# Beliefs and Group Dishonesty: The Role of Strategic Interaction and Responsibility

Fabio Galeotti, Rainer Michael Rilke, Eugenio Verrina

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Fabio Galeotti, Rainer Michael Rilke, Eugenio Verrina. Beliefs and Group Dishonesty: The Role of Strategic Interaction and Responsibility. 2025. hal-05170048

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Distributed under a Creative Commons Attribution 4.0 International License
Beliefs and Group Dishonesty: The Role of Strategic
Interaction and Responsibility

Fabio Galeotti<sup>a</sup> Rainer Michael Rilke<sup>b</sup> Eugenio Verrina<sup>c</sup>

June 10, 2024

**Abstract**

Dishonest behavior often occurs in groups where actions are interconnected and be-
liefs about others' behavior may play an important role. We study the relationship
between beliefs and dishonesty, focusing on the impact of the nature of the strategic
interaction (complements or substitutes) and the reduced feeling of responsibility
that arises from acting together with other group members. In settings of strategic
complements, we observe that individuals tend to lie more, the more they believe
their counterpart to be dishonest. Conversely, in settings of strategic substitutes,
individuals tend to lie less as their belief about their counterpart's dishonesty in-
creases. Acting together instead of acting alone — while holding the nature of
the strategic interaction and beliefs constant — does not influence the relationship
between beliefs and behavior in strategic complements. However, individuals with
higher lying costs lie less in strategic substitutes when they are the only active mem-
ber of the group. Our findings suggest that both beliefs and the type of strategic
interaction strongly shape group dishonesty, while responsibility plays a minor role.

**Keywords:** Dishonesty; Group behavior; Lying; Beliefs; Substitutes and complements; Responsibility

**JEL Classification:** C90; C91; C92; D01; D83; D91

<footnote>We thank Valeria Burdea, Felix Kölle, Wladislaw Mill, Anna Ressi, Marie Claire Villeval, Gari Walkowitz, participants at the 2024 Asia-Pacific Meeting of the Economic Science Association in Singapore, the 2024 Behavioral and Experimental Economics GATE-Lab-NTU Workshop in Singapore, the 2024 Winter Summit on Credence Goods in Innsbruck, the 12th International Conference of the French Association of Experimental Economics (ASFEE) in Lyon, the 15th Nordic Conference on Behavioral and Experimental Economics in Lund, the 2023 World Meeting of the Economic Science Association in Lyon, the 1st Matterhorn Symposium, seminar participants at CREED (University of Amsterdam), GATE (University of Lyon), the University of Verona, the University of Birmingham, WHU - Otto Beisheim School of Management, and the University of Warwick for helpful comments and suggestions. Research assistance from Blanche Monjour, Marie-Sophie Roul, and Quentin Thevenet is gratefully acknowledged.</footnote>

<footnote><sup>a</sup>CNRS, Université Lumière Lyon 2, Université Jean Monnet Saint-Etienne, emlyon business school, GATE, 69007, Lyon, France. fabio.galeotti@cnrs.fr.</footnote>

<footnote><sup>b</sup>WHU - Otto Beisheim School of Management, Economics Group, Burgplatz 2, 56179 Vallendar, Germany. rainer.rilke@whu.edu.</footnote>

<footnote><sup>c</sup>Sciences Po Paris, Department of Economics, CNRS, 28 rue des Saints Pères, 75007 Paris, France. eugenio.verrina@sciencespo.fr.</footnote>
# 1 Introduction

Dishonesty often arises in groups where individual actions are interconnected and the gains from dishonesty are shared. In such settings, beliefs about other group members’ behavior can play a crucial role in determining an individual’s propensity to lie for the group’s benefit. Previous research has demonstrated the importance of beliefs in various types of group interactions. For example, beliefs can explain the dynamics of free riding in public goods (e.g., Fischbacher and Gächter, 2010), why people form partnerships (e.g., Charness and Dufwenberg, 2006), and how trust develops within a community or group (e.g., Sapienza et al., 2013). Less explored is their role in group dishonesty, despite dishonesty being a significant aspect of numerous group interactions.<fnref n="1" />

In this paper, we fill this gap by experimentally studying the relationship between beliefs and dishonesty in group settings. We manipulate two factors that we expect to affect this relationship: the nature of the strategic interaction and whether everyone or only one group member actively decides in the group. This allows us to study how the relationship between beliefs and group dishonesty is influenced by strategic considerations and psychological factors linked to the feeling of responsibility for one's actions.

The nature of the strategic interaction defines how the actions of group members are combined to determine their payoffs. In some settings, there needs to be a high degree of coordination among group members for them to gain from dishonest behavior — actions are complements. For example, the recent Wirecard and Volkswagen scandals both involved concerted actions by multiple actors (Tabuchi et al., 2017; Schuetze and O'Donnell, 2020). Similarly, members of a hiring committee may decide to dishonestly favor one candidate over another, or members of a jury may accept a bribe to rule in favor of one party in a legal case. In such settings, if one group member does not act

<footnote n="1">¹Following Leib et al. (2021), we define group dishonesty as lies told by individuals in a group setting where multiple members can misrepresent the actual state of affairs, payoffs are interconnected, and multiple members benefit from these collective dishonest acts.</footnote>
dishonestly, the gains for the whole group may not realize. That is, the least dishonest action has a strong bearing on the group members' payoffs.

In other settings, there may be no need for coordination, and the dishonest act of a single group member may benefit the whole group — actions are substitutes. Consider, for example, the case of a trader working for a bank who may reap substantial profits through their fraudulent activities, benefiting not only themselves but also the entire firm in terms of increased revenue (as seen in the case of Jérôme Kerviel in the Société Générale scandal — see Schwartz 2008). Another example is the case of a scientific team in which one author may decide to manipulate the data to increase the probability of publication. Similarly, a player on a sport team may decide to use doping to increase the team's chances of winning. In such settings, the most dishonest action has a strong bearing on the final payoffs.

More in general, complements and substitutes are key features of economic behavior and are present — potentially in different degrees — whenever individuals interact in groups (see, e.g., Hirshleifer, 1983; Bulow et al., 1985; Potters and Suetens, 2009). However, they have not yet been systematically studied in the realm of group dishonesty. A first set of questions our study aims to answer concerns how dishonesty and its relationship with beliefs vary in these two strategic settings (complements and substitutes). Is group dishonesty equally prevalent in both settings? What is the sign and strength of the relationship between dishonesty and beliefs in these two settings?

A second set of questions concerns the role that the feeling of responsibility plays in group dishonesty. The feeling of responsibility for one's actions has been shown to play a crucial role in decisions with a moral connotation (Falk and Szech, 2013; Bartling et al., 2015; Rothenhäusler et al., 2018; Falk et al., 2020; Engl, 2022).<fnref n="2" /> In group dishonesty,

<footnote n="2">²Our work is linked to research on pivotality and moral behavior (e.g., Falk et al., 2020). A key difference from our study is that, in that literature, an individual can influence a(n) (im)moral outcome determined at the group level, but their decision only affects their own gains. In contrast, in our study, the (dis)honest decision is made at the individual level, and an individual can influence the payoff received</footnote>
when everyone can decide whether to behave dishonestly, people may feel that they are
accomplices (Barr and Michailidou, 2017) or “partners in crime” (Behnk et al., 2022), and
this may diffuse the responsibility for one’s own actions: a decision to act dishonestly is
no longer attributed to oneself but to the entire group. Indeed, dishonest decisions made
by groups are perceived as less normatively inappropriate than those made by individuals
(Behnk et al., 2022). This may explain why previous experimental research on dishonesty
consistently finds that individuals tend to lie more in group settings compared to when
acting alone (see, e.g., Conrads et al., 2013; Weisel and Shalvi, 2015; Kocher et al.,
2018). However, it is unclear to what extent this increase in dishonest behavior can be
attributed to the fact that individuals act together or to differences in incentives and
beliefs between group and individual settings. In addition, it is unclear how the effect of
acting together, if present, interacts with individuals’ beliefs and with the nature of the
strategic interaction. A second novel contribution of our study is to shed light on these
questions in a setting where incentives and beliefs are held constant.

To answer these questions, we design a laboratory experiment. Observational data
on dishonesty are difficult to gather or access due to their secretive, illegal, and immoral
nature, and the few available data are highly selected. Laboratory experiments offer an
ideal setting for collecting data under controlled conditions, allowing for a systematic
exploration of the mechanisms behind group dishonesty.<fnref n="3" />

Our experiment follows a 2×2 between-subject design in which we vary the type of
interaction (*Complements* and *Substitutes* condition) and whether everyone or only one
group member actively decides in the group (*Active* and *Passive* condition). Across all
treatments, we manipulate beliefs in a within-subject fashion. Subjects go through two
stages in the experiment, and we use the second stage for our main analysis. In the first

<footnote>by all group members.</footnote>

<footnote n="3">³Data on dishonest behavior collected in the lab are also highly correlated with a variety of unethical behaviors in the field (see, e.g., Potters and Stoop, 2016; Dai et al., 2018; Cohn and Maréchal, 2018; Rustagi and Kroell, 2022), which increases confidence in their external validity.</footnote>
stage of the experiment, subjects are randomly paired and play a “coin-flip task”. In this task, each subject flips a coin six times and reports the number of heads they obtain. The reports are combined to determine their payoff and higher reports correspond to higher payoffs. In the *Complements* condition, the minimum of the two reports counts for the payoffs. In the *Substitutes* condition, the maximum of the two reports counts for the payoffs.

