0.
In addition, player As may receive points from stage 2 based on the accuracy of their answers to somequestions that appear on the computer screen in this stage.
If you are assigned the role of player B, your earnings for this part will be calculated as:Your endowment from Stage 2 (= 60)minus
the sum of reduction points you assigned to player As
For instance, if a player B assigns 4 reduction points to Player A1 and 10 reduction points to the Player
A2, then the player B obtains a payoff after stage 2 of 46 points (= 60 – 4 – 10).
In addition, player Bs may receive points from stage 1 based on the accuracy of their answers to somequestions that appear on the computer screen in this stage.
Any questions? We will now move on to the comprehension quiz, which will appear on your computer
screen. Once everyone has successfully completed this, Stage 1 will begin. During the quiz, please raise
your hand if you are stuck on any question.
[Subjects complete the comprehension question – see Section A.3 of the Appendix][Subjects complete Part II][Instructions for Part III on screen]8(c) Higher-Order Treatment:
Instructions for Part II
A. Nature of Interactions
In this part of the session, you will be randomly assigned to a group of 5 persons. In each group, two
persons will be randomly assigned the role of player A, and the rest of persons will be assigned the roleof player B. Thus, the number of persons who will be assigned the role of player B is three. This partconsists of three stages. During this part, you will NOT communicate with any other player when
making your decisions.

Stage 1:
Two player As will interact with each other in their group. Specifically, each player A will be given an
endowment of 40 points, and then simultaneously decides whether or not to send 16 points to theother player A. We will refer to the two player As in a group as “Player A1” and “Player A2.” If Player
A1 sends 16 points to Player A2, the 16 points will be tripled and becomes earnings of Player A2.
Likewise, if Player A2 sends 16 points to Player A1, the 16 points will be tripled and becomes theearnings of Player A1. The possible payoffs from stage 1 are presented in the following decision matrix:

Player A2

Send
Player A1
Not send

Send

Not send(a)72, 72(b)88, 24(c)24, 88(d)40, 40Note: The first number in each cell is Player A1’s payoff, and thesecond number in each cell is Player A2’s payoff
Suppose that you are Player A1. There are 4 possible situations:(a) Both you and Player A2 send 16 points to each other. In this situation, each player obtains 40 –16 + (3 × 16) = 72 points.

(b) Player A2 sends 16 points to you, but you do not send 16 points to Player A2. In this situation,
your earnings are 88 points. Player A2’s earnings are 24 points.

(c) You send 16 points to Player A2, but Player A2 does not send 16 points to you. In this situation,
your earnings are 24 points. Player A2’s earnings are 88 points.

(d) Neither you nor Player A2 sends 16 points to each other. In this situation, you and Player A2 eachobtain earnings of 40 points.
9

As indicated in the calculations above, your own earnings will be maximized when you do not send 16
points but Player A2 sends 16 points. However, if both players send 16 points to each other, the total
earnings of the 2 players will be maximized and will be 72 × 2 points = 144 points; and each player
obtains 72 points as earnings. Your earnings will be minimized if you send 16 points to Player A2 but
Player A2 does not send 16 points to you.
[Pause for questions]Stage 2:In this stage, player Bs will be asked to decide how many points they want to reduce from the earningsof the two player As in their group. The number of player Bs in a group is 3 and player Bs
simultaneously make such reduction decisions.
Each player B will be given an endowment of 60 points. Each reduction point player B allocates toreduce a player A’s earnings reduces the player B’s earnings by 1 point and reduces the player A’s
earnings by 3 points. The reduction points targeted at each player A must be a multiple of 2, between
zero and 10. If all three player Bs choose zero as reduction points to a player A, the player A’s earnings
remain unchanged from Stage 1.
Specifically, each player B will be asked to make decisions for the following four scenarios:(a) how many reduction points he or she would like to assign to a Player A1 who sent 16 points toPlayer A2 when Player A2 also sent 16 points to Player A1.

(b) how many reduction points he or she would like to assign to a Player A1 who did not send 16
points to Player A2 when Player A2 sent 16 points to Player A1.

(c) how many reduction points he or she would like to assign to a Player A1 who sent 16 points toPlayer A2 when Player A2 did not send 16 points to Player A1.

(d) how many reduction points he or she would like to assign to a Player A1 who did not send 16
points to Player A2 when Player A2 also did not send 16 points to Player A1.
Two of the four scenarios will be applied based on the two player As’ actual sending decisions. For
example, suppose that Player A1 did not send 16 points while Player A2 did. In this case, player Bs’
decisions in (b) and (c) would be applied. Alternatively, suppose that both Player A1 and Player A2
did not send 16 points. In this case, player Bs’ decisions in (d) would be applied twice, i.e., to both
Player As.
[Pause for questions]Stage 3:In this stage, player Bs will be asked to decide how many points they want to reduce from theearnings of the other two player Bs in the group, based on their reduction decisions in Stage 2. The
player Bs simultaneously make such reduction decisions (they will not be informed of the otherplayer Bs’ reduction decisions at the decision stage).
10

The reduction schedule in Stage 3 is the same as in Stage 2. Specifically, each reduction point player
B allocates to reduce another player B’s earnings reduces his or her own earnings by 1 point andreduces the target’s earnings by 3 points. The reduction points targeted at each of the other player
Bs must be a multiple of 2, between zero and 10.
Each player B will be asked to assign reduction points to the other player Bs in the group for thirty
randomly chosen scenarios from stages 1 and 2. Each scenario consists of one of the four possible
situations from stage 1 and a pair of player B reduction decisions from stage 2.
The thirty scenarios include the real scenarios you have in your group after Stage 2. For example,
suppose that one Player A in your group did not send 16 points while the other Player A did. In thiscase, one scenario would include your peers’ reduction decisions in (b), and another scenario would
include your peers’ reduction decisions in (c). Alternatively, suppose that the two Player As in yourgroup did not send 16 points. In this case, only your peers’ reduction decisions in (d) are relevant.
You will not be informed of which are the real scenarios when you make your reduction decisions inthis stage. Your reduction decision in the real scenarios will affect the earnings of you and the other
Player Bs. Since there are two other Player Bs in your group, your decisions will be applied to bothplayer Bs.

Note:
Some further questions will appear on your screen during this part of the session when your role(either player A or player B) does not have a decision to make. In some cases, you will have an
opportunity to add to your payoff based on the accuracy of your answers. Instruction for these will
be provided to you on the computer screen.
[Pause for questions]

B. Your Earnings
If you are assigned the role of player A, your earnings for this part will be calculated as:Your earnings in Stage 1 (= 24, 40, 72 or 88)
minus
total reduction amounts you received from player Bs
Total reduction amounts you received from player Bs are sum of reduction points from all threeplayer Bs in your group times 3. If the net amount becomes negative, then the payoff will be 0.
In addition, player As may receive points from stages 2 and 3 based on the accuracy of their answers
to some questions that appear on the computer screen in these stages.
If you are assigned the role of player B, your earnings for this part will be calculated as:
11

Your endowment from Stage 2 (= 60)
minus(i) the sum of reduction points you assigned to player Asminus(ii) the sum of reduction points you assigned to other player Bs
minus(iii) total reduction amounts you received from other player Bs
Total reduction amounts you received from other player Bs (term (iii)) are the sum of reduction points
assigned to you by the other two player Bs in your group times 3. If the net amount becomes negative,then the payoff will be 0.
For instance, let us refer to the three player Bs in a group as “Player B1,” “Player B2” and “Player B3.”
If Player B1:(i)assigns 4 reduction points to Player A1 and 10 reduction points to Player A2,

then Player B1 obtains a payoff after stage 2 of 46 points (=60 – 4 – 10). If, in stage 3, Player B1:
(ii)
(iii)

assigns a sum of 0 reduction points to Player B2,
assigns a sum of 8 reduction points to Player B3; andreceives total reduction amounts of 18 from Players B2 and B3,then Player B1 obtains a final payoff of 20 points (=46 – 0 – 8 – 18).
In addition, player Bs may receive points from stage 1 based on the accuracy of their answers to somequestions that appear on the computer screen in this stage.
Any questions? We will now move on to the comprehension quiz, which will appear on your computer
screen. Once everyone has successfully completed this, Stage 1 will begin. During the quiz, please raise
your hand if you are stuck on any question.
[Subjects complete the comprehension question – see Section A.3 of the Appendix][Subjects complete Part II][Instructions for Part III on screen]12A.3. Comprehension Questions for Part 2 Instructions
1. How many persons in each group will be assigned the role of player A? Answer – 2.
2. How many persons in each group will be assigned the role of player B? Answer – 1 [3].
Suppose that Player A1 sends 16 points to Player A2, and Player A2 does not send 16 points to Player A1.

3. What is the Stage 1 payoff of Player A1? Answer – 24.
4. What is the Stage 1 payoff of Player A2? Answer – 88.
5. How much does it cost a player B to reduce the earnings of another player by 9 points? Answer – 3.
Suppose that Player A1 obtains 40 points in Stage 1 and receives total reduction amounts of 18 fromplayer B[s] in Stage 2.

6. What are Player A1’s earnings? Answer – 22.
[Baseline/Trio treatment:]
Each player B is endowed with 60 points. Suppose that a player B assigns 6 reduction points to Player
A1 and 4 reduction points to Player A2.

7. What are the player B’s earnings? Answer – 50.
[Higher-Order treatment:]
Each player B is endowed with 60 points. Let us refer to the three player Bs in a group as “Player
B1,” “Player B2” and “Player B3.” Suppose that Player B1:
(i)
(ii)
(iii)
7.

assigns 6 reduction points to Player A1 and 4 reduction points to Player A2,
assigns a sum of 10 reduction points to Player B2,
assigns a sum of 0 reduction points to Player B3; andreceives total reduction amounts of 12 from Players B2 and B3.

What are Player B1’s earnings? Answer – 28.

13

A.4. A Screen Image in Stage 3 of the Higher-Order treatment
Third-party player’s screen:
The following is a screen image for a third-party player in Stage 3 of the Higher-Order treatment.
In this example, Stage 1 is a scenario of “victim.”
Each third-party player will be presented with 30 scenarios from Stage 1 and 2 like this one (i.e., two PD
players’ decisions in Stage 1, and the third-party player’s and the other two third-party players’
punishment decisions in Stage 2). One scenario is a real one. You will then decide how to punish theother two third-party players in your group.

Note: Decisions in the screen image are for illustrations only.

14

PD player’s screen:
In Stage 3, each PD player will be presented with 30 scenarios from Stage 1 and 2 like the one below, andthen will be asked about their guess on their third-party players’ second-order punishment decisions. The
following screenshot is one example.

Note: Decisions in the screen image are for illustrations only.

15

A.5. Part 3: Post-Experiment Questionnaire
The post-experiment questionnaire contained the following modules.
Global Preferences Survey
Risk preferences
Please tell me, in general, how willing or unwilling you are to take risks. Please use a scale from 0 to 10,
where 0 means “completely unwilling to take risks” and a 10 means you are “very willing to take risks”.
You can also use any numbers between 0 and 10 to indicate where you fall on the scale, like 0, 1, 2, 3, 4,
5, 6, 7, 8, 9, 10.
Social preferences
How well do the following statements describe you as a person? Please indicate your answer on a scalefrom 0 to 10. A 0 means “does not describe me at all” and a 10 means “describes me perfectly”.
When someone does me a favor, I am willing to return it.
If I am treated very unjustly, I will take revenge at the first occasion, even if there is a cost to doso.
I assume that people have only the best intentions.
We now ask you for your willingness to act in a certain way. Please again indicate your answer on a scalefrom 0 to 10. A 0 means “completely unwilling to do so,” and a 10 means “very willing to do so.”
How willing are you to punish someone who treats you unfairly, even if there may be costs foryou?
How willing are you to punish someone who treats others unfairly, even if there may be costs foryou?
How willing are you to give to good causes without expecting anything in return?
World Values Survey
Generalized trust
Generally speaking, would you say that most people can be trusted or that you need to be very careful indealing with people? Please indicate on a scale from 1 to 10. 10 means “most people can be trusted” and 1means “need to be very careful”.
In-/out-group trust
We are interested in how much you trust people from various groups. For each of the below, please fill inwhether you trust people from this group completely, somewhat, not very much or not at all?
1.
2.
3.
4.

Trust completely
Trust somewhat
Do not trust very much
Do not trust at all[In-group:]
16

•
•
•

Your familyYour neighbourhood
People you know personally[Out-group:]•••

People you meet for the first time
People of another religion
People of another nationality

Religious beliefs
How important is God in your life? Please indicate on a scale from 1 to 11. 11 means “very important”
and 1 means “not at all important.” [or prefer not to say]
Which, if any, of the following do you believe in? Yes/No [or prefer not to say]
•
•
•
•

God
Life after death
Hell
HeavenConfidence
Below are listed a number of organizations. For each one, please indicate how much confidence you havein them: is it a great deal of confidence, quite a lot of confidence, not very much confidence or none at
all?
•
•
•
•
•
•

The armed forces.
The police.
The courts.
The government.
Political parties.
Parliament.

Family ties
How important would you say that family is in your life?
1.
2.
3.
4.

Very important
Rather important
Not very important
Not at all importantSocial norms in a community
Norm adherence
Due to M. J. Gelfand et al., Differences between tight and loose cultures: A 33-nation study. Science(80-.). 332, 1100–1104 (2011).
The following statements refer to the United Kingdom as a whole. Please indicate to what extent you
agree or disagree with each statement.
17

1. There are many social norms that people are supposed to abide by in this country.
2. In this country, there are very clear expectations for how people should act in most situations.
3. People agree upon what behaviours are appropriate versus inappropriate in most situations in thiscountry.
4. People in this country have a great deal of freedom in deciding how they want to behave in mostsituations. (Reverse coded)
5. In this country, if someone acts in an inappropriate way, others will strongly disapprove.
6. People in this country almost always comply with social norms.
Moral Foundations Questionnaire1
Relative importance of communal over universal moral values:
First, sum responses to all questions that belong to the communal values “Ingroup” and “Authority”; then,subtract responses to all questions that belong to the universal moral values of “Fairness” and “Harm”.
Moral relevance of purity and disgust:
Questions that belong to the dimension “Purity”.
Big Five model
Please evaluate the following statements, to complete the sentence:
Scale: 1 (“disagree strongly”) to 5 (“agree strongly”)
I see myself as someone who ...
is original, comes up with new ideas
values artistic experiences
has an active imagination
does a thorough job
does things eﬀectively and eﬃciently
tends to be lazy
is communicative, talkative
is outgoing, sociable
is reserved
has a forgiving nature
is considerate and kind to others

1

Moral Foundations Questionnaire: 20-Item Short Version Item Key, July 2008,https://moralfoundations.org/questionnaires/18

is sometimes somewhat rude to others
worries a lot
gets nervous easily
is relaxed, handles stress well
Test of Self-Conscious AffectDue to Tangney J. P., Dearing R. L., Wagner P. E., Gramzow R. (2000). The Test of Self-Conscious
Affect-3 (TOSCA-3). Fairfax, VA: George Mason University.
Guilt and Shame
Series of scenarios with possible emotional reactions on five-point Likert scale; the reactions designed toelicit guilt/shame are used to construct the measures.
Demographics
Age: Years. [or prefer not to say].
Gender: Male/Female/Other/Prefer not to say
Siblings: Number of.
Country of birth:
Central and Eastern Asia; Central and Western Africa; Central, South America and the Caribbean; Europe(excl. UK); Middle East and North Africa; North America; Oceania; South and Eastern Africa; SouthEast Asia; Southern Asia; UK.
Country of hometown: Free text.
Field of studies:
Arts and Education; Economics and Finance; Business and Management; Law and Social Sciences;
Medicine and Health Sciences; Engineering and Natural Sciences; Not a Student.
Income: When you were 16 years of age, what was the income of your parents in comparison to theaverage income in your hometown?
Far below average; Below average; Average; Above average; Far above average.

19A.6. Sample Characteristics
Table A.1: Cross-Societal Subject Pool Characteristics.

Positive reciprocity
Trust intentions
Generalized trust
Trust in-group
Trust out-group
Communal vs. universal values(z-score)
Moral purity and disgust

n
239
239
239
239
239
239

Newcastle
mean
8.80
4.72
5.50
3.20
2.68
0.07

sd.
1.42
2.40
2.19
0.37
0.46
0.96

239

10.56

4.12

n
262
262
262
262
262
262

Sonipat
mean
8.92
4.63
4.49
3.12
2.43
-0.06

sd.
1.68
2.92
2.29
0.47
0.58
1.03

Diff
0.125
-0.090-1.014***-0.078*-0.249***-0.132

262

9.85

4.36

-0.714

Guilt
239
45.20
5.44
261
45.13
6.33
-0.070
Shame
239
33.90
6.77
261
32.81
8.15
-1.087
Third-party vs. direct punishment
239
0.09
0.89
262
-0.08
1.06
-0.164**(z-score)
Charitable giving
239
7.40
2.07
262
7.41
2.42
0.011
Importance of God
239
3.92
3.30
262
5.49
3.43
1.572***
Family ties
239
3.67
0.58
262
3.65
0.60
-0.024
Risk preference
239
6.29
2.08
262
6.38
2.16
0.089
Norm adherence
239
4.43
0.71
262
4.07
0.75
-0.363***
Confidence in institutions
239
2.74
0.49
262
2.82
0.53
0.082
Female
237
0.49
0.50
261
0.43
0.50
-0.057
Econ major
237
0.30
0.46
261
0.30
0.46
-0.009
Age
225
21.48
3.55
243
20.44
5.27
-1.036*
Num. siblings
232
1.72
1.33
256
1.23
1.44
-0.481***
Relative income at 16
237
3.22
0.94
258
3.34
1.09
0.122
Openness
239
3.71
0.79
262
4.07
0.79
0.360***
Conscientiousness
239
3.54
0.77
262
3.32
0.77
-0.222***Extraversion
239
3.47
0.88
262
3.22
1.01
-0.257***
Agreeableness
239
3.82
0.71
262
3.68
0.79
-0.133**
Neuroticism
239
3.51
1.02
262
3.48
1.00
-0.034Raven’s test score
254
5.34
2.53
262
5.17
2.38
-0.167
Table shows averages pooled across treatments. The Diff column is the coefficient of a linear regression of subject
pool on the variable. Stars indicate whether this difference is significant. *** p<0.01, ** p<0.05, * p<0.1

20

Appendix B: Theoretical Analysis based on the Fehr-Schmidt (1999) model
Below, we summarize how the inequity-averse preference model by Fehr and Schmidt (1999) predicts thepunishment behaviors of third-party players in our experiment.
The Fehr-Schmidt (1999) utility function is given as follows: for a list of n players’ material
payoffs (x), player i receives the following utility:𝛼𝛽𝑖∑𝑗≠𝑖 max{𝑥𝑗 − 𝑥𝑖 , 0} − 𝑖 ∑𝑗≠𝑖 max{𝑥𝑖 − 𝑥𝑗 , 0},
𝑈𝑖 (𝑥) = 𝑥𝑖 − 𝑛−1
𝑛−1

(B1)

where 𝑥𝑖 is the payoff of player i, 𝛽𝑖 ≤ 𝛼𝑖 and 0 ≤ 𝛽𝑖 < 1. 𝛼𝑖 indicates player i’s aversion todisadvantageous inequality, while 𝛽𝑖 indicates player i’s aversion to advantageous inequality. For
simplicity, we use a continuous interval for i’s punishment activities, although a discrete interval {0, 2, 4,…, 10} is used as the choice space in the experiment.

B.1. Baseline Treatment
For the Baseline treatment, in which there is a single third-party player in Stage 2 (n = 3), the insights of
the analysis are summarized as follows:a. Scenario CC: i punishes a cooperator (PCC = 10) iff 𝛼𝑖 > 2.
b. Scenario CD/DC: i never punishes a cooperator; i punishes a defector (PDC = 10) iff 𝛼𝑖 + 𝛽𝑖 / 2 >1.
c. Scenario DD: i never punishes a defector.
d. Some PD players choose to cooperate with their paired PD players, driven by their inequality
concern or by the threat of punishment.

(a) i’s Punishment Behavior in Scenario CC
Given the strategy method implementation, i will impose the same punishment points on two cooperatorsand receive the following utility in Scenario CC:
𝑈𝑖 (𝑥) = 60 − 2𝑃𝐶𝐶 − 𝛼𝑖 max{(72 − 3𝑃𝐶𝐶 ) − (60 − 2𝑃𝐶𝐶 ), 0} − 𝛽𝑖 max{(60 −2𝑃𝐶𝐶 ) − (72 − 3𝑃𝐶𝐶 ), 0}.

(B2)

where 𝑥 = (72 − 3𝑃𝐶𝐶 , 72 − 3𝑃𝐶𝐶 , 60 − 2𝑃𝐶𝐶 ) and 𝑃𝐶𝐶 is punishment points assigned by i to acooperator. Since 𝑃𝐶𝐶 < 12, we obtain:
𝑈𝑖 (𝑥) = 60 − 12𝛼𝑖 + (𝛼𝑖 − 2)𝑃𝐶𝐶 .

(B3)

Thus, equation (B3) suggests that i will punish a cooperator and PCC = 10 (not punish a cooperator) in
Scenario CC if and only if 𝛼𝑖 > 2 (< 2).

(b) i’s Punishment Behavior in Scenario CD/DCIn Scenario CD/DC, the three players’ payoffs are 𝑥 = (24 − 3𝑃𝐶𝐷 , 88 − 3𝑃𝐷𝐶 , 60 − 𝑃𝐶𝐶 − 𝑃𝐷𝐶 ), where
21

𝑃𝐶𝐷 is punishment points from i to the cooperator and 𝑃𝐷𝐶 is punishment points from i to the defector in
i’s group. The third-party player will receive the following utility:
𝑈𝑖 (𝑥) = 60 − 𝑃𝐶𝐷 − 𝑃𝐷𝐶
𝛼2− 𝑖 max{(−36 − 2𝑃𝐶𝐷 + 𝑃𝐷𝐶 ), 0} −𝛽𝛼𝑖max{(28 + 𝑃𝐶𝐷 − 2𝑃𝐷𝐶 ), 0}
2

(B4)

𝛽

− 2𝑖 max{(36 + 2𝑃𝐶𝐷 − 𝑃𝐷𝐶 ), 0} − 2𝑖 max{(−28 − 𝑃𝐶𝐷 + 2𝑃𝐷𝐶 ), 0}.
By design, 𝑃𝐷𝐶 ≤ 10 and so it must be the case that 28 + 𝑃𝐶𝐷 − 2𝑃𝐷𝐶 > 0. In this case, 36 + 2𝑃𝐶𝐷 −𝑃

𝑃𝐷𝐶 > 0 because 36 + 2𝑃𝐶𝐷 − 𝑃𝐷𝐶 > 36 + 2𝑃𝐶𝐷 − 14 − 𝐶𝐷
= 22 +
2

3𝑃𝐶𝐷> 0. Thus, equation (B4)2reduces to:𝑈𝑖 (𝑥) = 60 − 14𝛼𝑖 − 18𝛽𝑖 − (1 +𝛼𝑖
𝛽+ 𝛽𝑖 ) 𝑃𝐶𝐷 + (𝛼𝑖 + 𝑖 − 1) 𝑃𝐷𝐶 .
2
2

(B5)

𝑑𝑈

Since 𝑑𝑃 𝑖 < 0, i never punishes a cooperator in Scenario CD. However, i will punish a defector and PDC
𝐶𝐷= 10 (not punish a defector) in Scenario DC if and only if 𝛼𝑖 + 𝛽𝑖 /2 > 1 (< 1).

(c) i’s Punishment Behavior in Scenario DD
Analogous to scenario (a) above, i will impose the same punishment points on two defectors and receive
the following utility in Scenario DD:
𝑈𝑖 (𝑥) = 60 − 2𝑃𝐷𝐷 − 𝛼𝑖 max{(40 − 3𝑃𝐷𝐷 ) − (60 − 2𝑃𝐷𝐷 ), 0} − 𝛽𝑖 max{(60 −2𝑃𝐷𝐷 ) − (40 − 3𝑃𝐷𝐷 ), 0}.

(B6)

where 𝑥 = (40 − 3𝑃𝐷𝐷 , 40 − 3𝑃𝐷𝐷 , 60 − 2𝑃𝐷𝐷 ) and 𝑃𝐷𝐷 is punishment points assigned by i to a
defector. Since 𝑃𝐷𝐷 ≥ 0, we obtain:
𝑈𝑖 (𝑥) = 60 − 15𝛽𝑖 − (𝛽𝑖 + 2)𝑃𝐷𝐷 .

(B7)

𝑑𝑈

Since 𝑑𝑃 𝑖 < 0, i never punishes a defector in Scenario DD.
𝐷𝐷(d) Cooperate/defect decision
Let 𝐹(𝛼) denote the CDF of the distribution over disadvantageous inequality held by PD players. By thedefinition of a CDF, F(.) is an increasing function. To simplify the exposition, we assume that β = 0.
Based on the preceding analysis, the expected payoffs to a PD player are given in Table B.2. If (F(2) –F(1)) > 8/15, then the social dilemma becomes a coordination game with a second equilibrium in purestrategies of mutual cooperation. Notice that if the PD player were to be averse to advantageous
inequality (i.e., β > 0), then the threshold would be strictly lower than 8/15 and so the probability ofchoosing cooperation would increase.

22

Table B.2: Expected payoffs to Player 1’s cooperate/defect decision in the Baseline treatment under the
threat of punishment.
Player 2

Send (cooperate)
Player 1
Not send (defect)

Send

Not send(a)F(2)(72) + (1 – F(2))(42)(b)
F(1)(88) + (1 – F(1))(58)

(c)
24
(d)
40

B.2. Trio Treatment
For the Trio treatment, in which there are three third-party players in Stage 2 (n = 5), we denote 𝑃𝑠,𝑖 ,where the indices denote scenario 𝑠 ∈ {𝐶𝐶, 𝐶𝐷, 𝐷𝐶, 𝐷𝐷} and third-party player 𝑖 ∈ {1,2,3}. As theidentities of third-party players in the experiment are anonymous, we assume the symmetric punishment
situation: for any player 𝑖 and scenario s, (i) 𝑃𝑠,𝑗 = 𝑃𝑠,𝑘 for 𝑗, 𝑘 ≠ 𝑖, and (ii) i’s belief about thepunishment choice of another third-party player in each scenario 𝑃𝑠′ is correct (𝑃𝑠′ = 𝑃𝑠,𝑗 , 𝑗 ≠ 𝑖). For easeof notation, we suppress the subscript i such that 𝑃𝑠,𝑖 = 𝑃𝑠 . The symmetric equilibria are characterized asfollows:′
a. Scenario CC: i punishes a cooperator iff 𝛼𝑖 /2 + 𝛽𝑖 > 2 and 0 < 𝑃𝐶𝐶≤ 12/7; this condition

implies a group size effect. The condition on social preference parameters is more restrictive, andthe per third-party player punishment strength is weaker, than in the Baseline treatment.2
b. Scenario CD/DC: i never punishes a cooperator; i punishes a defector iff 𝛼𝑖 /2 + 3𝛽𝑖 /4 > 1 and′
0 < 𝑃𝐷𝐶≤ 7/2; this condition implies a group size effect. The condition on social preference

parameters is more restrictive, and the per third-party player punishment strength is weaker, thanin the corresponding scenario of the Baseline treatment; however, these conditions are lessrestrictive than in Scenario CC.3
c. Scenario DD: i never punishes a defector.
d. Some PD players choose to cooperate with their paired PD players, driven by their inequality
concern or by the threat of punishment.

(a) i’s Punishment Behavior in Scenario CC
A third-party player i’s utility in Scenario CC is given by:
𝑈𝑖 (𝑥) = 60 − 2𝑃𝐶𝐶2
3

4 − 2𝛽𝑖 > 2 for all 𝛽𝑖 < 1.
2 − 𝛽𝑖 > 1 for all 𝛽𝑖 < 1.

23

(B8)

𝛼

′ )
− 2𝑖 max{(72 − 3𝑃𝐶𝐶 − 6𝑃𝐶𝐶
− (60 − 2𝑃𝐶𝐶 ), 0}𝛽′ ),− 2𝑖 max{(60 − 2𝑃𝐶𝐶 ) − (72 − 3𝑃𝐶𝐶 − 6𝑃𝐶𝐶
0}′′
−𝛼𝑖 max{𝑃𝐶𝐶 − 𝑃𝐶𝐶, 0} −𝛽𝑖 max{𝑃𝐶𝐶− 𝑃𝐶𝐶 , 0}.
′
′
′
′ ).
where 𝑥 = (72 − 3𝑃𝐶𝐶 − 6𝑃𝐶𝐶
, 72 − 3𝑃𝐶𝐶 − 6𝑃𝐶𝐶
, 60 − 2𝑃𝐶𝐶 , 60 − 2𝑃𝐶𝐶
, 60 − 2𝑃𝐶𝐶
Equation (B8)means we need to consider four cases to analyze i’s punishment behavior:′′
Case 1: 12 − 𝑃𝐶𝐶 − 6𝑃𝐶𝐶
≥ 0 and 𝑃𝐶𝐶 ≥ 𝑃𝐶𝐶

In this case, equation (B8) reduces to:𝛼2′
𝑈𝑖 (𝑥) = 60 − 6𝛼𝑖 − ( 𝑖 + 2) 𝑃𝐶𝐶 + 4𝛼𝑖 𝑃𝐶𝐶
.

(B9)

𝑑𝑈𝑖
′
< 0, the smaller punishment i inflicts, the higher utility i receives. That is, 𝑃𝐶𝐶 = 𝑃𝐶𝐶. Note𝑑𝑃𝐶𝐶′that i’s utility is increasing in 𝑃𝐶𝐶
whenever i is averse to disadvantageous inequality.

Since

′
′
Case 2: 12 − 𝑃𝐶𝐶 − 6𝑃𝐶𝐶
< 0 and 𝑃𝐶𝐶 ≥ 𝑃𝐶𝐶

In this case, equation (B8) reduces to:𝛽2′
𝑈𝑖 (𝑥) = 60 + 6𝛽𝑖 − (𝛼𝑖 + 𝑖 + 2) 𝑃𝐶𝐶 + (𝛼𝑖 − 3𝛽𝑖 )𝑃𝐶𝐶
.