In the second stage of the experiment, subjects are re-matched randomly and play the coin-flip task again, with one main difference: to investigate the role of beliefs, we manipulate the beliefs of one subject (the treated subject) using the other subject’s behavior in the first stage (the untreated subject).<fnref n="4" /> The treated subject goes through different “situations” that correspond to possible reports of the untreated subject in the first stage. They play the coin-flip task for each situation, and are informed that only the situation corresponding to the untreated subjects’ actual first-stage report determines the final payoff. This allows us to observe subjects’ behavior for all possible beliefs in an incentive-compatible way and without using deception (see Bardsley, 2000; Hartig et al., 2015; Galeotti and Zizzo, 2018).<fnref n="5" />

To investigate the role of all group members vs. only one group member actively making a decision, we introduce a *Passive* condition alongside the *Active* condition described above. The key difference is that, in *Passive*, during the second stage the untreated subject does not perform the coin-flip task. Instead, they are assigned the report of a subject from *Active*, who reported the same number of heads as them in the first stage. This ensures that the monetary incentives and beliefs of the treated subjects are the same in the two conditions, thus isolating the effect of acting together in a group.

<footnote n="4">⁴The advantage of manipulating beliefs instead of only eliciting them is that we can study how individuals behave in all possible belief states. In addition, we avoid the problem of subjects reporting distorted beliefs because they want to preserve their image or justify their behavior (Charness et al., 2021).</footnote>

<footnote n="5">⁵This approach is akin to the strategy method (Selten, 1965; Brandts and Charness, 2011) but for simultaneous instead of sequential decisions.</footnote>
We find that subjects in our experiment do not always report the outcome of the coin-flip task honestly in the first stage. In particular, we observe that a relatively large number of subjects lies to the full extent, and we classify them as “brazen subjects” (Weisel and Shalvi, 2015). The analysis of the first stage also reveals that subjects lie more in *Substitutes* than *Complements*. Concerning the relationship between beliefs and dishonesty in the second stage, we find that it is positive in *Complements* and negative in *Substitutes*. While the direction of the relationship between lying and beliefs is opposite in the two strategic conditions, its strength is equivalent. To evaluate the role of acting together vs. acting alone, we compare the *Active* with the *Passive* conditions in the two types of strategic interaction. In *Complements*, the relationship between beliefs and lying remains virtually unchanged. In *Substitutes*, we find a small but insignificant drop in dishonesty in *Passive* compared to *Active* for all levels of belief.

We also perform a heterogeneity analysis based on the behavior in the first stage of the experiment. This analysis allows us to investigate our main research questions by splitting our sample into subjects with lower lying costs (brazen subjects) and subjects with higher lying costs (non-brazen subjects). We expect changes in beliefs to exert a greater influence on brazen subjects, while the condition of acting together should have a stronger impact on non-brazen subjects. Indeed, We find that the gradient of the relationship between beliefs and lying is higher for brazen subjects in both types of strategic interactions. Interacting with a passive partner does not alter this relationship for brazen subjects. However, for non-brazen subjects, we observe a consistent decrease in dishonesty in *Substitutes*, with subjects lying less in *Passive* compared to *Active* across all beliefs.

A classification of subjects into different types based on their reaction to different beliefs sheds further light on how the type of strategic interaction and the fact of acting together in a group influence dishonest behavior. Taken together, our results show
that group dishonesty is strongly shaped by beliefs through the nature of the strategic interaction, while the feeling of acting together plays a more limited role.

We structure the remainder of the paper as follows. Section 2 briefly reviews the main related literature. Section 3 describes the design and procedures. Section 4 presents our main hypotheses. We report the results in Section 5. Section 6 discusses the potential mechanisms behind our results as well as the implications and limitations of our study.

## 2 Related literature

Our study contributes mainly to two strands of literature. First, we contribute to the literature on group decision-making and unethical behavior, which shows that individuals exhibit more unethical behavior when interacting in groups than when taking decisions individually (e.g., Conrads et al. 2013; Weisel and Shalvi 2015; Kocher et al. 2018; Feess et al. 2023; Jiang and Villeval 2024; for a recent meta-study of this literature, see Leib et al. 2021).<fnref n="6" /> Our contribution to this literature is twofold. First, no comprehensive study in this literature has systematically examined the role of beliefs in strategic interactions involving group dishonesty, despite previous research suggesting that individual beliefs can have a significant impact on strategic interactions in cooperative (e.g., Fischbacher and Gächter, 2010) as well as collusive (e.g., Noussair and Seres, 2020) environments.<fnref n="7" /> We address this gap by exogenously varying the beliefs individuals have about the dishonesty of other group members in two distinct types of strategic interactions: complements and substitutes. The distinction between strategic complements and strategic substitutes

<footnote n="6">⁶More generally, groups have been shown to behave less morally than individuals in a wide range of domains (see, e.g., Charness and Sutter, 2012; Falk and Szech, 2013; Bartling et al., 2015).</footnote>

<footnote n="7">⁷Previous research has highlighted the importance of empirical beliefs (i.e., beliefs about what others do) for *individual* dishonesty. Diekmann et al. (2015) and Kroher and Wolbring (2015) demonstrate that awareness of others’ dishonesty can encourage similar behavior in non-strategic contexts. Lefebvre et al. (2015) and Colzani et al. (2023) show that negative examples increase dishonesty, whereas positive ones do not necessarily decrease it. Rauhut (2013) and Necker et al. (2020) explore how such effects vary with individuals’ initial beliefs about others’ dishonesty. These studies, however, do not explore the role of beliefs in strategic group settings.</footnote>
is of great importance in economics and has wide-ranging applications in game theory, industrial organization, international economics, public economics, and many other fields (Hirshleifer, 1983; Bulow et al., 1985; Harrison and Hirshleifer, 1989; Curtis Eaton, 2004; Potters and Suetens, 2009). For example, Potters and Suetens (2009) demonstrates that the likelihood of successful collusion depends crucially on whether the actions are strategic substitutes or complements. Our study is the first to compare how strategic substitutability and strategic complementarity affect group dishonesty and its relationship with beliefs.

Second, we add to the literature exploring the mechanisms influencing unethical behavior in groups and especially to work focusing on the role of responsibility (e.g., Bartling and Fischbacher, 2012; Engl, 2022). When people act together in a group, they may feel less responsible for their actions, leading them to behave more dishonestly. Barr and Michailidou (2017) call this effect “complicity” and show that it can emerge in a group without the need for communication. Relatedly, Behnk et al. (2022) find that the active involvement of all group members increases the normative acceptability of unethical actions. Our study contributes to this literature by isolating the role that acting together plays in group dishonesty and examining how the effect varies depending on the nature of strategic interaction and the beliefs individuals hold regarding the dishonesty of other group members.

Another strand of literature to which our work contributes concerns the role of pivotality in moral decisions (Falk and Szech, 2013; Bartling et al., 2015; Falk et al., 2020; Rothenhäusler et al., 2018; Feess et al., 2023). These studies find that immoral behavior increases if an individual's pivotality is lessened. In these papers, an individual influences an (im)moral outcome determined at the group level by deciding whether or not to accrue a gain for themselves. In our setting, an individual influences the payoff all group members receive by individually deciding whether to behave dishonestly or not. Hence,
we study a different and new kind of pivotality in moral behavior.

# 3 Experimental design

The experiment consists of two stages, followed by a final questionnaire. In each stage, subjects play a coin-flip task in pairs, with perfect-stranger matching. We use a 2×2 between-subject factorial design to vary the type of strategic interaction (complements or substitutes) and whether both subjects or only one subject in the pair actively play the coin flip task in the second stage. This leads to four treatments: COMP-ACT, COMP-PASS, SUB-ACT and SUB-PASS (see Table 1). In the second stage, we employ a within-subject manipulation to vary the beliefs of one subject in the pair about the counterpart's honesty.

<table><thead><tr><th rowspan="2" colspan="2"></th><th colspan="2">Partner<br>(only second stage)</th></tr><tr><th>Active</th><th>Passive</th></tr></thead><tbody><tr><th rowspan="2">Interaction</th><th>Complements</th><td>COMP-ACT (N=82)</td><td>COMP-PASS (N=80)</td></tr><tr><th>Substitutes</th><td>SUB-ACT (N=84)</td><td>SUB-PASS (N=82)</td></tr></tbody></table>

Note: *N* corresponds to the total number of subjects.

<caption>Table 1: Experimental Design</caption>

## 3.1 First stage

In the first stage, subjects are paired at random to perform a coin-flip task. Subjects in a pair individually perform the coin-flip task simultaneously without any feedback until the end of the experiment.<fnref n="8" /> In the coin-flip task, each subject flips a one-euro coin six

<footnote n="8">⁸Simultaneous decisions (e.g., *Conrads et al., 2013*) are better suited for studying the impact of beliefs on group dishonesty. In joint decisions (e.g., *Kocher et al., 2018*), beliefs are difficult to control</footnote>
times and reports the number of times a head appears (between zero and six). We place
the coin inside a paper cup sealed with a plastic lid. Subjects can see the result of the
coin flip by looking through a small opening in the lid. To flip the coin, we ask subjects
to shake the cup and report which side faces upward. We adopt this procedure from
Shalvi et al. (2011) to increase privacy in the report. Subjects can misreport the number
of heads they flipped without the risk of being detected, as standard in these types of
experiments (see, e.g., Fischbacher and Föllmi-Heusi, 2013). The level of lying can thus
only be inferred at the aggregate level.<fnref n="9" />

**Type of strategic interaction.** Across sessions we vary how the two reports are combined to determine subjects’ monetary payoffs. Call $R_i$ the report of one subject, and $R_j$ the report of the other subject, with $R_i$ and $R_j \in \{\le 3, 4, 5, 6\}$.<fnref n="10" /> In the *Substitutes* condition, the maximum report within the pair determines the payoff of both subjects. That is $\pi_i = \pi_j = \max(R_i, R_j)$, where $\pi_i$ ($\pi_j$) is the payoff of subject $i$ ($j$). In the *Complements* condition, the minimum report within the pair determines the payoff of both subjects. That is, $\pi_i = \pi_j = \min(R_i, R_j)$. Note that both subjects always earned the same payoff. Table 2 displays the payoffs in the two conditions.<fnref n="11" />