(B10)

𝑑𝑈𝑖
< 0, equation (B10) suggests that the smaller punishment i inflicts, the higher utility i
𝑑𝑃𝐶𝐶
′
′
′
receives. In other words, 𝑃𝐶𝐶 = max {𝑃𝐶𝐶
, 12 − 6𝑃𝐶𝐶}. Note that i’s utility is increasing in 𝑃𝐶𝐶
if i isSince

sufficiently averse to disadvantageous inequality and not too averse to advantageous inequality.
′′
Case 3: 12 − 𝑃𝐶𝐶 − 6𝑃𝐶𝐶
≥ 0 and 𝑃𝐶𝐶 < 𝑃𝐶𝐶

In this case, equation (B8) reduces to:𝛼′𝑈𝑖 (𝑥) = 60 − 6𝛼𝑖 + ( 2𝑖 + 𝛽𝑖 − 2) 𝑃𝐶𝐶 + (3𝛼𝑖 − 𝛽𝑖 )𝑃𝐶𝐶
.

(B11)

Thus, equation (B11) suggests that i will punish (not punish) a cooperator in Scenario CC if 𝛼𝑖 /2 + 𝛽𝑖 >2 (< 2), up to:′′
𝑃𝐶𝐶 = min {𝑃𝐶𝐶
, 12 − 6𝑃𝐶𝐶}.
′
Note that i’s utility is increasing in 𝑃𝐶𝐶
if i is sufficiently averse to disadvantageous inequality and not too
averse to advantageous inequality.
′′
Case 4: 12 − 𝑃𝐶𝐶 − 6𝑃𝐶𝐶
< 0 and 𝑃𝐶𝐶 < 𝑃𝐶𝐶

In this case, equation (B8) reduces to:

24

𝛽

′
𝑈𝑖 (𝑥) = 60 + 6𝛽𝑖 − (2 − 2𝑖) 𝑃𝐶𝐶 − 4𝛽𝑖 𝑃𝐶𝐶
.

(B12)

𝑑𝑈

Since 𝑑𝑃 𝑖 < 0, the smaller punishment i inflicts, the higher utility i receives. That is,𝐶𝐶′
𝑃𝐶𝐶 = max {0,12 − 6𝑃𝐶𝐶}.
′
Note that i’s utility is decreasing in 𝑃𝐶𝐶
whenever i is averse to advantageous inequality.

Summary: These four cases can be summarized as in Figure B.1:
i’s punishment of cooperator (𝑃𝐶𝐶 )′𝑃𝐶𝐶 = 12 − 6𝑃𝐶𝐶

12′𝑃𝐶𝐶 = 𝑃𝐶𝐶

Case 2The symmetricstage 2 equilibrium
happens in this range.

Optimal Punishment schedule when
Optimal punishment schedule when

Case 1

12/7

𝛼𝑖
2

𝛼𝑖
2

+ 𝛽𝑖 > 2+ 𝛽𝑖 < 2

Case 4

Case 3′i’s belief on peers’ punishment (𝑃𝐶𝐶
)

2

12/7
Figure B.1. Optimal punishment schedule in Trio Scenario CC(b) i’s Punishment Behavior in Scenario CD/DCA third-party player i’s utility in Scenario CD/DC is given by:
𝑈𝑖 (𝑥) = 60 − 𝑃𝐶𝐷 − 𝑃𝐷𝐶𝛽′ )− 4𝑖 (36 + 2𝑃𝐶𝐷 − 𝑃𝐷𝐶 + 6𝑃𝐶𝐷

(B13)

𝛼

′ ),
− 4𝑖 max{(28 + 𝑃𝐶𝐷 − 2𝑃𝐷𝐶 − 6𝑃𝐷𝐶
0}
𝛽

′ ),
− 4𝑖 max{(−28 − 𝑃𝐶𝐷 + 2𝑃𝐷𝐶 + 6𝑃𝐷𝐶
0}

25

𝛼

′
′ ),
− 2𝑖 max{(𝑃𝐶𝐷 + 𝑃𝐷𝐶 ) − (𝑃𝐶𝐷
+ 𝑃𝐷𝐶
0}
𝛽

′
′ )
− 2𝑖 max{(𝑃𝐶𝐷+ 𝑃𝐷𝐶− (𝑃𝐶𝐷 + 𝑃𝐷𝐶 ), 0}.
′
′
′
′
′
′ ).
where 𝑥 = (24 − 3𝑃𝐶𝐷 − 6𝑃𝐶𝐷
, 88 − 3𝑃𝐷𝐶 − 6𝑃𝐷𝐶
, 60 − 𝑃𝐶𝐷 − 𝑃𝐷𝐶 , 60 − 𝑃𝐶𝐷− 𝑃𝐷𝐶, 60 − 𝑃𝐶𝐷− 𝑃𝐷𝐶
Equation (B13) means we need to consider four cases to analyze i’s punishment behavior:′′′ )Case 1: 28 + 𝑃𝐶𝐷 − 2𝑃𝐷𝐶 − 6𝑃𝐷𝐶
≥ 0 and (𝑃𝐶𝐷 + 𝑃𝐷𝐶 ) ≥ (𝑃𝐶𝐷
+ 𝑃𝐷𝐶

In this case, equation (B13) reduces to:𝑈𝑖 (𝑥) = 60 − 𝑃𝐶𝐷 − 𝑃𝐷𝐶𝛽′ )− 4𝑖 (36 + 2𝑃𝐶𝐷 − 𝑃𝐷𝐶 + 6𝑃𝐶𝐷

(B14)

𝛼
′ )
− 4𝑖 (28 + 𝑃𝐶𝐷 − 2𝑃𝐷𝐶 − 6𝑃𝐷𝐶
𝛼

′
′ )).
− 2𝑖 ((𝑃𝐶𝐷 + 𝑃𝐷𝐶 ) − (𝑃𝐶𝐷
+ 𝑃𝐷𝐶

which can be further simplified to:
𝛽

3𝛼

𝛽

𝛼

3𝛽

′
𝑈𝑖 (𝑥) = 60 − 9𝛽𝑖 − 7𝛼𝑖 − (1 + 2𝑖 + 4 𝑖) 𝑃𝐶𝐷 − (1 − 4𝑖) 𝑃𝐷𝐶 + ( 2𝑖 − 2 𝑖) 𝑃𝐶𝐷
+

(B15)

′
2𝛼𝑖 𝑃𝐷𝐶.
𝑑𝑈

𝑑𝑈

Since 𝑑𝑃 𝑖 < 0 and 𝑑𝑃 𝑖 < 0, equation (B15) suggests that the smaller punishment i inflicts, the higher
𝐶𝐷

𝐷𝐶

′
utility i receives. Note that i’s utility is increasing in 𝑃𝐶𝐷
if i is sufficiently averse to disadvantageous′
inequality and not too averse to advantageous inequality and is increasing in 𝑃𝐷𝐶
whenever i is averse todisadvantageous inequality.
′′′ )Case 2: 28 + 𝑃𝐶𝐷 − 2𝑃𝐷𝐶 − 6𝑃𝐷𝐶
< 0 and (𝑃𝐶𝐷 + 𝑃𝐷𝐶 ) ≥ (𝑃𝐶𝐷
+ 𝑃𝐷𝐶

In this case, equation (B13) reduces to:𝑈𝑖 (𝑥) = 60 − 𝑃𝐶𝐷 − 𝑃𝐷𝐶𝛽′ )− 4𝑖 (36 + 2𝑃𝐶𝐷 − 𝑃𝐷𝐶 + 6𝑃𝐶𝐷𝛽′ )− 𝑖 (−28 − 𝑃𝐶𝐷 + 2𝑃𝐷𝐶 + 6𝑃𝐷𝐶
4
𝛼

′
′ )).
− 2𝑖 ((𝑃𝐶𝐷 + 𝑃𝐷𝐶 ) − (𝑃𝐶𝐷
+ 𝑃𝐷𝐶

which can be further simplified to:

26

(B16)

𝛽

𝛼

𝛼

3𝛽

′
′ ).
𝑈𝑖 (𝑥) = 60 − 2𝛽𝑖 − (1 + 4𝑖 + 2𝑖) (𝑃𝐶𝐷 + 𝑃𝐷𝐶 ) + ( 2𝑖 − 2 𝑖) (𝑃𝐶𝐷
+ 𝑃𝐷𝐶
𝑑𝑈

(B17)

𝑑𝑈

Since 𝑑𝑃 𝑖 < 0 and 𝑑𝑃 𝑖 < 0, equation (B17) suggests that the smaller punishment i inflicts, the higher
𝐶𝐷

𝐷𝐶

′
′
utility i receives. Note that i’s utility is increasing in 𝑃𝐶𝐷
and in 𝑃𝐷𝐶
if i is sufficiently averse todisadvantageous inequality and not too averse to advantageous inequality.
′′′ )Case 3: 28 + 𝑃𝐶𝐷 − 2𝑃𝐷𝐶 − 6𝑃𝐷𝐶
≥ 0 and (𝑃𝐶𝐷 + 𝑃𝐷𝐶 ) < (𝑃𝐶𝐷
+ 𝑃𝐷𝐶

In this case, equation (B13) reduces to:𝑈𝑖 (𝑥) = 60 − 𝑃𝐶𝐷 − 𝑃𝐷𝐶𝛽′ )− 4𝑖 (36 + 2𝑃𝐶𝐷 − 𝑃𝐷𝐶 + 6𝑃𝐶𝐷

(B18)

𝛼

′ )
− 4𝑖 (28 + 𝑃𝐶𝐷 − 2𝑃𝐷𝐶 − 6𝑃𝐷𝐶
𝛽
2

′
′ )
− 𝑖 ((𝑃𝐶𝐷+ 𝑃𝐷𝐶− (𝑃𝐶𝐷 + 𝑃𝐷𝐶 )).

which can be further simplified to:
𝛼

𝛼

3𝛽

′
𝑈𝑖 (𝑥) = 60 − 9𝛽𝑖 − 7𝛼𝑖 − (1 + 4𝑖) 𝑃𝐶𝐷 + ( 2𝑖 + 4 𝑖 − 1) 𝑃𝐷𝐶 − 2𝛽𝑖 𝑃𝐶𝐷
+
3𝛼𝑖
𝛽
′
− 𝑖) 𝑃𝐷𝐶
.
2
2

(B19)

(
Since

𝑑𝑈𝑖
< 0, equation (B19) suggests that the smaller punishment i inflicts on the cooperator, the𝑑𝑃𝐶𝐷higher utility i receives. Equation (B19) suggests that i will punish (not punish) a defector in Scenario DC
if 𝛼𝑖 /2 + 3𝛽𝑖 /4 > 1 (< 1), up to:′′
𝑃𝐷𝐶 = min {14 − 3𝑃𝐷𝐶
, 𝑃𝐷𝐶
}.
′
Note that i’s utility is decreasing in 𝑃𝐶𝐷
whenever i is averse to advantageous inequality and is increasing′in 𝑃𝐷𝐶 if i is sufficiently averse to disadvantageous inequality and not too averse to advantageous
inequality.
′′′ )Case 4: 28 + 𝑃𝐶𝐷 − 2𝑃𝐷𝐶 − 6𝑃𝐷𝐶
< 0 and (𝑃𝐶𝐷 + 𝑃𝐷𝐶 ) < (𝑃𝐶𝐷
+ 𝑃𝐷𝐶

In this case, equation (B13) reduces to:𝑈𝑖 (𝑥) = 60 − 𝑃𝐶𝐷 − 𝑃𝐷𝐶𝛽′ )− 4𝑖 (36 + 2𝑃𝐶𝐷 − 𝑃𝐷𝐶 + 6𝑃𝐶𝐷𝛽

′ )− 4𝑖 (−28 − 𝑃𝐶𝐷 + 2𝑃𝐷𝐶 + 6𝑃𝐷𝐶

27

(B20)

𝛽
2

′
′ )
− 𝑖 ((𝑃𝐶𝐷+ 𝑃𝐷𝐶− (𝑃𝐶𝐷 + 𝑃𝐷𝐶 )).

which can be further simplified to:
𝛽

′
′ ).
𝑈𝑖 (𝑥) = 60 − 2𝛽𝑖 + ( 4𝑖 − 1) (𝑃𝐶𝐷 + 𝑃𝐷𝐶 ) − 2𝛽𝑖 (𝑃𝐶𝐷
+ 𝑃𝐷𝐶
𝑑𝑈

(B21)

𝑑𝑈

Since 𝑑𝑃 𝑖 < 0 and 𝑑𝑃 𝑖 < 0, equation (B21) suggests that the smaller punishment i inflicts, the higher
𝐶𝐷

𝐷𝐶

′
′
utility i receives. Note that i’s utility is decreasing in 𝑃𝐶𝐷
and in 𝑃𝐷𝐶
whenever i is averse to advantageous
inequality.

Summary:𝑑𝑈𝑖< 0 for all four cases, which means that 𝑃𝐶𝐷 = 0. As any other third party j faces the𝑑𝑃𝐶𝐷

same incentive structure as i and we assumed that i’s belief on j’s punishment activities are correct (𝑃𝑠′ =′𝑃𝑠𝑗 , 𝑗 ≠ 𝑖), 𝑃𝐶𝐷= 0. The conditions for the third party’s optimal punishment schedule 𝑃𝐷𝐶 can besummarized as in Figure B.2. Third parties inflict punishment under weaker conditions in Scenario DC
than in Scenario CC (7/2 > 12/7).
i’s punishment of defector (𝑃𝐷𝐶 )14′
𝑃𝐷𝐶 = 𝑃𝐷𝐶

Case 2′
𝑃𝐷𝐶 = −3𝑃𝐷𝐶+ 14

Optimal Punishment schedule when𝛼𝑖
3𝛽
+ 4𝑖 > 1
2

Case 1The symmetricstage 2 equilibrium
happens in thisrange.
Case 3𝛼𝑖+

3𝛽𝑖

Case 4

Optimal punishment schedule when

14/3′
i’s belief on peers’ punishment (𝑃𝐷𝐶
)

2

4

<1

7/2
Figure B.2. Optimal punishment schedule in Trio Scenario DC(c) i’s Punishment Behavior in Scenario DD
A third-party player i’s utility in Scenario DD is given by:
𝑈𝑖 (𝑥) = 60 − 2𝑃𝐷𝐷

28

(B22)

𝛽
2

′ ),
− 𝑖 max{(60 − 2𝑃𝐷𝐷 ) − (40 − 3𝑃𝐷𝐷 − 6𝑃𝐷𝐷
0}′′
−𝛼𝑖 max{𝑃𝐷𝐷 − 𝑃𝐷𝐷, 0} −𝛽𝑖 max{𝑃𝐷𝐷− 𝑃𝐷𝐷 , 0}.
′
′
′
′ ).
where 𝑥 = (40 − 3𝑃𝐷𝐷 − 6𝑃𝐷𝐷
, 40 − 3𝑃𝐷𝐷 − 6𝑃𝐷𝐷
, 60 − 2𝑃𝐷𝐷 , 60 − 2𝑃𝐷𝐷
, 60 − 2𝑃𝐷𝐷
Since the′expression 20 + 𝑃𝐷𝐷 + 6𝑃𝐷𝐷 ≥ 0, equation (B22) means we need to consider two cases to analyze i’spunishment behavior:′
Case 1: 𝑃𝐷𝐷 ≥ 𝑃𝐷𝐷

In this case, equation (B22) reduces to:𝛽′
𝑈𝑖 (𝑥) = 60 − 10𝛽𝑖 − (𝛼𝑖 + 2𝑖 + 2) 𝑃𝐷𝐷 + (𝛼𝑖 − 3𝛽𝑖 )𝑃𝐷𝐷
.

(B23)

𝑑𝑈𝑖
′
< 0, equation (B23) suggests that i never punishes a defector in Scenario DD more than 𝑃𝐷𝐷.
𝑑𝑃𝐷𝐷′
Note that i’s utility is increasing in 𝑃𝐷𝐷 if i is sufficiently averse to disadvantageous inequality and not

Since

too averse to advantageous inequality.
′
Case 2: 𝑃𝐷𝐷 < 𝑃𝐷𝐷

In this case, equation (B22) reduces to:𝛽2′
𝑈𝑖 (𝑥) = 60 − 10𝛽𝑖 − (2 − 𝑖) 𝑃𝐷𝐷 − 4𝛽𝑖 𝑃𝐷𝐷
.

(B24)

𝑑𝑈𝑖
< 0, equation (B24) i never punishes a defector in Scenario DD. Note that i’s utility is
𝑑𝑃𝐷𝐷′
decreasing in 𝑃𝐷𝐷
whenever i is averse to advantageous inequality.

Since

Summary: Regardless of the beliefs that i holds in Scenario DD, i never punishes a defector.

(d) Cooperate/defect decision
Analogous to the analysis for the Baseline treatment, the expected payoffs to a PD player in the Triotreatment are given in Table B.3. As (72 – 9*𝑃𝐶𝐶 ) ≥ (60 – 2*𝑃𝐶𝐶 ) for all 𝑃𝐶𝐶 ≤ 12/7, the PD player
remains in the region of advantageous inequality in any symmetric equilibrium of Scenario CC. Likewise,as (88 – 9*𝑃𝐷𝐶 ) ≥ (60 – 2*𝑃𝐷𝐶 ) for all 𝑃𝐷𝐶 ≤ 7/2, the PD player remains in the region of advantageous
inequality in any symmetric equilibrium of Scenario DC. Mutual cooperation is an equilibrium outcome if(1– F(2))𝑃𝐷𝐶 – (1– F(4))𝑃𝐶𝐶 > 16/9.

29

Table B.3: Expected payoffs to Player 1’s cooperate/defect decision in the Trio treatment under the
threat of punishment.
Player 2
Send
Send (cooperate)
Player 1
Not send (defect)(a)F(4)(72) + (1 – F(4))(72 – 9*𝑃𝐶𝐶 ),where 𝑃𝐶𝐶 ≤ 12/7(b)
F(2)(88) + (1 – F(2))(88 – 9*𝑃𝐷𝐶 ),where 𝑃𝐷𝐶 ≤ 7/2

Not send
(c)
24
(d)
40

B.3. Higher-Order Treatment
In the Higher-Order treatment, there are three third-party players (n = 5) each of whom can
inflict higher-order punishment on each other in Stage 3 after observing the first-order punishment
decisions from Stage 2. We denote higher-order punishment by 𝐻𝑠,𝑜,𝑡 , 𝑜 ≠ 𝑡, where the indices denote thethird-party originator 𝑜 ∈ {1,2,3} and the third-party target 𝑡 ∈ {1,2,3} in scenario 𝑠 ∈ {𝐶𝐶, 𝐶𝐷, 𝐷𝐶, 𝐷𝐷}.
We search for symmetric equilibria. Specifically, we assume that for any player 𝑖 and scenario s,(i) 𝑃𝑠,𝑗 = 𝑃𝑠,𝑘 = 𝑃𝑠∗ for 𝑗, 𝑘 ≠ 𝑖, (ii) 𝐻𝑠,𝑖,𝑗 = 𝐻𝑠,𝑖,𝑘 = 𝐻𝑠,𝑖 for 𝑗, 𝑘 ≠ 𝑖, (iii) 𝐻𝑠,𝑗,𝑖 = 𝐻𝑠,𝑘,𝑖 = 𝐻𝑠,𝑗,𝑘 = 𝐻𝑠,𝑘,𝑗
for 𝑗, 𝑘 ≠ 𝑖, and (iv) i’s beliefs about the higher-order punishment choice of another third-party player ineach scenario, 𝐻𝑠′ , are correct. For ease of notation, we suppress the subscript i such that 𝑃𝑠,𝑖 = 𝑃𝑠 and𝐻𝑠,𝑖 = 𝐻𝑠 .
We consider the possibility of efficient or inefficient higher-order punishment due to the relative
difference between 𝑃𝑠 and 𝑃𝑠∗ , which we denote as 𝑃̂𝑠 = 𝑃𝑠 − 𝑃𝑠∗. We define higher-order punishment fromi to j, 𝐻𝑠,𝑖,𝑗 where j  i, to be efficient (inefficient) if 𝑃̂𝑠 < (≥) 0 for scenario 𝑠 ∈ {𝐶𝐶, 𝐶𝐷}, and 𝑃̂𝑠 >(≤) 0 for scenario 𝑠 ∈ {𝐷𝐶, 𝐷𝐷}. The symmetric equilibria are characterized as follows:′a. Scenario CC: i punishes a cooperator iff 𝛼𝑖 /2 + 𝛽𝑖 > 2 and 0 < 𝑃𝐶𝐶≤ 12/7; this condition

implies a group size effect. The condition on social preference parameters is more restrictive, andthe per third-party player punishment strength is weaker, than the corresponding conditions in the
Baseline treatment. Regarding Stage 3, i never imposes higher-order punishment on another third
party.
b. Scenario CD/DC: i never punishes a cooperator; i punishes a defector iff 𝛼𝑖 /2 + 3𝛽𝑖 /4 > 1 and′
0 < 𝑃𝐷𝐶≤ 7/2; this condition implies a group size effect. The condition on social preference

parameters is more restrictive, and the per third-party player punishment strength is weaker, thanthe corresponding conditions in the Baseline treatment. Regarding Stage 3, i never imposes
higher-order punishment on another third party.
c. Scenario DD: i never punishes a defector; i imposes higher-order punishment on another third30

′party in Scenario DD iff: 𝛼𝑖 /2 + 𝛽𝑖 > 2 and 0 < 𝐻𝐷𝐷≤ 5/4.

d. Some PD players choose to cooperate with their paired PD players, driven by their inequality
concern or by the threat of punishment.
Outside of the symmetric equilibria, efficient or inefficient higher-order punishment is feasible in all
scenarios.

(a) i’s Punishment Behavior in Scenario CC
A third-party player i’s utility in Scenario CC is given by:′
𝑈𝑖 (𝑥) = 60 − 2𝑃𝐶𝐶 − 4𝐻𝐶𝐶 − 12𝐻𝐶𝐶
𝛼
2

∗ )
′ ),
− 𝑖 max{(72 − 3𝑃𝐶𝐶 − 6𝑃𝐶𝐶
− (60 − 2𝑃𝐶𝐶 − 4𝐻𝐶𝐶 − 12𝐻𝐶𝐶
0}
𝛽
2

′ )
∗ ),
− 𝑖 max{(60 − 2𝑃𝐶𝐶 − 4𝐻𝐶𝐶 − 12𝐻𝐶𝐶− (72 − 3𝑃𝐶𝐶 − 6𝑃𝐶𝐶
0}

(B25)

∗
′
−𝛼𝑖 max{𝑃𝐶𝐶 − 𝑃𝐶𝐶− 𝐻𝐶𝐶 + 𝐻𝐶𝐶, 0}∗′−𝛽𝑖 max{𝑃𝐶𝐶− 𝑃𝐶𝐶 − 𝐻𝐶𝐶+ 𝐻𝐶𝐶 , 0},
∗
∗
′
∗
′
where 𝑥 = (72 − 3𝑃𝐶𝐶 − 6𝑃𝐶𝐶
, 72 − 3𝑃𝐶𝐶 − 6𝑃𝐶𝐶
, 60 − 2𝑃𝐶𝐶 − 4𝐻𝐶𝐶 − 12𝐻𝐶𝐶, 60 − 2𝑃𝐶𝐶
− 10𝐻𝐶𝐶−∗′
6𝐻𝐶𝐶 , 60 − 2𝑃𝐶𝐶 − 10𝐻𝐶𝐶 − 6𝐻𝐶𝐶 ). Equation (B25) means we need to consider four cases to analyze i’shigher-order punishment behavior:∗′∗′
Case 1: 12 − 𝑃𝐶𝐶 − 6𝑃𝐶𝐶
+ 4𝐻𝐶𝐶 + 12𝐻𝐶𝐶≥ 0 and 𝑃𝐶𝐶 − 𝐻𝐶𝐶 ≥ 𝑃𝐶𝐶− 𝐻𝐶𝐶

In this case, equation (B25) reduces to:𝛼2∗′
𝑈𝑖 (𝑥) = 60 − 6𝛼𝑖 − ( 𝑖 + 2) 𝑃𝐶𝐶 + 4𝛼𝑖 𝑃𝐶𝐶− (4 + 𝛼𝑖 )𝐻𝐶𝐶 − (12 + 7𝛼𝑖 )𝐻𝐶𝐶
.

(B26)

𝑑𝑈

Since 𝑑𝐻 𝑖 < 0, the smaller higher-order punishment i inflicts, the higher utility i receives.
𝐶𝐶

∗
′
∗
′
Case 2: 12 − 𝑃𝐶𝐶 − 6𝑃𝐶𝐶
+ 4𝐻𝐶𝐶 + 12𝐻𝐶𝐶< 0 and 𝑃𝐶𝐶 − 𝐻𝐶𝐶 ≥ 𝑃𝐶𝐶− 𝐻𝐶𝐶

In this case, equation (B25) reduces to:𝑈𝑖 (𝑥) = 60 + 6𝛽𝑖 − (𝛼𝑖 +𝛽𝑖∗+ 2) 𝑃𝐶𝐶 + (𝛼𝑖 − 3𝛽𝑖 )𝑃𝐶𝐶
− (4 − 𝛼𝑖 − 2𝛽𝑖 )𝐻𝐶𝐶
2′−(12 + 𝛼𝑖 − 6𝛽𝑖 )𝐻𝐶𝐶
.

(B27)

Equation (B27) suggests that i will higher-order punish (not higher-order punish) in Scenario CC if
𝛼𝑖 /2 + 𝛽𝑖 > 2 (< 2), up to:
𝐻𝐶𝐶 = min {

∗
3𝑃𝐶𝐶
𝑃
′
′
+ 𝐶𝐶 − 3(𝐻𝐶𝐶+ 1), 𝐻𝐶𝐶
+ 𝑃̂𝐶𝐶 }.
2
4

31

∗
Conditional on the vector of punishment decisions (𝑃𝐶𝐶
, 𝑃𝐶𝐶 ), the arguments of the minima define theupper envelope of the higher-order punishment schedule as a function of i’s beliefs about the higher-order′punishment choice of another third-party player, 𝐻𝐶𝐶. The upper envelope is a piecewise linear function′of 𝐻𝐶𝐶, where the slope of the first argument is negative three and the slope of the second argument is
positive one. Thus, for higher-order punishment to be associated with a non-empty subset of first-order∗punishment vectors, we require that either of the following conditions must hold: (i) 𝑃̂𝐶𝐶 > −𝑃𝐶𝐶
/2 −′
̂𝑃𝐶𝐶 /12 + 1 if 𝑃𝐶𝐶 < 0 (i.e., if the vertical intercept of the second argument is negative in the 𝐻𝐶𝐶 -𝐻𝐶𝐶∗
plane), or (ii) 𝑃𝐶𝐶/2 + 𝑃𝐶𝐶 /12 − 1 > 0 if 𝑃̂𝐶𝐶 ≥ 0 (i.e., if the vertical intercept of the second argument is′
non-negative in the 𝐻𝐶𝐶-𝐻𝐶𝐶 plane).

Solving the system of inequalities for efficient (𝑃̂𝐶𝐶 < 0) and inefficient (𝑃̂𝐶𝐶 ≥ 0) higher-orderpunishment respectively, we obtain the following necessary conditions:•

Efficient:∗
𝑃𝐶𝐶 > 12/13 + 6𝑃𝐶𝐶
/13; and•Inefficient:∗
𝑃𝐶𝐶 > 12 − 6𝑃𝐶𝐶.

∗
In Figure B.3, we plot the feasible regions for higher-order punishment in (𝑃𝐶𝐶
, 𝑃𝐶𝐶 ) space and overlay
the optimal first-order punishment schedule from the Trio treatment. This implies that the symmetricequilibrium still exists for 0 < 𝑃𝐶𝐶 , 𝑃∗𝐶𝐶 < 12/7 with 𝐻𝐶𝐶 = 0. Outside of the symmetric equilibrium,
inefficient or efficient higher-order punishment is feasible.

12/7

Optimal first-order punishment schedule when𝛼𝑖
+ 𝛽𝑖 > 22

12/7

Figure B.3. Feasible region for higher-order punishment
in Scenario CC. The blue (red) region reflects efficient(inefficient) punishment.
∗′∗′
Case 3: 12 − 𝑃𝐶𝐶 − 6𝑃𝐶𝐶
+ 4𝐻𝐶𝐶 + 12𝐻𝐶𝐶≥ 0 and 𝑃𝐶𝐶 − 𝐻𝐶𝐶 < 𝑃𝐶𝐶− 𝐻𝐶𝐶

In this case, equation (B25) reduces to:
32

𝛼𝑖
∗
𝑈𝑖 (𝑥) = 60 − 6𝛼𝑖 + ( + 𝛽𝑖 − 2) 𝑃𝐶𝐶 + (3𝛼𝑖 − 𝛽𝑖 )𝑃𝐶𝐶
− (4 + 2𝛼𝑖 + 𝛽𝑖 )𝐻𝐶𝐶
2

(B28)

′
−(12 + 6𝛼𝑖 − 𝛽𝑖 )𝐻𝐶𝐶.
𝑑𝑈

Since 𝑑𝐻 𝑖 < 0, the smaller higher-order punishment i inflicts, the higher utility i receives.
𝐶𝐶

∗
′
∗
′
Case 4: 12 − 𝑃𝐶𝐶 − 6𝑃𝐶𝐶
+ 4𝐻𝐶𝐶 + 12𝐻𝐶𝐶< 0 and 𝑃𝐶𝐶 − 𝐻𝐶𝐶 < 𝑃𝐶𝐶− 𝐻𝐶𝐶

In this case, equation (B25) reduces to:𝑈𝑖 (𝑥) = 60 + 6𝛽𝑖 − (2 −𝛽𝑖∗
) 𝑃 − 4𝛽𝑖 𝑃𝐶𝐶− (4 − 𝛽𝑖 )𝐻𝐶𝐶
2 𝐶𝐶

(B29)

′
−(12 − 7𝛽𝑖 )𝐻𝐶𝐶.
𝑑𝑈

Since 𝑑𝐻 𝑖 < 0, the smaller higher-order punishment i inflicts, the higher utility i receives.
𝐶𝐶

Summary: The conditions for the third party’s optimal higher-order punishment schedule 𝐻𝐶𝐶 can be∗summarized as in Figure B.4. Along the optimal punishment schedule, 0 < 𝑃𝐶𝐶 , 𝑃𝐶𝐶< 2, we have∗∗
5𝑃𝐶𝐶 /8 − 3𝑃𝐶𝐶 /16 − 3/4 < 0 and 𝑃𝐶𝐶 /12 + 𝑃𝐶𝐶 /2 − 1 ≤ 0 (i.e., the upper envelope of the higher-order′punishment schedule is below the x-axis for all positive values of 𝐻𝐶𝐶). In sum, this means that nosymmetric higher-order punishment equilibrium exists and so no higher-order punishment is predicted in
Scenario CC.
i’s higher-order punishment in Scenario CC (𝐻𝐶𝐶 )

𝐻𝐶𝐶 =

∗
3𝑃𝐶𝐶
𝑃𝐶𝐶
′
+
− 3(𝐻𝐶𝐶+ 1)
2
4′
𝐻𝐶𝐶 = 𝐻𝐶𝐶
+ 𝑃̂𝐶𝐶

Optimal higher-order punishment𝛼schedule when 𝑖 + 𝛽𝑖 > 2

Case 32

Case 4The symmetric stage 3 equilibrium
happens in this range.
∗
13𝑃𝐶𝐶 3𝑃𝐶𝐶
3
−
−
16
8
4
Case 2

−𝑃̂𝐶𝐶

∗
5𝑃𝐶𝐶

8

−

3𝑃𝐶𝐶 3−
16
4

Optimal higher-order punishment𝛼schedule when 𝑖 + 𝛽𝑖 < 22Case 1′
i’s belief on peers’ higher-order punishment (𝐻𝐶𝐶
)
∗
𝑃𝐶𝐶
𝑃𝐶𝐶
+
−1
12
2

Figure B.4. Optimal punishment schedule in Higher-Order Scenario CC
33

Remark 1. The area for total higher-order punishment in the lower triangle of Scenario CC is given by:∆𝐶𝐶 =(13𝑃𝐶𝐶 − 6𝑃∗𝐶𝐶 −12)2
384.