The first stage provides a straight comparison of group dishonesty under the two types
of strategic interaction (complements or substitutes). We also use this stage to construct

<footnote>because subjects interact in real time as a group through, for example, a chat and generally must reach
a unanimous decision. In sequential decisions (e.g., Weisel and Shalvi, 2015; Rilke et al., 2021), beliefs
are relevant only for the first mover. Additionally, assigning different roles can distort decisions (for
example, by introducing subjective feelings of entitlement or status).</footnote>

<footnote n="9">⁹We do not implement any possibility for subjects to be detected or sanctioned for their lies, as is customary in the literature (see Abeler et al., 2019). This allows us to keep the experimental protocol simple and understandable for subjects. We consider that the possibility to be detected or sanctioned should be orthogonal to our treatment manipulations and should thus not alter our results.</footnote>

<footnote n="10">¹⁰To reduce the number of situations in the second stage (see Section 3.2) and better control subjects’ beliefs in that stage, all reports equal to or smaller than three produce the same effect on the payoffs and are pooled in the data analysis.</footnote>

<footnote n="11">¹¹The fact that subjects always earn the same monetary payoff ensures that our results cannot be affected by any form of inequity-aversion motives and guarantees further control on the phenomena we want to investigate.</footnote>
<table><thead><tr><th>R<sub>i</sub></th><th>≤ 3</th><th>4</th><th>5</th><th>6</th></tr></thead><tbody><tr><th>≤ 3</th><td>3</td><td>3</td><td>3</td><td>3</td></tr><tr><th>4</th><td>3</td><td>4</td><td>4</td><td>4</td></tr><tr><th>5</th><td>3</td><td>4</td><td>5</td><td>5</td></tr><tr><th>6</th><td>3</td><td>4</td><td>5</td><td>6</td></tr></tbody></table>

<table><thead><tr><th>R<sub>i</sub></th><th>≤ 3</th><th>4</th><th>5</th><th>6</th></tr></thead><tbody><tr><th>≤ 3</th><td>3</td><td>4</td><td>5</td><td>6</td></tr><tr><th>4</th><td>4</td><td>4</td><td>5</td><td>6</td></tr><tr><th>5</th><td>5</td><td>5</td><td>5</td><td>6</td></tr><tr><th>6</th><td>6</td><td>6</td><td>6</td><td>6</td></tr></tbody></table>

Notes: $R_i$ ($R_j$) is the report of subject $i$ ($j$). The numbers in the white cells correspond to the payoff of both subjects for a given $R_i$ and $R_j$.

<caption>Table 2: Payoff table of the coin-flip task for Complements (left) and Substitutes (right) the belief manipulation for the second stage.</caption>

## 3.2 Second stage

In the second stage, subjects receive a new set of instructions and new pairs are formed (perfect-stranger matching). Subjects perform the coin-flip task under the same incentive structure they faced in the first stage but with two notable differences that we describe below.

**Beliefs.** The first difference concerns the manipulation of beliefs. We manipulate the beliefs of only one subject in the pair (the treated subject), while the other subject performs the coin-flip task as in the first stage (untreated subject).<fnref n="12" /> To exogenously vary beliefs, we use a within-subject manipulation adapted from the “Conditional Information Lottery” method proposed by Bardsley (2000). This method allows us to elicit behavior under different information conditions without deceiving subjects.

The treated subject plays the coin-flip task under four different “situations”. In each situation, they receive different information about the behavior of their counterpart (the untreated subject) in the first stage. In particular, the treated subject learns in each situation how many heads the untreated subject reported in the first stage: either ‘six’,

<footnote n="12">¹²We do this to avoid that both subjects change their behavior as a response to the belief manipulation (with the risk of losing control over the actual beliefs that subjects hold). Another reason for this design choice is that it allows us to more cleanly manipulate responsibility (see below).</footnote>
'five', 'four', or 'three or less'. These situations are presented in random order to the treated subject. We tell the treated subject that only one of these situations contains the true information, i.e., the actual number of heads reported by the untreated subject in the first stage. The situation that provides the true information ultimately determines the payoffs of the second stage. Since the treated subjects do not know in advance which information corresponds to the truth, each choice can potentially determine their payoff. This procedure is public knowledge. We also tell the treated subjects that, based on previous experiments, 90% of subjects report in the second stage either the same number they reported in the first stage or a number that is one higher or lower. This information gives us further control over the beliefs of the treated subjects: It ensures that all of them have the same beliefs. We truthfully tell the subjects that this information comes from previous sessions of the experiment (pilot sessions).

Crucially, this belief manipulation allows us to observe the behavior of each treated
subject for each possible belief about the partner’s dishonesty, which can be inferred from
their report in the first stage. To ensure that our manipulation worked, we performed
a separate experiment as a manipulation check ($N = 40$; see the Online Appendix A),
which confirms that the beliefs move in the desired direction.<fnref n="13" />

**Partner.** The second difference from the first stage concerns the manipulation of whether the partner plays an active or passive role. While in the first stage of the experiment, all subjects are active — that is, they all flip the coin and report the outcome — in the second stage, we vary between-subject whether both subjects in the pair or only one of them (the treated subject) is active.

<footnote n="13"><sup>13</sup>We ran this experiment for each type of strategic interaction (Substitutes or Complements), separately. The beliefs respond as predicted by the manipulation. The higher the report in the first stage, the higher the belief about the report in the second stage. Comparing beliefs at successive levels yields highly significant results (Mann-Whitney test, *p* < 0.006). The results are confirmed by a regression analysis. Note that another indirect test of whether the belief manipulation has worked is simply to look at how subjects behave as beliefs change (see our results in Section 5).</footnote>
In the *Active* condition, both treated and untreated subjects perform the coin-flip task (as in the first stage). In the *Passive* condition, the untreated subject does not perform the coin-flip task. Instead, we randomly assign this subject the report of a past untreated subject from the *Active* condition, who performed under the same type of strategic interaction and reported the exact same number of heads as the untreated passive subject in the first stage. This information is public knowledge. Thus, from the point of view of the treated subjects in the *Passive* condition, beliefs and incentives are the same as in the *Active* condition. The only difference is that the two subjects in the group do not act together in the second stage.

Our test of whether acting together for the group instead of acting alone increases dishonest behavior closely mirrors that proposed by Barr and Michailidou (2017) to study complicity.<fnref n="14" /> However, there is a crucial distinction: rather than drawing the report for the passive subject from all reports made in a past session, we draw it from the reports made by past untreated (active) subjects who behaved like the passive subject in the first stage. We do this to keep the subjective beliefs of the treated subjects in the *Active* and *Passive* conditions as constant as possible. This provides a stricter test of the diffusion of responsibility that results from both subjects being active. Like in Barr and Michailidou (2017), this manipulation has one potential drawback: the active subject could still perceive the past participants as partners in crime or accomplices. However, the results of Barr and Michailidou (2017) suggest that this manipulation is sufficient to trigger a change in behavior.

<footnote n="14">¹⁴Behnk et al. (2022) also test the effect of being “partners in crime” by employing a sender-receiver game with two senders and one receiver. They vary whether both senders or only one sender actively decide which signal to send. In contrast to our approach and that of Barr and Michailidou (2017), they do not assign an action to the passive player.</footnote>
## 3.3 Questionnaire

At the end of the two stages of the coin-flip task, subjects complete a final questionnaire. We elicit an incentivized measure of distributional preferences taken from Kerschbamer (2015), in which subjects are asked to make ten binary choices on how to distribute money between themselves and another subject (see the Online Appendix D.7). For each participant, one decision is randomly selected for payment. We then collect a measure of social desirability using the 17-item Social Desirability Scale of Stöber (2001). We use this measure as a control for the sensitivity to social pressure. Finally, we collect some socio-demographic information and a unincentivized measure of risk attitudes (“In general, how willing are you to take risks on a scale of 0 (not at all) to 10 (fully)?”) similar to Dohmen et al. (2011).

## 3.4 Procedures

We conducted the experiment between September 2022 and January 2023 at the GATE-Lab using z-tree (Fischbacher, 2007). We pre-registered design and hypotheses on AsPredicted (#106969). We recruited participants via hroot (Bock et al., 2014). In total, 328 subjects participated in the experiment (82 in COMPL-ACT, 80 in COMPL-PASS, 84 in SUBST-ACT, and 82 in SUBST-PASS).<fnref n="15" /> Variations in the number of subjects between treatments reflected variation in attendance rates across sessions. We determined the sample size based on power analysis using a Monte Carlo simulation on data from a pilot, assuming an alpha level of 0.05 and a power of at least 80%.<fnref n="16" />

Upon their arrival at the lab, subjects were randomly assigned to computer desks,

<footnote n="15">¹⁵Information on the socio-demographic characteristics of the subjects is reported in the Online Appendix C.</footnote>

<footnote n="16">¹⁶The pilot (N=40) was identical to the main experiment except for some improvements in the way the instructions for the second stage were written. Due to these changes, we did not include the data from the pilot in the data analysis. However, their inclusion does not change our results (if anything, it makes our inferences stronger due to the increased sample size).</footnote>
which were separated by partitions to prevent verbal and non-verbal communication. Subjects then received the instructions for the first stage. They received the instructions for the second stage only after completion of the first stage. Before each stage, they also answered comprehension questions and could proceed in the experiment only when they correctly answered all questions. The instructions and control questions can be found in the Online Appendix E. At the end of the experiment, subjects received their earnings from one randomly selected stage of the coin-flip task plus their earnings from the final questionnaire. On average, they earned €11.80 for a duration of about 40 minutes.