By the necessary conditions for efficient punishment, the expression in the numerator is strictly positive,∗
and so the total area of efficient higher-order punishment is decreasing in 𝑃𝐶𝐶.

(b) i’s Punishment Behavior in Scenario CD/DCA third-party player i’s utility in Scenario CD/DC is given by:′′
𝑈𝑖 (𝑥) = 60 − 𝑃𝐶𝐷 − 𝑃𝐷𝐶 − 2(𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) − 6(𝐻𝐶𝐷
+ 𝐻𝐷𝐶
)
𝛼

∗
′
′ ),
− 4𝑖 max{−36 − 2𝑃𝐶𝐷 − 6𝑃𝐶𝐷
+ 𝑃𝐷𝐶 + 2(𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) + 6(𝐻𝐶𝐷
+ 𝐻𝐷𝐶
0}
𝛽

∗
′
′ ),
− 4𝑖 max{36 + 2𝑃𝐶𝐷 + 6𝑃𝐶𝐷
− 𝑃𝐷𝐶 − 2(𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) − 6(𝐻𝐶𝐷
+ 𝐻𝐷𝐶
0}
𝛼

∗
′
′ ),
− 4𝑖 max{28 − 2𝑃𝐷𝐶 − 6𝑃𝐷𝐶
+ 𝑃𝐶𝐷 + 2(𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) + 6(𝐻𝐶𝐷
+ 𝐻𝐷𝐶
0}

(B30)

𝛽
4

∗
′
′ ),
− 𝑖 max{−28 + 2𝑃𝐷𝐶 + 6𝑃𝐷𝐶
− 𝑃𝐶𝐷 − 2(𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) − 6(𝐻𝐶𝐷
+ 𝐻𝐷𝐶
0}
𝛼

∗
∗ )
′
′ )
− 2𝑖 max{(𝑃𝐶𝐷 + 𝑃𝐷𝐶 ) − (𝑃𝐶𝐷
+ 𝑃𝐷𝐶
+ (𝐻𝐶𝐷+ 𝐻𝐷𝐶− (𝐻𝐶𝐷 + 𝐻𝐷𝐶 ), 0}
𝛽

∗
∗ )
′
′
− 2𝑖 max{(𝑃𝐶𝐷+ 𝑃𝐷𝐶− (𝑃𝐶𝐷 + 𝑃𝐷𝐶 ) + (𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) − (𝐻𝐶𝐷
+ 𝐻𝐷𝐶
),0},
∗
∗
′
′ ),
where 𝑥 = (24 − 3𝑃𝐶𝐷 − 6𝑃𝐶𝐷
, 88 − 3𝑃𝐷𝐶 − 6𝑃𝐷𝐶
, 60 − 𝑃𝐶𝐷 − 𝑃𝐷𝐶 − 2(𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) − 6(𝐻𝐶𝐷
+ 𝐻𝐷𝐶
60 −
∗
∗
′
′ )
∗
∗
′
′ )
𝑃𝐶𝐷
− 𝑃𝐷𝐶
− 5(𝐻𝐶𝐷+ 𝐻𝐷𝐶− 3(𝐻𝐶𝐷 + 𝐻𝐷𝐶 ), 60 − 𝑃𝐶𝐷− 𝑃𝐷𝐶− 5(𝐻𝐶𝐷+ 𝐻𝐷𝐶− 3(𝐻𝐶𝐷 + 𝐻𝐷𝐶 )).

Equation (B30) means we need to consider eight cases to analyze i’s higher-order punishment
behavior:
Case 1:i.

∗′′ )−36 − 2𝑃𝐶𝐷 − 6𝑃𝐶𝐷
+ 𝑃𝐷𝐶 + 2(𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) + 6(𝐻𝐶𝐷
+ 𝐻𝐷𝐶
≥ 0;

ii.

∗
′
′ )
28 − 2𝑃𝐷𝐶 − 6𝑃𝐷𝐶
+ 𝑃𝐶𝐷 + 2(𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) + 6(𝐻𝐶𝐷+ 𝐻𝐷𝐶≥ 0; and

iii.

∗
∗ )
′
′ )
(𝑃𝐶𝐷 + 𝑃𝐷𝐶 ) − (𝑃𝐶𝐷
+ 𝑃𝐷𝐶
+ (𝐻𝐶𝐷+ 𝐻𝐷𝐶− (𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) ≥ 0.

From equation (B30), the coefficient on each of 𝐻𝐶𝐷 and 𝐻𝐷𝐶 in this case is −(2 + 𝛼𝑖 ⁄2), and so thesmaller higher-order punishment i inflicts, the higher utility i receives.
Case 2:i.

∗′′ )−36 − 2𝑃𝐶𝐷 − 6𝑃𝐶𝐷
+ 𝑃𝐷𝐶 + 2(𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) + 6(𝐻𝐶𝐷
+ 𝐻𝐷𝐶
< 0;

34

ii.

∗
′
′ )
28 − 2𝑃𝐷𝐶 − 6𝑃𝐷𝐶
+ 𝑃𝐶𝐷 + 2(𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) + 6(𝐻𝐶𝐷+ 𝐻𝐷𝐶≥ 0; and

iii.

∗
∗ )
′
′ )
(𝑃𝐶𝐷 + 𝑃𝐷𝐶 ) − (𝑃𝐶𝐷
+ 𝑃𝐷𝐶
+ (𝐻𝐶𝐷+ 𝐻𝐷𝐶− (𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) ≥ 0.

From equation (B30), the coefficient on each of 𝐻𝐶𝐷 and 𝐻𝐷𝐶 in this case is (𝛽𝑖 ⁄2 − 2). Given ourassumption on 𝛽𝑖 , this coefficient is negative and so the smaller higher-order punishment i inflicts, thehigher utility i receives.
Case 3:i.

∗′′ )−36 − 2𝑃𝐶𝐷 − 6𝑃𝐶𝐷
+ 𝑃𝐷𝐶 + 2(𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) + 6(𝐻𝐶𝐷
+ 𝐻𝐷𝐶
< 0;

ii.

∗
′
′ )
28 − 2𝑃𝐷𝐶 − 6𝑃𝐷𝐶
+ 𝑃𝐶𝐷 + 2(𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) + 6(𝐻𝐶𝐷+ 𝐻𝐷𝐶< 0; and

iii.

∗
∗ )
′
′ )
(𝑃𝐶𝐷 + 𝑃𝐷𝐶 ) − (𝑃𝐶𝐷
+ 𝑃𝐷𝐶
+ (𝐻𝐶𝐷+ 𝐻𝐷𝐶− (𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) ≥ 0.

From equation (B30), the coefficient on each of 𝐻𝐶𝐷 and 𝐻𝐷𝐶 in this case is (𝛼𝑖 /2 + 𝛽𝑖 − 2). Thus, anecessary condition for i to higher-order punish in Scenarios CD and DC is 𝛼𝑖 /2 + 𝛽𝑖 > 2.
First, we consider the possibility of higher-order punishment in Scenario CD. As we are searching∗′∗for symmetric equilibria, we assume that 𝑃𝐷𝐶 = 𝑃𝐷𝐶
and 𝐻𝐷𝐶 = 𝐻𝐷𝐶= 𝐻𝐷𝐶. Constraint i. is non-binding∗
for all 0 < 𝑃𝐷𝐶 ≤ 7/2 (the range in which the symmetric stage 2 equilibrium happens) and so we proceed
under the assumption that constraint ii. binds. In this case, i will higher-order punish (not higher-orderpunish) in Scenario CC if 𝛼𝑖 /2 + 𝛽𝑖 > 2 (< 2), up to:
𝑃

∗
∗
′
′
𝐻𝐶𝐷 = min {−14 + 4𝑃𝐷𝐶
− 𝐶𝐷
− 4𝐻𝐷𝐶− 3𝐻𝐶𝐷, 𝐻𝐶𝐷+ 𝑃̂𝐶𝐷 }.
2∗∗∗
Conditional on the vector of punishment decisions (𝑃𝐶𝐷 , 𝑃𝐶𝐷
, 𝑃𝐷𝐶
, 𝐻𝐷𝐶
), the arguments of the minima
define the upper envelope of the higher-order punishment schedule as a function of i’s beliefs about the′higher-order punishment choice of another third-party player, 𝐻𝐶𝐷. Thus, for higher-order punishment tobe associated with a non-empty subset of first-order punishment vectors, we require that either of the∗∗following conditions must hold: (i) 𝑃̂𝐶𝐷 > 14/3 − 4𝑃𝐷𝐶
/3 + 𝑃𝐶𝐷 /6 + 4𝐻𝐷𝐶
/3 if 𝑃̂𝐶𝐷 < 0, or (ii)∗∗∗
−14/3 + 4𝑃𝐷𝐶 /3 − 𝑃𝐶𝐷 /6 − 4𝐻𝐷𝐶 /3 > 0 if 𝑃̂𝐶𝐷 ≥ 0. Neither condition is satisfied for any 𝑃𝐷𝐶≤ 7/2∗
and so the symmetric equilibrium for 𝑃𝐶𝐷 = 𝑃𝐶𝐷 = 0 still exists with 𝐻𝐶𝐷 = 0.

Second, we consider the possibility of higher-order punishment in Scenario DC, given the zero∗punishment outcome in Scenario CD. Constraint i. (ii.) binds for all 𝑃𝐷𝐶 > (<) 64/3 − 2𝑃𝐷𝐶
. Thus, iwill higher-order punish (not higher-order punish) in Scenario DC if 𝛼𝑖 /2 + 𝛽𝑖 > 2 (< 2), up to:∗′′min {−14 + 𝑃𝐷𝐶 + 3𝑃𝐷𝐶
− 3𝐻𝐷𝐶, 𝐻𝐷𝐶+ 𝑃̂𝐷𝐶 } ,𝐻𝐷𝐶 = {
𝑃𝐷𝐶′′
min {18 −− 3𝐻𝐷𝐶, 𝐻𝐷𝐶+ 𝑃̂𝐷𝐶 } ,264∗− 2𝑃𝐷𝐶;
364∗
𝑖𝑓 𝑃𝐷𝐶 >− 2𝑃𝐷𝐶.
3

𝑖𝑓 𝑃𝐷𝐶 <∗Conditional on the vector of punishment decisions (𝑃𝐷𝐶 , 𝑃𝐷𝐶), the arguments of the minima define theupper envelope of the higher-order punishment schedule as a function of i’s beliefs about the higher-order′punishment choice of another third-party player, 𝐻𝐷𝐶. Thus, for higher-order punishment to be associatedwith a non-empty subset of first-order punishment vectors, we require that either of the following

35

∗
conditions must hold: (i) 𝑃̂𝐷𝐶 > min{14⁄3 − 𝑃𝐷𝐶 ⁄3 − 𝑃𝐷𝐶, 𝑃𝐷𝐶 ⁄6 − 6} if 𝑃̂𝐷𝐶 ≤ 0, or (ii)∗min{𝑃𝐷𝐶 ⁄3 + 𝑃𝐷𝐶 − 14⁄3 , 6 − 𝑃𝐷𝐶 ⁄6} > 0 if 𝑃̂𝐷𝐶 > 0.

Solving the system of inequalities for efficient (𝑃̂𝐷𝐶 > 0) and inefficient (𝑃̂𝐷𝐶 ≤ 0) higher-orderpunishment respectively, we obtain the following necessary conditions:•

Efficient:∗
𝑃𝐷𝐶 > 14 − 3𝑃𝐷𝐶
; and

•

Inefficient:∗
𝑃𝐷𝐶 > min{7⁄2 , − 36⁄5 + 6𝑃𝐷𝐶
/5}.

∗In Figure B.5, we plot the feasible regions for higher-order punishment in (𝑃𝐷𝐶
, 𝑃𝐷𝐶 ) space and overlay
the optimal first-order punishment schedule from the Trio treatment. This implies that the symmetricequilibrium still exists for 0 < 𝑃𝐷𝐶 , 𝑃∗𝐷𝐶 < 7/2 with 𝐻𝐷𝐶 = 0. Outside of the symmetric equilibrium,
inefficient or efficient higher-order punishment is feasible.

7/2

Optimal first-order punishment schedule when𝛼𝑖
+ 𝛽𝑖 > 22

7/2

Figure B.5. Feasible region for higher-order punishment
in Scenario CC. The blue (red) region reflects efficient(inefficient) punishment.
Case 4:i.

∗′′ )−36 − 2𝑃𝐶𝐷 − 6𝑃𝐶𝐷
+ 𝑃𝐷𝐶 + 2(𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) + 6(𝐻𝐶𝐷
+ 𝐻𝐷𝐶
< 0;

ii.

∗
′
′ )
28 − 2𝑃𝐷𝐶 − 6𝑃𝐷𝐶
+ 𝑃𝐶𝐷 + 2(𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) + 6(𝐻𝐶𝐷+ 𝐻𝐷𝐶< 0; and

iii.

∗
∗ )
′
′ )
(𝑃𝐶𝐷 + 𝑃𝐷𝐶 ) − (𝑃𝐶𝐷
+ 𝑃𝐷𝐶
+ (𝐻𝐶𝐷+ 𝐻𝐷𝐶− (𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) < 0.

From equation (B30), the coefficient on each of 𝐻𝐶𝐷 and 𝐻𝐷𝐶 in this case is (𝛽𝑖 /2 − 2). Given our
36assumption on 𝛽𝑖 , this coefficient is negative and so the smaller higher-order punishment i inflicts, thehigher utility i receives.
Case 5:i.

∗′′ )−36 − 2𝑃𝐶𝐷 − 6𝑃𝐶𝐷
+ 𝑃𝐷𝐶 + 2(𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) + 6(𝐻𝐶𝐷
+ 𝐻𝐷𝐶
≥ 0;

ii.

∗
′
′ )
28 − 2𝑃𝐷𝐶 − 6𝑃𝐷𝐶
+ 𝑃𝐶𝐷 + 2(𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) + 6(𝐻𝐶𝐷+ 𝐻𝐷𝐶< 0; and

iii.

∗
∗ )
′
′ )
(𝑃𝐶𝐷 + 𝑃𝐷𝐶 ) − (𝑃𝐶𝐷
+ 𝑃𝐷𝐶
+ (𝐻𝐶𝐷+ 𝐻𝐷𝐶− (𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) ≥ 0.

From equation (B30), the coefficient on each of 𝐻𝐶𝐷 and 𝐻𝐷𝐶 in this case is (𝛽𝑖 /2 − 2). Given ourassumption on 𝛽𝑖 , this coefficient is negative and so the smaller higher-order punishment i inflicts, thehigher utility i receives.
Case 6:i.

∗′′ )−36 − 2𝑃𝐶𝐷 − 6𝑃𝐶𝐷
+ 𝑃𝐷𝐶 + 2(𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) + 6(𝐻𝐶𝐷
+ 𝐻𝐷𝐶
≥ 0;

ii.

∗
′
′ )
28 − 2𝑃𝐷𝐶 − 6𝑃𝐷𝐶
+ 𝑃𝐶𝐷 + 2(𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) + 6(𝐻𝐶𝐷+ 𝐻𝐷𝐶< 0; and

iii.

∗
∗ )
′
′ )
(𝑃𝐶𝐷 + 𝑃𝐷𝐶 ) − (𝑃𝐶𝐷
+ 𝑃𝐷𝐶
+ (𝐻𝐶𝐷+ 𝐻𝐷𝐶− (𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) < 0.

From equation (B30), the coefficient on each of 𝐻𝐶𝐷 and 𝐻𝐷𝐶 in this case is −(2 + 𝛼𝑖 /2), and so thesmaller higher-order punishment i inflicts, the higher utility i receives.
Case 7:i.

∗′′ )−36 − 2𝑃𝐶𝐷 − 6𝑃𝐶𝐷
+ 𝑃𝐷𝐶 + 2(𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) + 6(𝐻𝐶𝐷
+ 𝐻𝐷𝐶
< 0;

ii.

∗
′
′ )
28 − 2𝑃𝐷𝐶 − 6𝑃𝐷𝐶
+ 𝑃𝐶𝐷 + 2(𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) + 6(𝐻𝐶𝐷+ 𝐻𝐷𝐶≥ 0; and

iii.

∗
∗ )
′
′ )
(𝑃𝐶𝐷 + 𝑃𝐷𝐶 ) − (𝑃𝐶𝐷
+ 𝑃𝐷𝐶
+ (𝐻𝐶𝐷+ 𝐻𝐷𝐶− (𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) < 0.

From equation (B30), the coefficient on each of 𝐻𝐶𝐷 and 𝐻𝐷𝐶 in this case is −(2 + 𝛼𝑖 /2), and so thesmaller higher-order punishment i inflicts, the higher utility i receives.
Case 8:i.

∗′′ )−36 − 2𝑃𝐶𝐷 − 6𝑃𝐶𝐷
+ 𝑃𝐷𝐶 + 2(𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) + 6(𝐻𝐶𝐷
+ 𝐻𝐷𝐶
≥ 0;

ii.

∗
′
′ )
28 − 2𝑃𝐷𝐶 − 6𝑃𝐷𝐶
+ 𝑃𝐶𝐷 + 2(𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) + 6(𝐻𝐶𝐷+ 𝐻𝐷𝐶≥ 0; and

iii.

∗
∗ )
′
′ )
(𝑃𝐶𝐷 + 𝑃𝐷𝐶 ) − (𝑃𝐶𝐷
+ 𝑃𝐷𝐶
+ (𝐻𝐶𝐷+ 𝐻𝐷𝐶− (𝐻𝐶𝐷 + 𝐻𝐷𝐶 ) < 0.

From equation (B30), the coefficient on each of 𝐻𝐶𝐷 and 𝐻𝐷𝐶 in this case is −(2 + 𝛼𝑖 + 𝛽𝑖 /2), and so thesmaller higher-order punishment i inflicts, the higher utility i receives.
∗
Summary: In the symmetric equilibrium, 𝑃𝐶𝐷 = 𝑃𝐶𝐷= 0 and no higher-order punishment is predicted in37

Scenario CD. The conditions for the third party’s optimal higher-order punishment schedule 𝐻𝐷𝐶 can be∗summarized as in Figure B.6. Along the optimal punishment schedule, 0 < 𝑃𝐷𝐶 , 𝑃𝐷𝐶< 7/2, we have
∗
∗
∗
⁄
⁄
min{𝑃𝐷𝐶 /4 − 3𝑃𝐷𝐶 /8 + 9/2, 𝑃𝐷𝐶 − 7/2} < 0, min{𝑃𝐷𝐶 3 + 𝑃𝐷𝐶 − 14 3 , 6 − 𝑃𝐷𝐶 ⁄6} < 0. In sum,
this means that no symmetric higher-order punishment equilibrium exists and so no higher-orderpunishment is predicted in Scenario DC.
i’s higher-order punishment in Scenario DC (𝐻𝐷𝐶 )′18 − 𝑃𝐷𝐶 ⁄2 − 3𝐻𝐷𝐶
𝐻𝐷𝐶 = min ൜∗′−14 + 𝑃𝐷𝐶 + 3𝑃𝐷𝐶
− 3𝐻𝐷𝐶′𝐻𝐷𝐶 = 𝐻𝐷𝐶
+ 𝑃̂𝐷𝐶

Optimal higher-order punishment schedule𝛼when 𝑖 + 𝛽𝑖 > 2

Cases 6,7,8

2

Optimal higher-order punishment schedule𝛼when 𝑖 + 𝛽𝑖 < 2

The symmetric stage 3 equilibrium
happens in this range.
min ൜

2

Case 4∗−3𝑃𝐷𝐶/4 + 5𝑃𝐷𝐶 /8 + 9/2,

Cases 1,2,5

𝑃𝐷𝐶 − 7⁄2′
i’s belief on peers’ higher-order punishment (𝐻𝐷𝐶)

Case 30∗
𝑃 ⁄3 + 𝑃𝐷𝐶− 14⁄3,min ൜ 𝐷𝐶
6 − 𝑃𝐷𝐶 ⁄6

𝑃∗ /4 − 3𝑃𝐷𝐶 /8 + 9/2,
min ൜ 𝐷𝐶
∗
𝑃𝐷𝐶
− 7/2

Figure B.6. Optimal punishment schedule in Higher-Order Scenario DC
Remark 2. The area for total higher-order punishment in the lower triangle of Scenario CD is given by:
∆𝐶𝐷 =

∗
∗
∗ )2
(6𝑃𝐶𝐷
−5𝑃𝐶𝐷 +28−8𝑃𝐷𝐶+ 8𝐻𝐷𝐶96.

∗∗
The expression in the numerator is strictly positive for any efficient punishment (𝑃𝐶𝐷 < 𝑃𝐶𝐷) when 𝑃𝐷𝐶≤∗
7/2, in which case the total area of efficient higher-order punishment is increasing in 𝑃𝐶𝐷 .

Remark 3. The area for total higher-order punishment in the lower triangle of Scenario DC is given by:∗ )2(36+5𝑃𝐷𝐶 −6𝑃𝐷𝐶∆𝐷𝐶 = min {96(2𝑃𝐷𝐶 −7)2

.

6
∗
∗
The numerator in the first case is strictly positive for any efficient punishment (𝑃𝐷𝐶 > 𝑃𝐷𝐶) because 𝑃𝐷𝐶<∗
36, and so the total area of efficient higher-order punishment is increasing as 𝑃𝐷𝐶 falls.

38

(c) i’s Punishment Behavior in Scenario DD
A third-party player i’s utility in Scenario DD is given by:′
𝑈𝑖 (𝑥) = 60 − 2𝑃𝐷𝐷 − 4𝐻𝐷𝐷 − 12𝐻𝐷𝐷
𝛼

∗ )
′ ),
− 2𝑖 max{(40 − 3𝑃𝐷𝐷 − 6𝑃𝐷𝐷
− (60 − 2𝑃𝐷𝐷 − 4𝐻𝐷𝐷 − 12𝐻𝐷𝐷
0}
𝛽

′ )
∗ ),
− 2𝑖 max{(60 − 2𝑃𝐷𝐷 − 4𝐻𝐷𝐷 − 12𝐻𝐷𝐷− (40 − 3𝑃𝐷𝐷 − 6𝑃𝐷𝐷
0}

(B31)

∗
′
−𝛼𝑖 max{𝑃𝐷𝐷 − 𝑃𝐷𝐷− 𝐻𝐷𝐷 + 𝐻𝐷𝐷, 0}∗′−𝛽𝑖 max{𝑃𝐷𝐷− 𝑃𝐷𝐷 − 𝐻𝐷𝐷+ 𝐻𝐷𝐷 , 0},∗∗′∗
where 𝑥 = (40 − 3𝑃𝐷𝐷 − 6𝑃𝐷𝐷
, 40 − 3𝑃𝐷𝐷 − 6𝑃𝐷𝐷
, 60 − 2𝑃𝐷𝐷 − 4𝐻𝐷𝐷 − 12𝐻𝐷𝐷, 60 − 2𝑃𝐷𝐷−′∗′
10𝐻𝐷𝐷 − 6𝐻𝐷𝐷 , 60 − 2𝑃𝐷𝐷 − 10𝐻𝐷𝐷 − 6𝐻𝐷𝐷 ). Mirroring the analysis of Scenario CC, we obtain fourcases from equation (B31):′∗∗′
Case 1: 4𝐻𝐷𝐷 + 12𝐻𝐷𝐷− 𝑃𝐷𝐷 − 6𝑃𝐷𝐷
− 20 ≥ 0 and 𝑃𝐷𝐷 − 𝐻𝐷𝐷 ≥ 𝑃𝐷𝐷
− 𝐻𝐷𝐷
′
∗
∗
′
Case 2: 4𝐻𝐷𝐷 + 12𝐻𝐷𝐷− 𝑃𝐷𝐷 − 6𝑃𝐷𝐷
− 20 < 0 and 𝑃𝐷𝐷 − 𝐻𝐷𝐷 ≥ 𝑃𝐷𝐷
− 𝐻𝐷𝐷
′
∗
∗
′
Case 3: 4𝐻𝐷𝐷 + 12𝐻𝐷𝐷− 𝑃𝐷𝐷 − 6𝑃𝐷𝐷
− 20 ≥ 0 and 𝑃𝐷𝐷 − 𝐻𝐷𝐷 < 𝑃𝐷𝐷
− 𝐻𝐷𝐷
′
∗
∗
′
Case 4: 4𝐻𝐷𝐷 + 12𝐻𝐷𝐷− 𝑃𝐷𝐷 − 6𝑃𝐷𝐷
− 20 < 0 and 𝑃𝐷𝐷 − 𝐻𝐷𝐷 < 𝑃𝐷𝐷− 𝐻𝐷𝐷

It follows directly from our analysis of Scenario CC that, for cases 1, 3 and 4, the smaller higher-orderpunishment i inflicts, the higher utility i receives.4 We thus confine our analysis to case 2.
′∗∗′
Case 2: 4𝐻𝐷𝐷 + 12𝐻𝐷𝐷− 𝑃𝐷𝐷 − 6𝑃𝐷𝐷
− 20 < 0 and 𝑃𝐷𝐷 − 𝐻𝐷𝐷 ≥ 𝑃𝐷𝐷− 𝐻𝐷𝐷

In this case, equation (B31) reduces to:𝑈𝑖 (𝑥) = 60 − 10𝛽𝑖 − (𝛼𝑖 +𝛽𝑖∗+ 2) 𝑃𝐷𝐷 + (𝛼𝑖 − 3𝛽𝑖 )𝑃𝐷𝐷
− (4 − 𝛼𝑖 − 2𝛽𝑖 )𝐻𝐷𝐷
2

(B32)

′
−(12 + 𝛼𝑖 − 6𝛽𝑖 )𝐻𝐷𝐷.

Equation (B32) suggests that i will higher-order punish (not higher-order punish) in Scenario DD if
𝛼𝑖 /2 + 𝛽𝑖 > 2 (< 2), up to:
𝐻𝐷𝐷 = min {5 +

∗
3𝑃𝐷𝐷
𝑃
′
′
+ 𝐷𝐷
− 3𝐻𝐷𝐷, 𝐻𝐷𝐷+ 𝑃̂𝐷𝐷 }.
2
4∗
Conditional on the vector of punishment decisions (𝑃𝐷𝐷
, 𝑃𝐷𝐷 ), the arguments of the minima define theupper envelope of the higher-order punishment schedule as a function of i’s beliefs about the higher-order′punishment choice of another third-party player, 𝐻𝐷𝐷. Thus, for higher-order punishment to be associated4

The coefficients on 𝐻𝐷𝐷 are the same.

39

with a non-empty subset of first-order punishment vectors, we require that either of the following∗∗
conditions must hold: (i) 𝑃̂𝐷𝐷 > −𝑃𝐷𝐷
/2 − 𝑃𝐷𝐷 /12 − 5/3 if 𝑃̂𝐷𝐷 ≤ 0, or (ii) 𝑃𝐷𝐷/2 + 𝑃𝐷𝐷 /12 + 5/3 >̂
0 if 𝑃𝐷𝐷 > 0.
The condition (ii) for efficient (𝑃̂𝐷𝐷 > 0) higher-order punishment is always satisfied. Solving thesystem of inequalities for inefficient (𝑃̂𝐷𝐷 ≤ 0) higher-order punishment, we obtain the necessary∗
condition that 𝑃𝐷𝐷 > 6𝑃𝐷𝐷
/13 − 20/13. In Figure B.7, we plot the feasible regions for higher-order∗punishment in (𝑃𝐷𝐷 , 𝑃𝐷𝐷 ) space. To check whether positive first-order punishment of a defector can be
optimal in a symmetric equilibrium with higher-order punishment possibilities, we differentiate equation(B32) with respect to 𝑃𝐷𝐷
•

𝑑𝑈𝑖
∗
′
(𝑃𝐷𝐷 = 𝑃𝐷𝐷, 𝐻𝐷𝐷 = 𝐻𝐷𝐷) = −2 − 𝛼𝑖 − 𝛽𝑖 ⁄2 < 0.
𝑑𝑃𝐷𝐷

∗
′
Here, the restrictions 𝑃𝐷𝐷 = 𝑃𝐷𝐷
and 𝐻𝐷𝐷 = 𝐻𝐷𝐷
do not affect the derivative as the coefficient of 𝑃𝐷𝐷∗
does not have 𝑃𝐷𝐷 . Thus, the smaller punishment i inflicts, the higher utility i receives. The maximum
higher-order punishment value in any symmetric stage 3 equilibrium is 5/4. Then, from our constraints,
𝑃𝐷𝐷 ≥ 0 and so i never punishes a defector in Scenario DD in any symmetric equilibrium with higherorder punishment possibilities.

Optimal first-order punishment schedule

Figure B.7. Feasible region for higher-order punishment
in Scenario DD. The blue (red) region reflects efficient(inefficient) punishment.
∗
Summary: Given 𝑃𝐷𝐷 = 𝑃𝐷𝐷= 0, the conditions for the third party’s optimal higher-order punishment
schedule 𝐻𝐶𝐶 can be summarized as in Figure B.8.

40

i’s higher-order punishment in Scenario DD (𝐻𝐷𝐷 )′𝐻𝐷𝐷 = 5 − 3𝐻𝐷𝐷′
𝐻𝐷𝐷 = 𝐻𝐷𝐷

Optimal higher-order punishment𝛼schedule when 𝑖 + 𝛽𝑖 > 2

Case 3

2

The symmetric stage 3 equilibrium
happens in this range.
Case 4
5/4

Optimal higher-order punishment𝛼schedule when 𝑖 + 𝛽𝑖 < 22Case 1′
i’s belief on peers’ higher-order punishment (𝐻𝐷𝐷)

Case 20

5/3

Figure B.8. Optimal5/4
punishment schedule in Higher-Order Scenario DD
Remark 4. The area for total higher-order punishment in the lower triangle of Scenario DD is given by:∆𝐷𝐷 =∗(13𝑃𝐷𝐷 − 6𝑃𝐷𝐷+ 20)2384.