# 4 Hypotheses

In this section, we state our main hypotheses about the effect that the type of strategic interaction and responsibility have on the relationship between beliefs and dishonesty. We describe a simple utility function and illustrate the intuitions leading to our main hypotheses.<fnref n="17" /> We use the following utility function to derive our hypotheses:

$$E[U_i] = \pi_S(R_i, R_{ij}) + \alpha\pi_S(R_i, R_{ij}) - c(\theta, d_j). \quad (1)$$

$E[U_i]$ is the expected utility of subject $i$ at the time of making the reporting decision in the coin-flip task. As in previous studies on lying, we assume that subjects are risk-neutral and do not lie downward.<fnref n="18" /> $R_i$ is the report of subject $i$. $R_{ij}$ is subject $i$'s belief about what $j$ will report. $\pi_S(R_i, R_{ij})$ is the payoff both $i$ and $j$ get depending on their respective reports, which depends on the type of strategic interaction $S$ (see Section 3.1). In *Complements*, $\pi_S(R_i, R_{ij}) = \min(R_i, R_{ij})$. In *Substitutes*, $\pi_S(R_i, R_{ij}) = \max(R_i, R_{ij})$. The parameter $\alpha \in [0, 1]$ expresses $i$'s concern for $j$'s payoff in the form of some other-

<footnote n="17">¹⁷In Appendix B, we corroborate these intuitions with a simple comparative statics analysis.</footnote>

<footnote n="18">¹⁸We control for the effect of risk aversion in our regression analysis, showing that it does not alter our results.</footnote>
regarding motive.<fnref n="19" /> Finally, the function $c(\theta, d_j)$ denotes the psychological costs $i$ suffers from misreporting the outcome from the coin-flip task (lying costs).

We assume that lying costs have two components. First, an individual suffers a fixed psychological cost $\theta$ of lying if their report leads to a higher payoff than that implied by the true outcome.<fnref n="20" /> Second, $i$'s lying costs also depend on their belief about $j$'s dishonesty ($d_j$). More precisely, $i$'s lying costs decrease in the probability $i$ assigns to $j$ being dishonest (Barr and Michailidou, 2017; Rothenhäusler et al., 2018). This captures the idea that interacting with someone who is thought to be dishonest may decrease one's lying costs.

First, we focus on the effect of beliefs on reporting in the *Active* condition. For beliefs to have an effect on reports, we have to assume that lying costs are positive for at least some subjects. Otherwise, everyone would always report the number that yields the highest payoff. For the moment, we abstract away from the second component of lying costs ($d_j$). If individuals experience only a fixed lying cost when misreporting the outcome of the coin-flip task, reports will have a positive relationship with beliefs in *Complements*, while the relationship will be negative in *Substitutes*.

The intuition is straightforward. In *Complements*, if a subject believes that the other subject will report a high number — possibly lying — they have an incentive to do so as well, because otherwise the high payoff is not realized. On the contrary, if a subject believes that the other subject will report a low number, they have little incentive to lie because they would suffer a lying cost with a low probability of a gain.

The opposite is true in *Substitutes*. In this case, if a subject believes that the other subject will report a high number, they have little incentive to lie because the probability of obtaining a high payoff is already high without the need to suffer any lying cost. In

<footnote n="19">¹⁹Note that outcome-based preferences related to inequality aversion do not play a role here, because subjects always earn the same.</footnote>

<footnote n="20">²⁰Various lying cost models have been proposed in the literature. Some models assume that the cost of lying depends on the amount overreported (e.g., Abeler et al., 2019; Gneezy et al., 2018). To keep our framework simple, we do not incorporate this assumption.</footnote>
contrast, if a subject believes that the other subject will report a low number, they have
an incentive to lie to achieve a higher payoff. In other words, the same manipulation of
beliefs will have opposing effects in the two incentive conditions.

While this intuition mirrors standard situations of strategic complementarity and substitutability, lying costs might be influenced by other factors that could alter the relationship described above. In particular, lying costs may decrease with the belief about the other's dishonesty ($d_j$). This could happen for a number of reasons. An individual may feel less shame or guilt when lying if they expect the counterpart to lie as well (Barr and Michailidou, 2017). Similarly, they may experience less disutility from lying if this is done to reciprocate the expected “kind” action of the counterpart. As a result, we may expect a more positive relationship between lying and beliefs, regardless of the type of strategic interaction. This could strengthen the positive relationship between reports and beliefs in the case of *Complements*, while it could weaken or even offset it in the case of *Substitutes*. Our first hypothesis is as follows.

**Hypothesis 1** *The relationship between beliefs and reports will be positive in Complements and negative in Substitutes.*

Next, we look at how responsibility influences the relationship between beliefs and dis-
honesty. We conjecture that having an active vs. passive partner could affect dishonesty
by varying one's feeling of responsibility (Barr and Michailidou, 2017; Behnk et al., 2022).
We consider that this effect could operate via two different channels: either as a function
of one's beliefs or independently of beliefs. In the first case, the presence of a passive
partner could decrease the importance of $d_j$, which directly enters lying costs. If being
actively involved with someone who is likely to be dishonest (captured by $d_j$) reduces
one's lying costs, we should observe more lying in both strategic conditions (*Substitutes*
and *Complements*) in *Active* compared to *Passive* for high beliefs, i.e., a belief that the
partner is dishonest. This means that a high belief in *Active* has a stronger impact com-
pared to *Passive*, because in the former this information comes from the individual with whom one is actively interacting.

Second, the presence of an active partner could affect behavior independently of beliefs. In this case, it could increase the extent to which one cares about the other's payoff ($\alpha$) or equivalently reduce the fixed component of lying costs ($\theta$). This would lead to more lying for all belief levels in the *Active* compared to the *Passive* condition. We formulate these two effects of responsibility in our second hypothesis.

**Hypothesis 2a** *Reports will be higher for high beliefs in Active compared to Passive in both Complements and Substitutes.*

**Hypothesis 2b** *Reports will be higher across all beliefs in Active compared to Passive in both Complements and Substitutes.*

# 5 Results

In this section, we first examine the behavior of subjects in the first stage of the coin-flip task by comparing overreporting in *Complements* and *Substitutes*. We then focus on the second stage to explore the relationship between lying and beliefs under the two types of strategic interaction and assess the role responsibility plays in this relationship. In addition, we analyze the behavior of subjects with different lying costs through a heterogeneity analysis. We then present a hierarchical clustering analysis in which we identify behavioral types by looking at patterns of behavior in response to our belief manipulation. We conclude with a series of robustness checks of our main results. Throughout our analysis, we use two-sided tests, treat each subject as an independent observation, and evaluate significance at the 5% level, unless otherwise specified.
<figure><img src="image_3.png" /><figcaption>Figure 1: Theoretical and empirical distribution of reports in the first stage</figcaption></figure>

## 5.1 Behavior in the first stage

We first examine whether subjects overreported the number of heads they flipped in the first stage.<fnref n="21" /> Figure 1 shows the distribution of the number of heads reported in *Complements* (white bars) and *Substitutes* (black bars), together with the expected distribution under truthful reporting (grey bars). The latter distribution is significantly different from the distributions under both types of strategic interaction ($\chi^2$ goodness-of-fit tests, *p* < 0.001).<fnref n="22" /> The average number of heads reported is equal to 4.63 in *Complements* and 4.83 in *Substitutes*. Both values are significantly higher than the expected mean value of three, which we should observe under truthful reporting (Wilcoxon signed-rank tests, *p* < 0.001). In both conditions, the distribution of the number of heads reported is highly skewed to the right: the frequency of three or fewer heads is significantly lower than expected under truthful reporting (Binomial test, *p* < 0.001), while the frequency of

<footnote n="21">²¹Here, we merge the data from the *Active* and *Passive* conditions since their design was identical in the first stage. We also find that the number of heads reported is statistically indistinguishable between the *Active* and *Passive* conditions in both *Complements* and *Substitutes* (Mann-Whitney tests, *p* ≥ 0.193).</footnote>

<footnote n="22">²²Kolmogorov-Smirnov tests give similar results.</footnote>
five and six heads is significantly higher ($p < 0.001$). The frequency of four heads is not different from the expected frequency under truthful reporting ($p = 0.234$ in *Substitutes* and $p = 0.578$ in *Complements*).

The data from the first stage also allow us to test whether lying is more prevalent in *Substitutes* or *Complements*. The average number of heads reported in *Substitutes* is slightly higher than in *Complements* (4.83 vs. 4.63; Mann-Whitney test, $p = 0.092$).<fnref n="23" /> The distribution of reports is also slightly more skewed to the right ($\chi^2$ test, $p = 0.096$). If we compare the frequency of each possible report, we find that the frequency of six heads is significantly higher in *Substitutes* than *Complements* (41.57% vs. 29.01%: $\chi^2$ test, $p = 0.017$).<fnref n="24" /> A subject who reported six heads is highly likely to be a liar, because the probability of truly flipping six heads is extremely low (1.56%).<fnref n="25" /> Hence, we can classify a subject who reported six heads as a “brazen subject” (see Weisel and Shalvi, 2015), and conclude that the fraction of brazen subjects is larger in *Substitutes* than *Complements*.

We also find that earnings are higher in *Substitutes* than *Complements* (5.40 vs. 4; Mann-Whitney test, $p < 0.001$). This, in itself, is not surprising because, in expectation, subjects should earn more in *Substitutes* than in *Complements* under truthful reporting (3.81 vs. 3.13). However, we also find that the increase in earnings relative to what subjects should earn under truthful reporting is greater in *Substitutes* than in *Complements* (+51% vs. +28%; Mann-Whitney test, $p < 0.001$), corroborating the fact that subjects lied more in *Substitutes* than in *Complements*. We can present our first result.

**Result 1** *We observe substantial overreporting in both *Complements* and *Substitutes*. Subjects lie more in *Substitutes* than in *Complements*.*

<footnote n="23">²³If we include the data from the pilot (N=40), the difference is significant at the 5% level (4.83 vs. 4.58, $p = 0.029$). Note that, with regard to the first stage, the pilot was identical to the main experiment (cf. footnote 16).</footnote>

<footnote n="24">²⁴For the other reports (three or less, four and five), we find no difference between *Substitutes* and *Complements* ($p \ge 0.189$).</footnote>

<footnote n="25">²⁵This is also confirmed by a binomial test: when one reports six heads (out of six coin flips) we can conclude that the underlying binomial process is not random, i.e., the probability of flipping a head is significantly higher than 50% ($p = 0.031$).</footnote>
## 5.2 Behavior in the second stage

We now turn to our two main research questions, namely, how the type of strategic interaction and responsibility affect the relationship between beliefs and lying. First, we look at the effect of the strategic interaction. Our hypothesis is that the relationship between beliefs and lying is positive in *Complements* and negative in *Substitutes*. To test this hypothesis, we look at the behavior of the treated subjects in the second stage.<fnref n="26" /> Figure 2 displays the average report for each belief in all four treatments. We first focus on the *Active* condition, that is, treatments COM-ACT and SUB-ACT (solid lines and solid bars in Figure 2).

If we average the reports across beliefs, we find that the average report is higher in *Substitutes* than *Complements* (4.91 vs. 4.36: Mann-Whitney test, *p* = 0.010). The fraction of reports of six heads (which identify brazen lying) is also higher in *Substitutes* than *Complements* (0.45 vs. 0.25: *p* = 0.017). This is in line with Result 1 from the first stage. If we consider the reports separately for each belief, the reports in SUB-ACT are significantly higher than the reports in COMP-ACT for beliefs of three or less (Mann-Whitney test, 5.14 vs. 4.15, *p* < 0.001), for beliefs of four (5.02 vs. 4.24, *p* = 0.003) and (although only marginally significantly) for beliefs of five (4.88 vs. 4.44, *p* = 0.066). For beliefs of six, the reports are statistically indistinguishable between the two strategic conditions (4.60 vs. 4.61, *p* = 0.926). In SUB-ACT, average reports significantly decrease with higher beliefs (Page's trend test, *p* = 0.021), while the opposite trend is observed in COMP-ACT (*p* = 0.013). We can present our next result, which confirms Hypothesis 1.

**Result 2** *The relation between beliefs and lying is negative under *Substitutes* and positive under *Complements*.*

<footnote n="26">²⁶Untreated subjects in *Active* reported, on average, 4.68 heads in *Complements* and 4.67 in *Substitutes* in the second stage (Mann-Whitney test, *p* = 0.998). These values are higher than the expected value under honest reporting (Wilcoxon signed-rank tests, *p* < 0.001). The reports of the untreated subjects in the second stage are also similar to their reports in the first stage (*Complements*: 4.68 vs. 4.51, *p* = 0.112; *Substitutes*: 4.67 vs. 4.67, *p* = 0.805).</footnote>
<figure><img src="image_4.png" /><figcaption>Figure 2: Reporting behavior in the second stage</figcaption></figure>

Note: Error bars indicate standard errors of the mean.

Next, we consider the *Passive* condition to study the role that acting together plays in the relationship between beliefs and behavior. We again turn to Figure 2, but we now focus on the comparison between *Active* and *Passive* in the two types of strategic interaction. First, we confirm the relationships between beliefs and behavior observed in the *Active* condition. In line with Result 2, average reports in SUB-PASS (COMP-ACT) decrease (increase) significantly if beliefs increase (Page's trend tests: SUB-PASS, *p* = 0.008; COMP-ACT, *p* = 0.003). The strength of the relationships between beliefs and behavior (captured by the slope of the lines depicted in Figure 2) is analogous to the one observed in the *Active* condition.

When comparing *Active* and *Passive* in *Complements*, we find that the difference in the average reports is not significant and, if anything, goes in the opposite direction compared to what we hypothesized.<fnref n="27" /> For *Substitutes*, the average reports are overall lower in

<footnote n="27">²⁷The difference is never statistically significant except at a belief level of five. At this belief level, we observe a marginally significant increase in the number of heads reported in *Passive* compared to *Active* (Mann-Whitney test; *p* = 0.055).</footnote>
*Passive* compared to *Active*. However, this difference is not statistically significant neither in aggregate nor at any belief level (Mann-Whitney tests, *p* ≥ 0.165). Hence, it seems that when only one subject is responsible for the outcome, this only slightly reduces lying behavior across all beliefs under *Substitutes*. In Section 5.3 we show that acting together with a partner does have a significant effect on non-brazen subjects. For now, we report the following result.

**Result 3** *The relation between beliefs and lying is not affected by responsibility at aggregate level.*

In Appendix D.1, we confirm the validity of our main findings in a regression analysis where the dependent variable is the report of a treated subject in a given situation. The main independent variables are treatment dummies, the belief of a subject in a given situation, and interaction terms between treatment dummies and the belief.

**5.3 Heterogeneity analysis**

As mentioned above, subjects who reported six heads in the first stage can be classified as brazen subjects. Using this classification, we can perform a heterogeneity analysis looking at the effect of the type of strategic interaction and responsibility for brazen subjects and non-brazen subjects (those who report five or fewer heads in the first stage).<fnref n="28" /> This analysis allows us to compare the behavior of subjects with higher vs. lower lying costs.<fnref n="29" /> We expect subjects with high lying costs to respond less to the belief manipulation. This is because these costs act as a deterrent against excessive lying, setting a limit on how much these individuals can adjust their reports to their beliefs. In contrast, subjects with low lying costs can adjust their reports more easily. On the contrary, we expect the effect of responsibility to be higher for subjects with high lying costs compared to subjects with

<footnote n="28">²⁸This heterogeneity analysis was included in our pre-registration (AsPredicted #106969).</footnote>

<footnote n="29">²⁹If we relax the definition of brazen subjects and also include those who reported 5 heads, the results are qualitatively similar to those reported in this section.</footnote>
low lying costs. This is simply because subjects' lying costs are already low and there is less scope for responsibility to further lower them.

<figure><img src="image_5.png" /><figcaption>(a) *Brazen* subjects (N=65)</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>(b) *Non-brazen* subjects (N=99)</figcaption></figure>

Notes: In each panel, blue (darker) lines identify the *Complements* treatments, while the yellow (lighter) lines the *Substitutes* treatments. Solid lines identify the *Active* treatments, while dashed lines the *Passive* treatments. Error bars indicate standard errors of the mean.

<caption>Figure 3: Reporting behavior of brazen and non-brazen subjects in the second stage</caption>

Figure 3 reproduces Figure 2 splitting the data into brazen subjects (N = 65) and
non-brazen subjects (N = 99). In all treatments, brazen subjects exhibit higher reports than non-brazen subjects. This is significant in aggregate and for each belief level (Mann-Whitney tests, $p \le 0.010$ for all comparisons except for beliefs of six in SUB-ACT where $p = 0.080$). Figure 3 also suggests a positive (negative) relationship between beliefs and reporting behavior in both COMP-ACT (SUB-ACT) and COMP-PASS (SUB-PASS) for brazen and non-brazen subjects. These relationships appear to be stronger for brazen subjects than for non-brazen subjects. This is confirmed by non-parametric tests. For brazen subjects, the average report decreases significantly as beliefs increase in both SUB-ACT (Page's trend test, $p = 0.052$) and SUB-PASS, ($p = 0.007$) while it increases significantly in both COMP-ACT ($p = 0.024$) and COMP-PASS ($p = 0.009$). For non-brazen subjects, the increase in the average report in COMP-ACT and COMP-PASS is only weakly significant ($p = 0.076$ and $0.056$, respectively), while the decrease in SUB-ACT and COMP-ACT is not statistically significant ($p = 0.103$ and $0.163$, respectively), despite the sample size being larger than that of brazen subjects.

Concerning the effect of responsibility, for brazen subjects, we find no difference between *Active* and *Passive* under both *Complements* and *Substitute* (Mann-Whitney tests, $p \ge 0.587$ in aggregate and for each belief level). For non-brazen subjects, this is the case only in *Complements* ($p \ge 0.196$ in aggregate and for all belief levels). In *Substitutes*, we find consistently higher reports in *Active* than *Passive* ($p = 0.009$ in aggregate; $p = 0.084$ for a belief of three or less; $p = 0.052$ for a belief of four; $p = 0.024$ for a belief of five; $p = 0.087$ for a belief of six). This suggests that reducing the feeling of responsibility mitigates lying behavior, but only in *Substitutes* and for subjects with relatively high lying costs. These results are confirmed in a regression analysis reported in Appendix D.1. We can summarize these findings into the following two results.