∗
The expression in the numerator is strictly positive for any efficient punishment (𝑃𝐷𝐷 > 𝑃𝐷𝐷) and∗
so the total area of efficient higher-order punishment is increasing as 𝑃𝐷𝐷 falls.

(d) Cooperate/defect decision
As the introduction of higher-order punishment opportunities does not influence predicted behaviors instages 1 or 2, this analysis is unchanged from the Trio treatment.

41

Appendix C: Additional Figures and Tables
Figure C.1: Raven’s Progressive Matrices Test Score Distributions

Notes: Raven’s test score means the number of correct answers in the task. The vertical lines are placed at the meanscores, 5.34 for the Newcastle sample and 5.17 for the Sonipat sample. The standard deviations of the scores are 2.53
for the Newcastle sample and 2.38 for the Sonipat sample. The average Raven’s test scores are not significantly
different between the two locations with two-sided p = 0.646 (Mann-Whitney test).

42

Table C.1: Across-Scenario Difference in First-Order Punishment – A Pooled Regression(supplementing Figure 3 of the paper).
A. Average Decisions
Independent Variable
Sonipat
Betrayal
Mutual defection
VictimSonipat * Betrayal
Sonipat * Mutual defection
Sonipat * Victim
Constant

Punishment frequencies(1)(2)-0.123(0.177)1.308***(0.140)0.656***(0.134)0.129(0.148)-0.481**(0.191)-0.268(0.183)-0.046(0.202)-0.863***(0.125)-0.124(0.193)
1.394***(0.159)0.727***(0.151)
0.093(0.173)-0.483**(0.210)-0.284(0.202)-0.027(0.228)-1.142(0.713)

Punishment points given(3)(4)-0.447(0.975)6.792***(0.768)3.248***(0.679)0.664(0.790)-2.131**(0.975)-0.686(1.019)-0.297(1.133)-4.814***(0.809)-0.296(1.052)
7.348***(0.879)3.609***(0.775)0.587(0.936)-2.145**(1.048)-0.628(1.105)-0.224(1.277)-7.050**(3.411)

Observations
1,104
968
1,104
968
Control
No
Yes
No
Yes
# left-censored obs.
751
660
# right-censored obs.
26
26
Loglikelihood-625.6-532.3-1416-1222
Pseudo R2
0.0958*0.121
0.0457**0.0571*
H0: Betrayal = Mutual defection(Do third parties punish defectors differently between “betrayal” and “mutual defection in the UK?)
F/Chi-squared-stat.
36.56833.25648.52145.382p-value (two-sided)
0.000***
0.000***
0.000***
0.000***
H0: Sonipat = Sonipat + Betrayal + Sonipat*Betrayal (Do third parties punish more strongly in “betrayal” than in
the reference “mutual cooperation” in India?)
F/Chi-squared-stat.
40.47043.55734.56937.966p-value (two-sided)
0.000***
0.000***
0.000***
0.000***
H0: Betrayal + Sonipat*Betrayal = Mutual defection + Sonipat*Mutual defection(Do third parties punish defectors differently between “betrayal” and “mutual defection in India?)
F/Chi-squared-stat.
22.09921.12320.297p-value (two-sided)
0.000***
0.000***
0.000***

19.4990.000***

Notes: Probit regressions with robust standard errors clustered by subject ID for columns (1) and (2); and Tobit
regressions with robust standard errors clustered by subject ID for columns (3) and (4). The dependent variable is anindicator for a third-party player i’s decision to first-order punish for columns (1) and (2), and a third-party player i’spunishment points given to a PD player for columns (3) and (4). The control variables in the even-numbered columns
include a dummy for female, age, number of siblings, income rank and the Raven’s test score. *** p<0.01, ** p<0.05,* p<0.1.

43

B. Beliefs
Independent Variable
Sonipat
Betrayal
Mutual defection
VictimSonipat * Betrayal
Sonipat * Mutual defection
Sonipat * Victim
Constant

Beliefs about punishment frequencies(1)(2)-0.021(0.162)
1.467***(0.172)0.896***(0.152)-0.042(0.126)-0.490**(0.219)-0.406**(0.186)0.021(0.164)-0.084(0.115)-0.070(0.172)
1.466***(0.190)0.913***(0.170)-0.072(0.139)-0.523**(0.235)-0.398*(0.203)0.027(0.175)-0.074(0.328)Beliefs about punishment points given
(3)
(4)
0.260
(0.599)4.524***(0.415)2.293***(0.436)-0.109(0.440)-1.615***(0.569)-1.136**(0.542)-0.152(0.565)-0.082(0.419)0.123(0.619)4.420***(0.433)
2.183***(0.453)-0.194(0.466)-1.738***(0.575)-0.992*(0.558)-0.205(0.581)0.487(1.039)Observations
960
868
960
868
Control
No
Yes
No
Yes
# left-censored obs.
361
318
# right-censored obs.
26
24
Loglikelihood-563-500.1-1874-1703
Pseudo R2
0.114
0.123
0.04060.0427
H0: Betrayal = Mutual defection(Do third parties punish defectors differently between “betrayal” and “mutual defection in the UK?)
F/Chi-squared-stat.
12.9259.631
56.57153.494p-value (two-sided)
0.000***
0.002***
0.000***
0.000***
H0: Sonipat = Sonipat + Betrayal + Sonipat*Betrayal (Do third parties punish more strongly in “betrayal” than in
the reference “mutual cooperation” in India?)
F/Chi-squared-stat.
52.03546.57754.72850.758p-value (two-sided)
0.000***
0.000***
0.000***
0.000***
H0: Betrayal + Sonipat*Betrayal = Mutual defection + Sonipat*Mutual defection(Do third parties punish defectors differently between “betrayal” and “mutual defection in India?)
F/Chi-squared-stat.
17.63113.32730.173p-value (two-sided)
0.000***
0.000***
0.000***

26.5510.000***

Notes: Probit regressions with robust standard errors clustered by subject ID for columns (1) and (2); and Tobit
regressions with robust standard errors clustered by subject ID for columns (3) and (4). The dependent variable is anindicator for a PD player’s beliefs about a third-party player i’s decision to first-order punish for columns (1) and (2),and about a third-party player i’s punishment points given to a PD player for columns (3) and (4). The control variablesin the even-numbered columns include a dummy for female, age, number of siblings, income rank and the Raven’s
test score. *** p<0.01, ** p<0.05, * p<0.1

44

Table C.2: Cross-Societal Difference in Cooperation and First-Order Punishment – A Pooled Regression (supplementing Figure 3 of thepaper).
A. Average Decisions
I. Cooperation and punishment frequencies
Data:

PD players’ decision tocooperate

Independent Variable
India (Sonipat) dummy(a)-0.441***(0.166)
0.524***(0.121)(b)-0.498***(0.182)-0.112(0.565)

240
No
7.009
0.008***

217
Yes
19.99
0.006***

Constant
Observations
ControlChi-squared-stat.
p-value (two-sided)

Third parties’ decision to first-order punish
Scenario
I. “mutual cooperation”
II. “betrayal”
III. “victim”
(a)
(b)
(a)
(b)
(a)
(b)
-0.123-0.079-0.604*** -0.640***-0.169-0.223(0.177)(0.204)(0.154)(0.179)(0.171)(0.196)-0.863***-1.4000.444***
0.528-0.734***0.447(0.125)(1.109)(0.112)(0.922)(0.120)(1.091)
276
No
0.483
0.487

242
Yes
6.478
0.485

276
No
15.30
0.000***

242
Yes
18.40
0.0103**

276
No
0.974
0.324

242
Yes
7.794
0.351

IV. “mutual defection”(a)(b)-0.392**-0.358**(0.157)(0.180)-0.207*-1.551*(0.109)(0.912)
276
No
6.230
0.0126**

242
Yes
12.80
0.0771*

Notes: Probit regressions with robust standard errors in parentheses. The control variables in the even-numbered columns include a dummy for female, age, numberof siblings, income rank and the Raven’s test score. *** p<0.01, ** p<0.05, * p<0.1

II. Punishment strength per third-party player
Dependent variable:

Independent Variable
India (Sonipat) dummy
Constant
Observations
Control
F-stat.
p-value (two-sided)A third-party player’s punishment points given to a PD player
Scenario
I. “mutual cooperation”
II. “betrayal”
III. “victim”
IV. “mutual defection”
(a)
(b)
(a)
(b)
(a)
(b)
(a)
(b)
-0.489-0.309-2.485***-2.214***-0.762-1.083-1.175-0.767(1.030)(1.145)(0.706)(0.817)(0.939)(1.107)(0.819)(0.922)-5.254***-6.1912.052***-1.141-4.307***2.699-1.679**-8.582**(1.036)(5.864)(0.469)(3.807)(1.003)(5.496)(0.691)(4.243)
276
No
0.225
0.636

242
Yes
0.742
0.637

276
No
12.38
0.000507***

242
Yes
2.247
0.0314**

276
No
0.660
0.417

242
Yes
1.213
0.296

276
No
2.059
0.152

242
Yes
1.236
0.284

Notes: Tobit regressions with robust standard errors in parentheses. The control variables in the even-numbered columns include a dummy for female, age, numberof siblings, income rank and the Raven’s test score. *** p<0.01, ** p<0.05, * p<0.1.

45

B. Beliefs
I. Cooperation and punishment frequencies
Data:

Beliefs about PD players’
decision to cooperate

Independent Variable
India (Sonipat) dummy(a)-0.224***(0.086)
0.279***(0.058)(b)-0.196**(0.095)-0.155(0.478)

276
No
6.850
0.00886***

242
Yes
13.20
0.0674*

Constant

Observations
ControlChi-squared-stat.
p-value (two-sided)

Beliefs about third parties’ decision to first-order punish
Scenario
I. “mutual cooperation”
II. “betrayal”
III. “victim”
IV. “mutual defection”
(a)
(b)
(a)
(b)
(a)
(b)
(a)
(b)
-0.021-0.091-0.511**-0.569**0.000-0.036-0.427**-0.453**(0.162)(0.174)(0.211)(0.245)(0.163)(0.174)(0.175)(0.189)-0.0840.139
1.383***
0.430-0.1260.509
0.812***
0.302(0.115)(0.452)(0.165)(0.931)(0.115)(0.472)(0.130)(0.509)240
No0.0167
0.897

217
Yes
4.713
0.695

240
No
5.858
0.0155**

217
Yes
11.29
0.126

240
No
0
1.000

217
Yes
8.911
0.259

240
No
5.946
0.0148**

217
Yes
9.698
0.206

Notes: Probit regressions with robust standard errors in parentheses (fractional Probit regression for columns (a) and (b)). The control variables in the evennumbered columns include a dummy for female, age, number of siblings, income rank and the Raven’s test score. *** p<0.01, ** p<0.05, * p<0.1

II. Punishment strength per third-party player
Dependent variable:

Independent Variable
India (Sonipat) dummy
Constant

Observations
Control
F-stat.
p-value (two-sided)

Beliefs about a third-party player’s punishment points given to a PD player
Scenario
I. “mutual cooperation”
II. “betrayal”
III. “victim”
IV. “mutual defection”
(a)
(b)
(a)
(b)
(a)
(b)
(a)
(b)
0.254
0.016
-1.306*** -1.568***
0.114-0.091-0.829*-0.769*(0.691)(0.719)(0.416)(0.443)(0.616)(0.636)(0.454)(0.460)-0.6190.534
4.459***
4.349***-0.4772.465
2.262***
1.418(0.512)(2.031)(0.273)(1.039)(0.489)(1.804)(0.293)(1.000)
240
No
0.135
0.714

217
Yes
0.519
0.820

240
No
9.855
0.00191***

217
Yes
2.122
0.0426**240
No0.0341
0.854

217
Yes
1.357
0.225

240
No
3.337
0.0690*

217
Yes
2.521
0.0165**

Notes: Tobit regressions with robust standard errors in parentheses. The control variables in the even-numbered columns include a dummy for female, age, numberof siblings, income rank and the Raven’s test score. *** p<0.01, ** p<0.05, * p<0.1.

46

Table C.3: Across-Scenario Difference in First-Order Punishment by Treatment – with demographic
controls (supplementing Table 3 of the paper).
(A) Frequency of first-order punishment given to PD players
Dependent variable
Independent Variable
India (Sonipat) dummy

Baseline#1
Decisions
Beliefs
(1)
(2)

Trio
Decisions
Beliefs(3)(4)

Higher-Order
Decisions
Beliefs(5)(6)-1.541***(0.485)
1.967***(0.392)0.847***(0.289)0.179(0.465)-0.220(0.527)0.333(0.321)1.406***(0.284)0.916***(0.289)0.388(0.294)-0.391(0.371)-0.330(0.369)-0.364(0.400)-1.092(1.416)-0.246(0.330)1.519***(0.360)0.779**(0.319)0.002(0.245)-0.621(0.432)-0.179(0.378)0.063(0.299)1.341(1.604)-0.101(0.309)1.524***(0.254)0.639***(0.246)-0.158(0.253)-0.723**(0.319)-0.309(0.307)0.293(0.329)-0.073(1.042)-0.008(0.333)
1.661***(0.405)1.299***(0.316)0.007(0.298)-0.582(0.468)-0.533(0.376)-0.074(0.352)0.124(0.571)

432
Yes-218.6
0.144

292
Yes
-168.6
0.119

380
Yes
-212.7
0.150

264
Yes
-140.40.177

Constant-1.257(1.147)-0.088(0.298)1.362***(0.279)0.858***(0.270)-0.173(0.211)-0.425(0.363)-0.629**(0.317)0.018(0.303)-1.253(1.512)

Observations
Control
Loglikelihood
Pseudo R2

120
Yes-60.17
0.255

312
Yes
-177.40.147

Betrayal
Mutual defection
VictimSonipat * Betrayal
Sonipat * Mutual defection
Sonipat * Victim

H0: Betrayal = Mutual defection(Do third parties punish defectors differently between “betrayal” and “mutual defection in the UK?)
Chi-squared-stat.
10.061
3.617
8.426
5.978
17.4820.831
p-value (two-sided)
0.000***
0.057*
0.004***
0.014**
0.000***
0.362
H0: Sonipat = Sonipat + Betrayal + Sonipat*Betrayal(Do third parties punish more strongly in “betrayal” than in the reference “mutual cooperation” in India?)Chi-squared-stat.
15.15215.06818.99013.76518.48219.149p-value (two-sided)
0.000*** 0.000***
0.000***
0.000***
0.000***
0.000***
H0: Betrayal + Sonipat*Betrayal = Mutual defection + Sonipat*Mutual defection(Do third parties punish defectors differently between “betrayal” and “mutual defection in India?)Chi-squared-stat.
6.049
10.352
8.100
1.904
8.190
p-value (two-sided)
0.014**
0.001***
0.004***
0.168
0.004***

3.450
0.063*

Notes: Probit regressions with robust standard errors in parentheses clustered by subject ID. The dependent
variable is an indicator for a third-party player i’s decision (or a PD player’s beliefs about a third-party player i’s
decision) to first-order punish. The control variables include a dummy for female, age, number of siblings, income
rank and the Raven’s test score. #1 The interaction Sonipat * Victim is omitted because Sonipat * Mutual
cooperation is empty (Figure 4). *** p<0.01, ** p<0.05, * p<0.1