**Result 4** *Subjects with low lying costs react more to changes in beliefs than subjects with high lying costs.*
**Result 5** *Subjects with high lying costs increase their overall lying behavior when they interact with an active partner compared to when their partner is passive, but only under Substitutes.*

## 5.4 Behavioral types analysis

In this section, we investigate whether we can identify behavioral types by looking at patterns of behavior in the second stage.<fnref n="30" /> By looking at patterns of behavior, we can gain a more precise understanding of how the relationship between beliefs and dishonesty is influenced by the type of strategic interaction and responsibility. Instead of pre-defining types based on some ad hoc criteria, we “let the data speak”. We use a hierarchical clustering analysis, which groups data points together based on a similarity measure and end up with four distinct types (see Appendix D.2 for more details).<fnref n="31" />

Figure 5 provides an overview of the patterns of reports associated with each behavioral type using bubble charts. The size and shading of each circle indicate how often a given report is observed among subjects of a given type. The larger and darker the circles, the more frequent the reports. The figure also shows the medoid (the red line that connects the circles), that is, the report profile with the smallest average distance from the other report profiles within a cluster (Fallucchi et al., 2019). Therefore, the medoid captures the most representative report profile of each behavioral type.

<table><caption>Table 3: Subjects types by treatment</caption><thead><tr><th></th><th>COMP-ACT</th><th>COM-PASS</th><th>SUB-ACT</th><th>SUB-PASS</th></tr></thead><tbody><tr><td>Honest</td><td>39.02% (16)</td><td>27.5% (11)</td><td>11.9% (5)</td><td>29.27% (12)</td></tr><tr><td>Conditional dishonest</td><td>14.63% (6)</td><td>25% (10)</td><td>2.38% (1)</td><td>4.88% (2)</td></tr><tr><td>Strongly dishonest</td><td>24.39% (10)</td><td>30% (12)</td><td>42.86% (18)</td><td>39.02% (16)</td></tr><tr><td>Others</td><td>21.95% (9)</td><td>17.5% (7)</td><td>42.86% (18)</td><td>26.83% (11)</td></tr></tbody></table>

<footnote n="30">³⁰This analysis is exploratory and was not pre-registered</footnote>

<footnote n="31">³¹A similar approach has been used by Fallucchi et al. (2019), Galeotti et al. (2019) and Mittone et al. (2021) to identify behavioral types in the context of public goods games and bargaining.</footnote>
<figure><img src="image_7.png" /></figure>

Notes: The four panels display the bubble charts of each behavioral type that we identify with the clustering analysis. The circles indicate how often a given report is observed among subjects classified in a given type. The larger and darker the circle, the more frequent the report. The red line identifies the medoid (the report profile with the smallest average distance from the other report profiles within a type) for each type.

<caption>Figure 5: Report strategies for each behavioral type</caption>
We assign a label to each of the four distinct types based on their medoid. *Honest* subjects (N=44) report mostly three or fewer heads across all beliefs. *Conditional dishonest* subjects (N=19) report a number of heads that closely matches the belief about their partner's report. *Strongly dishonest* subjects (N = 44) have a modal report of six for all beliefs. The last group of subjects (*Others*) is a residual category (N=45). Their stereotypical reporting strategy is to compensate, to some degree, for their partner's report.

We can examine how the distribution of the different types varies in our treatments. Table 3 reports the proportion of each type for each treatment. Consistently with our main results, we find that the share of strongly dishonest subjects is (weakly significantly) larger in *Substitutes* than in *Complements* ($\chi^2$ test, *p* = 0.062). Similarly, the share of others (those who partly compensate for the other's report) is significantly higher in *Substitutes* than in *Complements* (*p* = 0.029).<fnref n="32" /> The opposite is true for honest subjects, who are more common in *Complements* than in *Substitutes*, but only when everyone is active (COMP-ACT vs. SUB-ACT, *p* = 0.004). In the *Passive* condition, the share of honest subjects is similar under *Complements* and *Substitutes* (COM-PASS vs. SUB-PASS, *p* = 0.860). Interestingly, the share of honest subjects significantly decreases in SUB-ACT compared to SUB-PASS (*p* = 0.050), but not in COMP-ACT compared to COMP-PASS (*p* = 0.271). We attribute this to the effect that acting together has in *Substitutes*. Finally, conditional dishonest subjects are almost only present under *Complements* (COMP-ACT vs. SUB-ACT, *p* = 0.045; COM-PASS vs. SUB-PASS, *p* = 0.001), as one would also expect from our main results. The fact that the share of conditional dishonest subjects and the share of others (who tend somewhat to compensate for their partner's report) do not vary significantly between SUB-ACT and SUB-PASS (*p* = 0.542 and 0.126, respectively), nor between COMP-ACT and COMP-PASS (*p* =

<footnote n="32">³²The difference is larger in *Active* than in *Passive* (COMP-ACT vs. SUB-ACT, *p* = 0.042; COMP-PASS vs. SUB-PASS, *p* = 0.313). The same applies to strongly dishonest subjects (COMP-ACT vs. SUB-ACT, *p* = 0.075; COMP-PASS vs. SUB-PASS, *p* = 0.393).</footnote>
0.241 and 0.615, respectively), also confirms that the gradient of the relationship between beliefs and lying is not affected by responsibility (see Result 3). This suggests that responsibility has, if anything, only a level effect on dishonesty.

## 5.5 Robustness checks

We conduct a number of robustness checks to confirm the validity of the main results above. Below, we briefly describe each of these robustness exercises. More details can be found in Appendix D. First, we checked whether the results of our regression analysis reported in Appendix D.1 are robust to the use of a different dependent variable, namely a dummy that takes the value one if a treated subject reported six heads, and zero otherwise. Our results are robust to this change in the model specification (see Appendix D.3). Our regression results are also robust to a number of sample restrictions. In particular, they hold qualitatively if we restrict the sample to subjects who do not report six heads for all belief levels in the second stage (see Appendix D.4), and if we run separate regressions for the *Active* and *Passive* condition (see Appendix D.5).

We also check whether our results are robust to alternative ways of specifying the beliefs that subjects hold about their counterpart's behavior (see Appendix D.6). Instead of assuming that subjects take the information we provide to them at face value, we redefine the “Belief” variable as the average report of the untreated subjects in the second stage given their reports in the first stage or as the average belief of subjects in the Manipulation check (see Section 3.2 and Appendix A). The results of these analyses (qualitatively) replicate those reported in the paper.

Finally, we look at whether the reporting behavior is influenced by social preferences. We classify subjects based on the “Equality Equivalence Test” (Kerschbamer, 2015) and examine whether the reporting behavior differs across different types (see the Appendix D.7). We find only little variation in behavior between types, suggesting that social
preferences cannot account for our results.

# 6 Discussion and conclusion

We experimentally investigate the relationship between beliefs and group dishonesty under two types of strategic interaction (*Complements* and *Substitutes*) and study the role of responsibility for one's actions. We document more lying and a higher proportion of brazen subjects (subjects who lie maximally) in *Substitutes* compared to *Complements*. We also find that beliefs strongly shape dishonest behavior through the type of strategic interaction. In *Substitutes*, a higher belief that one's partner is dishonest leads to less lying. Conversely, in *Complements*, a higher belief that one's partner is dishonest leads to more lying. Although the direction of the relationship between lying and beliefs is opposite in the two strategic conditions, its magnitude is the same.

Moreover, we find that the negative (or positive) relationship between beliefs and dishonesty is much more pronounced for brazen subjects compared to non-brazen subjects. The explanation is that brazen subjects can respond more strongly to changes in beliefs due to their lower lying costs. In contrast, non-brazen subjects are more constrained in their report.

Our design also allows us to study the role that responsibility plays in the relationship between dishonesty and beliefs when actions are complements and when they are substitutes. We find that acting together with someone else generally has little impact on dishonest behavior. When actions are complements, the relationship between beliefs and dishonesty remains the same regardless of whether both (*Active*) or only one subject in the pair (*Passive*) actively decides. This also holds true in our heterogeneity analysis for both brazen and non-brazen subjects. When actions are substitutes, we only find a minor and statistically insignificant aggregate difference between *Active* and *Passive* across all belief levels. However, when we look at brazen and non-brazen subjects separately, we
find that non-brazen subjects lie significantly less at all belief levels in *Passive* compared
to *Active*. For brazen subjects, we find no difference.

Our findings on the effect of responsibility suggest that it affects group dishonesty independently of beliefs. This indicates that the effect of responsibility operates through a reduction of the intrinsic component of lying costs or an increase in the extent to which one cares about the other’s payoff. This is also in line with evidence from Behnk et al. (2022), who find that the active involvement of another group member increases dishonest behavior by making it more normatively acceptable. Our results suggest that the mechanism through which this effect operates in group dishonesty is independent of beliefs.

The fact that we observe this level effect only for non-brazen subjects in *Substitutes*
is intriguing and deserves some discussion. First, the fact that we do not observe this
effect on brazen subjects is not completely surprising, since, as mentioned above, there is
little scope for the active involvement of the partner to affect their behavior. The second
point of discussion is that we observe an effect in *Substitutes* but not in *Complements*. In
*Substitutes*, a subject can ensure that both them and their partner get at least the payoff
that matches their report. This is not the case in *Complements*. Therefore, a potential
explanation is that the risk of paying the lying cost without any gain for oneself and the
partner could constrain dishonesty in *Complements*. In other words, the cost of lying
when one receives no monetary gain could “burn more” compared to the case in which
lying results in a gain.

Although we are not able to rigorously test this explanation in our experiment, our
analysis of types offers some suggestive evidence in favor of this interpretation. We find
that the behavior in *Complements* is highly constrained by the type of interaction. A large
proportion of subjects (20% if we combine the *Active* and *Passive* conditions together)
behave as conditional dishonest and make a report that matches the one of their partner,
thus displaying a (nearly) perfect positive relationship between the report and the belief.
An even larger proportion of subjects is classified as Honest (33%) or Strongly dishonest
(27%). In *Substitutes*, we find a lower proportion of subjects classified as Honest (20%)
and a much higher proportion of subjects classified as Strongly dishonest (41%). At
the same time, we do not identify a group of subjects that exhibit a (nearly) perfectly
negative relationship between reports and behavior, indicating a more volatile behavior.
This suggests that this relationship is more “flexible” in *Substitutes* than in *Complements*
and that there is, thus, more space for the active involvement of the other subject to play
a role.

Taken together, the evidence we present indicates that the type of strategic interac-
tion and beliefs strongly shape dishonest behavior in groups. In contrast, the effect of
responsibility-sharing arising from the fact of acting together with someone else seems
to play a more limited role. This suggests that the responsibility for one's actions is
only lessened in group settings where the (im)imoral action is determined at the group
level. Our results also inform the discussion on the differences in lying behavior between
individual and group settings. They suggest that psychological factors linked to beliefs
about other group members' behavior do not greatly influence lying costs and lying in
these settings. Rather, the difference between group and individual settings may mostly
arise from the role that beliefs about others' behavior have in affecting one's strategic
considerations.

While we do not directly test measures to reduce group dishonesty, our study pro-
vides some insights for organizations that may be interested in trying to curtail such
behavior. A first implication of our results is that the type of interaction matters and
should be carefully examined. In settings close to our *Complements* condition (i.e., when
group members need to jointly act dishonestly for the spoils to realize), intervening on
individuals' beliefs by lowering the expectation that others are dishonest may help to re-
duce dishonest behavior. This may be achieved, for example, with campaigns showcasing virtuous behavior by moral exemplars in the organization. In contrast, these types of intervention may be less effective or could even backfire in settings close to our *Substitutes* condition (i.e., when a single dishonest act by an individual could benefit the whole group). In this case, organizations may want to increase one's feeling of responsibility. More research is needed to assess the effectiveness of concrete interventions.
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# Online Appendix

## A Manipulation check

To make sure that our belief manipulation worked in the intended way, we ran an additional experiment (N=40), included in the original pre-registration. The aim was to assess the beliefs that subjects hold in the second stage of the main experiment when provided with a given information about the untreated subject's behavior in the first stage. We ran this experiment with a separate set of subjects for two main reasons. First, we wanted to keep the task of the treated subjects in our main experiment as simple as possible and focus their attention on the belief manipulation. Second, beliefs elicited after such lying tasks — even if incentivized — can easily fall prey of the false consensus bias or can be used in a self-serving way. This would result in subjects not providing their true beliefs and would create a fictitious positive correlation between beliefs and lying.

In the additional experiment, we ask a different set of subjects to predict the report of an untreated subject from the main experiment in the second stage based on what this person reported in the first stage. We design the additional experiment following the same structure of the main experiment for the treated subjects. Each subject is matched with a random untreated subject from the main experiment. Subjects then face four different situations, of which only one contains the true information about the untreated subject that is matched with them. Subjects earn a bonus if they correctly guess the number of heads reported by this untreated subject in the second stage. Hence, they receive the exact same information as the treated subjects of the main experiment, but do not perform the coin-flip task. The instructions and comprehension questions can be found in the Online Appendix E.2.

We, first, check whether beliefs in *Complements* and *Substitutes* are different. We expect no difference here and find this to be the case ($p > 0.51$ for t-tests and $p > 0.33$
<table><thead><tr><th></th><th>belief</th></tr></thead><tbody><tr><td>(Intercept)</td><td>1.78***<br>(0.28)</td></tr><tr><td>first stage report</td><td>0.60***<br>(0.06)</td></tr><tr><td>Adj. R<sup>2</sup></td><td>0.46</td></tr><tr><td>Num. obs.</td><td>160</td></tr></tbody></table>

Table A1: Linear regression with clustered standard errors at individual level (n=40) for Wilcoxon rank-sum tests). We, hence, pool the data in the subsequent analysis. We, then, compare beliefs for different reports in the first stage successively, i.e., three or less heads vs. four heads, four heads vs. five heads, and five heads vs. six heads. We expect a significant increase from a lower report to a higher one. We find highly significant differences in the expected direction in all cases (*p* < 0.03 for paired t-tests, and, *p* < 0.006 for Wilcoxon signed-rank tests). Finally, we confirm that these results also hold in a regression framework where we simply regress beliefs on the report in the first stage clustering standard errors at the individual level (see Table A1).

<footnote>***p < 0.001; **p < 0.01; *p < 0.05</footnote>
# B Hypotheses

In this section, we perform a simple comparative statics analysis to corroborate the intuitions presented in the main text for our main hypotheses (see Section 4) and to further clarify the underlying behavioral mechanisms. Recall our utility function:

$$E[U_i] = \pi_S(R_i, R_{ij}) + \alpha \pi_S(R_i, R_{ij}) - c(\theta, d_j).$$

$R_i$ is an integer in the interval (3, 6) and correspond to i's report in the coin-flip task. $R_{ij}$ is a probability distribution over the possible outcomes and represents individual i's belief about what j will report, which is evaluated in a risk-neutral way. $\pi_S(R_i, R_{ij})$ is the payoff both i and j get based on their respective reports and depending on the strategic interaction. It is equal to $\max(R_i, R_{ij})$ in *Substitutes* and to $\min(R_i, R_{ij})$ in *Complements*. The parameter $\alpha \in [0, 1]$ expresses i's concern for j's payoff. The function $c(\theta, d_j)$ denotes the psychological costs incurred by i due to misreporting the outcome from the coin-flip task. We assume that these costs have two components. First, an individual incurs a fixed lying cost $\theta$ if $R_i \neq O_i$, where $O_i$ is the observed outcome. $\theta$ follows a continuous distribution in the interval [0, $\bar{\theta}$]. $d_j$ depends on i's belief about j's dishonesty. It captures the idea that i's lying costs decrease in the probability i assigns to j being dishonest. For the moment, we abstract from $d_j$. Our utility function becomes
$$E[U_i] = (1 + \alpha)\pi_S(R_i, R_{ij}) - \theta.$$

Since the lying costs are fixed, we have that for a given outcome of the coin-flip task $O_i$ and a given belief $R_{ij}$ there will be a cutoff level of $\theta$ below which an individual will lie.<fnref n="33" /> We denote these cutoffs as $\theta_k(R_{ij})$, where $k = 3, 4, 5, 6$ stands for the observed outcome. Note that an individual who decides to lie will lie maximally by reporting $R_i = 6$. Hence, given a certain belief, we can calculate the aggregate share of subjects

<footnote n="33">³³Rothenhäusler et al. (2018) find that Bayesian Nash equilibria in similar situations take the form of threshold equilibria, which underscores the validity of our analysis.</footnote>
who lie in expectations across the possible outcomes. We can call this share $s(R_{ij})$.

To see how reports change as beliefs change, we start from an arbitrary belief about $j$'s report, call it $R_{ij}^L$. Given $R_{ij}^L$ and for each observed outcome $O_i$, we denote the cutoff values below which an individual will lie as $\theta_k(R_{ij}^L)$ and the resulting expected share of individuals who lie as $s(R_{ij}^L)$. Now, consider a belief $R_{ij}^H$ such that $E[R_{ij}^H] > E[R_{ij}^L]$. We denote the cutoff values below which an individual will lie as $\theta_k(R_{ij}^H)$ and the resulting expected share of individuals who lie as $s(R_{ij}^H)$.<fnref n="34" /> In *Substitutes*, we have that $\theta_k(R_{ij}^H) \ge \theta_k(R_{ij}^L), \forall k$ and, thus, that $s(R_{ij}^H) \le s(R_{ij}^L)$. In *Complements*, we have that $\theta_k(R_{ij}^H) \le \theta_k(R_{ij}^L), \forall k$ and, thus, that $s(R_{ij}^H) \ge s(R_{ij}^L)$. This implies a monotonic negative (positive) relationship between beliefs and the share of individuals lying in *Substitutes* (*Complements*), which translates into a negative (positive) relationship between beliefs and the average report, as described in Hypothesis 1.

We now move on to our hypothesis on the effect of having an active vs. passive partner on the relationship between beliefs and reports. We conjecture that this could affect behavior either as a function of one's beliefs or independently of them. In the first case, the idea is that acting together with another individual increases the importance of $d_j$. In the second case, we posit that having an active partner increases the weight of $\alpha$ or, equivalently, reduce $\theta$. To capture the first idea, we consider $d_j = \beta I_d \theta$. $d_j$ is only activated if an individual lies ($R_i \ne O_i$). The utility is now given by $E[U_i] = (1+\alpha)\pi_S(R_i, R_{ij}) - (\theta - \beta I_d \theta)$. Here, $\beta \in [0, 1]$ expresses how close an individual feels to their partner, while $I_d$ is an indicator function, which expresses whether an individual thinks that their partner is a liar or not. We define a cutoff probability $\bar{q}$ such that if the likelihood of a given report falls below it ($q \le \bar{q}$) one believes that their partner is a liar ($I=1$) and not otherwise ($I=0$). In our setting, we assume that subjects will

<footnote n="34">³⁴In our experiment, we manipulate beliefs by providing treated subjects in Stage 2 with their partner's report in Stage 1 and informing them that based on previous experiments there is a probability of 90% that their partner reports either the same number they reported in the Stage 1 or a number that is one below or above. In a manipulation check, we confirm that this moves beliefs in the desired direction (see Appendix A).</footnote>
believe that a report of six comes from a liar.<fnref n="35" /> Note that if an individual feels perfectly
close to their partner ($\beta = 1$) and believes their partner to be a liar ($q \le \bar{q}$), they will
experience no lying costs at all. We assume that $\beta_{Active} > \beta_{Passive}$. This should lead to
higher average reports for high beliefs (belief equal to six) in *Active* compared to *Passive*
under both incentive structures, as stated in the first part of Hypothesis 2a.