47

(B) Punishment strength per third-party player
Baseline
Decisions
Beliefs(1)(2)-18.368***-0.244(2.602)(0.921)
Betrayal
6.994***
4.633***(1.890)(0.647)
Mutual defection
3.271***
2.004***(1.007)(0.618)Victim1.056-0.063(1.789)(0.694)
Sonipat * Betrayal
13.112***-1.766*(2.268)(0.964)
Sonipat * Mutual defection 13.327***-1.116(2.822)(0.825)
Sonipat * Victim-1.056-0.561(1.789)(0.899)Constant-5.394-4.483(3.954)(3.970)Trio
Decisions
Beliefs
(3)
(4)
2.333
-0.471(2.116)(1.231)
9.264***
3.898***(2.045)(0.852)5.467***
1.823*(1.841)(1.026)2.541-0.508(1.891)(0.823)-2.316-1.563(2.323)(1.035)-0.792-0.689(2.396)(1.122)-1.9480.536(2.621)(0.971)-8.8344.293(8.988)(5.211)Higher-Order
Decisions
Beliefs(5)(6)-0.3360.465(1.414)(1.067)6.085***
4.503***(0.934)(0.711)2.524**
2.666***(1.044)(0.681)-0.664-0.084(1.208)(0.938)-2.466**-1.638*(1.127)(0.989)-0.769-1.217(1.343)(0.945)0.866-0.575(1.514)(1.153)-1.8130.019(4.377)(1.606)

Observations
Control# left-censored obs.
# right-censored obs.
Loglikelihood
Pseudo R2

432
Yes
312
16
-498.20.0578

380
Yes
240
7
-518.30.0710Dependent variable
Independent Variable
India (Sonipat) dummy

156
Yes
108
3
-164
0.186

312
Yes
120
8
-582.80.0667

292
Yes
106
10
-581.40.0390

264
Yes
92
6
-516.20.0584

H0: Betrayal = Mutual defection(Do third parties punish defectors differently between “betrayal” and “mutual defection” in the UK?)
F-stat.
7.156
26.16514.14713.25427.97915.365p-value (two-sided)
0.008***
0.000***
0.000***
0.000***
0.000***
0.000***
H0: Sonipat = Sonipat + Betrayal + Sonipat*Betrayal(Do third parties punish more strongly in “betrayal” than in the reference “mutual cooperation” in India?)
F-stat.
43.79416.29114.89815.40620.17918.740p-value (two-sided)
0.000***
0.000***
0.000***
0.000***
0.000***
0.000***
H0: Betrayal + Sonipat*Betrayal = Mutual defection + Sonipat*Mutual defection(Do third parties punish defectors differently between “betrayal” and “mutual defection in India?)
F-stat.
6.296
7.352
7.290
7.264
7.250
17.465p-value (two-sided)
0.013**
0.007***
0.007***
0.007***
0.007***
0.000***
Notes: Tobit regressions with robust standard errors in parentheses clustered by subject ID. The dependent variable
is a third-party player i’s punishment points (or a PD player’s beliefs about a third-party player i’s punishment
points) given to a PD player. The control variables include a dummy for female, age, number of siblings, income
rank and the Raven’s test score. *** p<0.01, ** p<0.05, * p<0.1

48

Table C.4: Across-Treatment, and Cross-societal Difference in Beliefs about First-Order Punishment (supplementing Table 4 of the paper)(A) Frequency of cooperation and first-order punishment given to PD players
Data:

Independent Variable
India (Sonipat) dummy
TrioHigher-Order
Sonipat * Trio
Sonipat * Higher-Order
Constant

Beliefs about PD
players’ decision tocooperate(1)(2)-0.244-0.201(0.218)(0.234)0.080
0.152(0.153)(0.168)0.036-0.001(0.152)(0.166)-0.039-0.090(0.255)(0.274)0.082
0.107(0.255)(0.275)0.231*-0.256(0.121)(0.487)

Beliefs about third parties’ decision to first-order punish
Scenario
I. “mutual cooperation”
II. “betrayal”
III. “victim”
IV. “mutual defection”
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
-0.132-0.077-0.334-0.490-0.035-0.039-0.715**-0.661**(0.276)(0.289)(0.342)(0.366)(0.277)(0.290)(0.291)(0.307)-0.070
0.072
0.360
0.209
0.164
0.221
-0.016-0.011(0.280)(0.292)(0.421)(0.448)(0.280)(0.294)(0.312)(0.329)-0.199-0.0810.179
0.113-0.035
0.040
0.118
0.284
(0.276)(0.305)(0.387)(0.473)(0.277)(0.306)(0.315)(0.360)0.082-0.146-0.468-0.293-0.025-0.1540.381
0.315(0.397)(0.417)(0.530)(0.559)(0.398)(0.419)(0.423)(0.446)0.269
0.122-0.144
0.019
0.109
0.134
0.490
0.251
(0.397)(0.426)(0.510)(0.586)(0.398)(0.434)(0.433)(0.479)-0.0000.162
1.233***
0.418-0.1640.475
0.781***
0.324(0.185)(0.473)(0.247)(0.917)(0.186)(0.496)(0.207)(0.535)Observations
276
242
240
217
240
217
240
217
240
Control
No
Yes
No
Yes
No
Yes
No
Yes
No
Loglikelihood-187.8-163.5-165.4-147.6-92.56-80.95-164.8-144.7-136.8
Pseudo R2
0.006410.01280.001850.0176
0.03680.07150.002360.03250.0373
H0: Trio + Sonipat * Trio = Sonipat (Do the behaviors differ between the Trio and Baseline treatments in India?)Chi-squared-stat.
0.52
0.39
0.09
0.00
0.15
0.46
0.13
0.04
4.67
p-value (two-sided)
0.47
0.53
0.77
0.99
0.69
0.50
0.72
0.84
0.03**
H0: Higher-Order + Sonipat * Higher-Order = Sonipat (Do the behaviors differ between the Higher-Order and Baseline treatments in India?)Chi-squared-stat.
0.84
0.53
0.17
0.05
0.40
1.06
0.05
0.16
6.85
p-value (two-sided)
0.36
0.47
0.68
0.82
0.53
0.30
0.83
0.69
0.01**
H0: Sonipat + Sonipat * Trio = Trio (Do the behaviors differ between the UK and India in the Trio treatment?)
Chi-squared-stat.
2.27
2.89
0.00
0.32
2.35
1.53
0.20
0.61
0.34
p-value (two-sided)
0.13
0.09*
0.97
0.57
0.13
0.22
0.65
0.43
0.56
H0: Sonipat + Sonipat * Higher-Order= Higher-Order (Do the behaviors differ between the UK and India in the Higher-Order treatment?)
Chi-squared-stat.
0.68
0.12
0.47
0.05
0.92
0.46
0.05
0.01
0.38
p-value (two-sided)
0.41
0.73
0.50
0.82
0.34
0.50
0.83
0.92
0.54

217
Yes
-119
0.0478
3.28
0.07*
4.95
0.03**
0.34
0.56
1.11
0.29

Notes: Probit regressions with robust standard errors in parentheses (fractional Probit regression for columns (1) and (2)). The control variables in the evennumbered columns include a dummy for female, age, number of siblings, income rank and the Raven’s test score. *** p<0.01, ** p<0.05, * p<0.149

(B) Punishment strength per third-party player
Dependent variable:

Independent Variable
India (Sonipat) dummy
TrioHigher-Order
Sonipat * Trio
Sonipat * Higher-Order
Constant
Observations
Control# left-censored obs.
# right-censored obs.
Loglikelihood
Pseudo R2

Beliefs about a third-party player’s punishment points given to a PD player
Scenario
I. “mutual cooperation”
II. “betrayal”
III. “victim”
IV. “mutual defection”
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
-0.598-0.313-1.605**-2.056***-0.531-0.739-1.474*-1.352*(1.068)(1.083)(0.734)(0.766)(1.026)(1.032)(0.794)(0.795)0.342
0.802-0.040-0.234
0.400
0.426
0.605
0.353
(1.171)(1.179)(0.683)(0.732)(1.027)(1.026)(0.794)(0.789)-0.536-0.082-0.192-0.326-0.462-0.0540.224
0.377(1.120)(1.177)(0.646)(0.695)(1.031)(1.124)(0.625)(0.636)0.615-0.246
0.062
0.245
0.772
0.586
0.290
0.460
(1.665)(1.668)(1.048)(1.110)(1.486)(1.461)(1.163)(1.143)
1.884
1.174
0.842
1.307
1.081
1.238
1.469
1.092
(1.632)(1.662)(1.001)(1.043)(1.484)(1.566)(1.078)(1.086)-0.5390.457
4.532***
4.758***-0.4432.410
2.015***
1.492(0.739)(2.095)(0.468)(1.036)(0.750)(1.886)(0.452)(1.113)
240
No
129
6
-404.50.00242

217
Yes
113
6
-372.10.00768

240
No
33
10
-557.20.00963

217
Yes
30
9
-500.10.0163

240
No
132
2
-391.60.00238

217
Yes
118
2
-351.50.0170

240
No
67
8
-504
0.00831

217
Yes
57
7
-458.10.0115

H0: Trio + Sonipat * Trio = Sonipat (Do the behaviors differ between the Trio and Baseline treatments in India?)
F-stat.
0.65
0.20
1.46
2.10
0.88
0.92
2.53
2.08
p-value (two-sided)
0.42
0.66
0.23
0.15
0.35
0.34
0.11
0.15
H0: Higher-Order + Sonipat * Higher-Order = Sonipat (Do the behaviors differ between the Higher-Order and Baseline treatments in India?)
F-stat.
1.02
0.51
2.87
4.77
0.40
1.09
4.45
3.45
p-value (two-sided)
0.31
0.48
0.09*
0.03**
0.53
0.30
0.04**
0.06*
H0: Sonipat + Sonipat * Trio = Trio (Do the behaviors differ between the UK and India in the Trio treatment?)
F-stat.
0.02
0.39
1.49
1.37
0.01
0.10
1.44
0.72
p-value (two-sided)
0.88
0.53
0.22
0.24
0.93
0.75
0.23
0.40
H0: Sonipat + Sonipat * Higher-Order= Higher-Order (Do the behaviors differ between the UK and India in the Higher-Order treatment?)
F-stat.
0.80
0.19
0.25
0.11
0.31
0.07
0.04
0.30
p-value (two-sided)
0.37
0.66
0.61
0.74
0.58
0.79
0.84
0.59
Notes: Tobit regressions with robust standard errors in parentheses. The control variables in the even-numbered columns include a dummy for female, age,
number of siblings, income rank and the Raven’s test score. *** p<0.01, ** p<0.05, * p<0.1.

50

Table C.5: Cross-societal Difference in Beliefs about Efficient and Inefficient Higher-Order Punishment (using beliefs about first-orderpunishment in each scenario as the reference point for efficiency) – supplementing Table 7 of the paper.
(A) Frequency of higher-order punishment given to other third parties
Data:

Independent Variable
India (Sonipat) dummy
Efficient
Sonipat * Efficient
Constant

Beliefs about third parties’ decision to higher-order punish
Scenario
I. “mutual cooperation”
II. “betrayal”
III. “victim”
IV. “mutual defection”
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
0.264
0.089
-0.248-0.064-0.089-0.121-0.585**-0.394(0.269)(0.285)(0.234)(0.263)(0.261)(0.277)(0.262)(0.277)0.954***
0.895***
0.568***
0.720***
0.783***
0.794**-0.112-0.165(0.230)(0.257)(0.208)(0.234)(0.292)(0.355)(0.186)(0.176)-0.715**-0.480-0.140-0.234-0.279-0.1520.743**
0.746**(0.330)(0.355)(0.295)(0.317)(0.352)(0.407)(0.325)(0.327)0.185
0.608
0.576***
0.342
0.381**
0.357
0.851***
0.954*(0.190)(0.492)(0.169)(0.560)(0.189)(0.412)(0.191)(0.557)

Observations
1,180
1,022
1,196
1,018
1,148
986
1,120
Control
No
Yes
No
Yes
No
Yes
No
Loglikelihood-616.7-519.6-667.8-566.3-575.6-470.9-639
Pseudo R2
0.05130.07490.03730.04490.0494
0.09390.0384
H0: Sonipat + Constant = 0 (Is the frequency of inefficient higher-order punishment behavior significant in India?)Chi-squared-stat.
5.62
1.92
4.09
0.24
2.62
0.31
2.18
p-value (two-sided)
0.02**
0.17
0.04**
0.63
0.11
0.58
0.14
H0: Sonipat = Efficient + Sonipat * Efficient (Is efficient higher-order punishment more frequent than inefficient punishment in India?)Chi-squared-stat.
0.00
0.55
3.57
2.13
2.38
3.37
7.67
p-value (two-sided)
0.95
0.46
0.06*
0.14
0.12
0.07*
0.01**

934
Yes-531.30.0510
1.12
0.29
4.49
0.03**

Notes: Probit regressions with robust standard errors in parentheses clustered by subject ID. The control variables in the even-numbered columns include a dummy
for female, age, number of siblings, income rank and the Raven’s test score. *** p<0.01, ** p<0.05, * p<0.1

51

(B) Punishment strength per third-party player
Data:

Independent Variable
India (Sonipat) dummy
Efficient
Sonipat * Efficient
Constant

Beliefs about a third-party player’s punishment points given to another third-party player
Scenario
I. “mutual cooperation”
II. “betrayal”
III. “victim”
IV. “mutual defection”
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
1.462*
1.066-0.368
0.370
0.695
0.542
-1.189-0.506(0.883)(0.862)(0.734)(0.828)(0.931)(0.957)(0.732)(0.763)2.906***
2.798***
0.991*
1.802***
2.997***
3.180***-0.335-0.378(0.630)(0.655)(0.572)(0.646)(0.737)(0.855)(0.483)(0.528)-2.131**-1.4850.420-0.361-2.159**-1.989*2.406***
2.324**(0.974)(0.962)(0.831)(0.896)(1.039)(1.160)(0.910)(1.001)0.525
1.584
1.946***
1.073
1.195**
1.029
2.557***
2.442(0.614)(1.364)(0.480)(1.562)(0.596)(1.378)(0.434)(1.614)

Observations
1,180
1,022
1,196
1,018
1,148
986
Control
No
Yes
No
Yes
No
Yes
# left-censored obs.
283
244
319
274
253
217
# right-censored obs.
44
39
36
33
61
55
Loglikelihood
-2635
-2271
-2628
-2210
-2616
-2235
Pseudo R2
0.01290.01650.005770.01740.01510.0209H0: Sonipat + Constant = 0 (Are inefficient punishment behaviors significant in India?)
F-stat.
9.62
4.46
8.01
0.69
6.98
1.21
p-value (two-sided)
0.00**
0.03**
0.00**
0.41
0.01**
0.27
H0: Sonipat = Efficient + Sonipat * Efficient (Is efficient punishment stronger than inefficient punishment in India?)
F-stat.
0.23
0.03
2.43
0.77
0.01
0.17
p-value (two-sided)
0.63
0.86
0.12
0.38
0.92
0.68

1,120
No
314
41
-2443
0.00759

934
Yes
268
40
-1991
0.02695.19
0.02**

1.43
0.23

6.18
0.01***

3.04
0.08*

Notes: Tobit regressions with robust standard errors in parentheses clustered by subject ID. The control variables in the even-numbered columns include a dummy
for female, age, number of siblings, income rank and the Raven’s test score. *** p<0.01, ** p<0.05, * p<0.152