To capture the second idea, we again assume that acting together with another indi-
vidual leads to a higher feeling of closeness, but conjecture that this could translate into
a higher other-regarding concern ($\alpha_{Active} > \alpha_{Passive}$) or lower fixed lying costs ($\theta_{Active} < \theta_{Passive}$). We denote the cutoff values of $\theta$ below which an individual will lie as $\theta_k^A(R_{ij})$ in *Active* and as $\theta_k^P(R_{ij})$ in *Passive*. In both cases, we have that $\theta_k^A(R_{ij}) < \theta_k^P(R_{ij})$, $\forall k$ and for a given $R_{ij}$. This means that for each outcome $O_i$ the share $s_k$, $k = 3, 4, 5, 6$ of subjects who lie will be higher in *Active* compared to the *Passive*: $s_k^A < s_k^P$, $\forall k$. This should lead to higher average reports across all beliefs in the *Active* compared to *Passive* condition, as stated in Hypothesis 2b.

<footnote n="35">³⁵Recall that such an outcome is extremely unlikely ($p = 0.0156$) and note that one can statistically classify a subject as a liar in this case (see Section 5.1). Moving this cutoff will not change the essence of the idea we want to capture. Alternatively, one could define a function that maps the probability of a report to the probability of being a liar, which would capture the same intuition.</footnote>
C Demographics

Table C1 presents the mean socio-demographic characteristics of the sample. We can test whether the characteristics are balanced across treatments by conducting balance tests (either a Kruskal-Wallis test or a χ² depending on the type of variable). The results are reported in the Column “Test”. It is reassuring to see that we only reject the null hypothesis at the 5% level in one out of eleven comparisons.<fnref n="36" /> We can therefore conclude that the randomization of subjects into different treatments worked well.

<footnote n="36">³⁶We find that subjects in COMP-ACT and SUB-PASS have, on average, slightly less experience in economic experiments than subjects in COMP-PASS and SUB-ACT. Note that we control for this variable in our regression analysis, thus eliminating any possible bias due to a slight imbalance in this characteristic.</footnote>
<table><thead><tr><th>Socio-demographics</th><th>COMP-ACT</th><th>COM-PASS</th><th>SUB-ACT</th><th>SUB-PASS</th><th>Total</th><th>Test</th></tr></thead><tbody><tr><td><strong>Male</strong></td><td>0.61</td><td>0.56</td><td>0.46</td><td>0.52</td><td>0.54</td><td>0.287</td></tr><tr><td><strong>Age</strong></td><td>20.48</td><td>20.84</td><td>20.76</td><td>20.61</td><td>20.67</td><td>0.136</td></tr><tr><td><strong>SDS17 Score</strong></td><td>8.57</td><td>8.45</td><td>8.74</td><td>8.05</td><td>8.45</td><td>0.379</td></tr><tr><td><strong>French native</strong></td><td>0.96</td><td>0.95</td><td>1</td><td>1</td><td>0.98</td><td>0.054</td></tr><tr><td><strong>Risk attitude</strong></td><td>6.4</td><td>6.64</td><td>6.56</td><td>6.55</td><td>6.54</td><td>0.863</td></tr><tr><td><strong>Experience</strong></td><td>0.90</td><td>1.54</td><td>1.45</td><td>1.12</td><td>1.25</td><td>0.033**</td></tr><tr><td><strong>Accademic degree</strong></td><td>4.91</td><td>5.24</td><td>5.23</td><td>4.90</td><td>5.07</td><td>0.115</td></tr><tr><td><strong>Field of studies</strong></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Management</td><td>0.46</td><td>0.41</td><td>0.54</td><td>0.57</td><td>0.5</td><td></td></tr><tr><td>Economics</td><td>0.04</td><td>0.04</td><td>0.08</td><td>0.05</td><td>0.05</td><td></td></tr><tr><td>Engineering</td><td>0.46</td><td>0.5</td><td>0.32</td><td>0.29</td><td>0.39</td><td>0.195</td></tr><tr><td>Computer Science</td><td>0</td><td>0</td><td>0</td><td>0.01</td><td>0</td><td></td></tr><tr><td>Mathematics</td><td>0.01</td><td>0</td><td>0</td><td>0</td><td>0</td><td></td></tr><tr><td>Other</td><td>0.02</td><td>0.05</td><td>0.06</td><td>0.07</td><td>0.05</td><td></td></tr><tr><td><strong>School</strong></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Ecole Centrale de Lyon</td><td>0.45</td><td>0.39</td><td>0.24</td><td>0.27</td><td>0.34</td><td></td></tr><tr><td>Ecole de Management de Lyon</td><td>0.48</td><td>0.46</td><td>0.58</td><td>0.61</td><td>0.53</td><td></td></tr><tr><td>ISOSTEO</td><td>0</td><td>0</td><td>0</td><td>0.01</td><td>0</td><td>0.122</td></tr><tr><td>ITECH</td><td>0.04</td><td>0.1</td><td>0.08</td><td>0.04</td><td>0.06</td><td></td></tr><tr><td>Faculté d'économie</td><td>0</td><td>0.01</td><td>0.01</td><td>0</td><td>0.01</td><td></td></tr><tr><td>Other</td><td>0.04</td><td>0.04</td><td>0.08</td><td>0.07</td><td>0.06</td><td></td></tr><tr><td><strong>Relationship status</strong></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Engaged</td><td>0</td><td>0</td><td>0.02</td><td>0</td><td>0.01</td><td></td></tr><tr><td>Cohabiting Partner</td><td>0.13</td><td>0.1</td><td>0.12</td><td>0.11</td><td>0.12</td><td></td></tr><tr><td>Married</td><td>0.01</td><td>0</td><td>0.01</td><td>0</td><td>0.01</td><td>0.403</td></tr><tr><td>Single</td><td>0.79</td><td>0.89</td><td>0.77</td><td>0.84</td><td>0.82</td><td></td></tr><tr><td>Separated/Divorced</td><td>0</td><td>0</td><td>0</td><td>0.01</td><td>0</td><td></td></tr><tr><td>Prefer not to answer</td><td>0.06</td><td>0.01</td><td>0.07</td><td>0.04</td><td>0.05</td><td></td></tr><tr><td><strong>Distributional types</strong></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Altruist</td><td>0.72</td><td>0.76</td><td>0.75</td><td>0.68</td><td>0.73</td><td></td></tr><tr><td>Equality averse</td><td>0.1</td><td>0</td><td>0.11</td><td>0.1</td><td>0.08</td><td>0.122</td></tr><tr><td>Inconsistent</td><td>0.02</td><td>0.05</td><td>0.02</td><td>0.05</td><td>0.04</td><td></td></tr><tr><td>Inequality averse</td><td>0.09</td><td>0.17</td><td>0.1</td><td>0.12</td><td>0.12</td><td></td></tr><tr><td>Spiteful</td><td>0.07</td><td>0.01</td><td>0.02</td><td>0.05</td><td>0.04</td><td></td></tr></tbody></table>

Notes: The academic degree was measured on a scale from 1 ("Less than BAC"), 2 ("BAC"), 3 ("BAC+1"), 4 ("BAC+2"), 5 ("BAC+3 or undergraduate degree"), 6 ("BAC+4"), 7 ("BAC+5 or master") to 8 ("More than BAC+5"), where BAC corresponds to the secondary education degree in France. Experience is the number of economic experiments a subject participated in. The SDS17 score measures social desirability and is obtained from the 17-item Social Desirability Scale of Stöber (2001). Risk attitude captures how much a participant is willing to take risks in general on a scale from 0 (not at all) to 10 (fully) (Dohmen et al., 2011). Distributional types are obtained from the Kerschbamer (2015)'s task (see Online Appendix D.7). **p < 0.05.

<caption>Table C1: Demographics and balancing tests</caption>
# D Additional Analysis

In this section, we report additional analyses complementing the one in the main text, as well as evidence from a number of robustness checks to confirm the validity of our main results.

## D.1 Regression analysis

We test the robustness of our main results in a regression framework (see Section 5.2). We report the results of the regression analysis in Table D1, where the dependent variable is the report of a treated subject in a given situation. In Model 1, the independent variables are treatment dummies (using SUB-ACT as the reference category), the belief faced by the subject in a given situation, and interaction terms between treatment dummies and the belief.<fnref n="37" /> In Model 2, we also include controls for individual characteristics (age, sex, participation in previous experiments, risk attitude and social desirability).<fnref n="38" /> We use Tobit regressions with standard errors clustered at the subject level.

In line with our main results, we find that the report of a subject in SUB-ACT significantly decreases when beliefs increase (see the positive coefficient of “Belief”). The direction and intensity of the relationship between behavior and beliefs do not change in SUB-PASS (see the coefficient of the interaction between “Belief × SUB-PASS”). The relationship between behavior and beliefs becomes positive in *Complements* ($\beta_{Belief} + \beta_{Belief \times COMP-ACT} = 0$, $p < 0.01$ for both models; $\beta_{Belief} + \beta_{Belief \times COMP-PASS} = 0$, $p < 0.01$ for both models) and the effect is statistically indistinguishable in COMP-

<footnote n="37">³⁷To lessen the correlation between the belief variable and its interaction with the treatment dummies, we centered the belief variable at its mean (see Marquardt, 1980). We also ran our regression with the inclusion of a squared term for beliefs. The squared term turned out to be insignificant and the other results remained unchanged.</footnote>

<footnote n="38">³⁸We find that older subjects lie less, which is consistent with previous studies (see, e.g., Serota et al., 2010; Glätzle-Rützler and Lergetporer, 2015). Higher participation in previous experiments is associated with more lying. However, we are not able to assess whether exposure to a specific type of experiments drives this effect (for example, Fischbacher and Föllmi-Heusi, 2013, find that subjects who participated twice in a die-rolling experiment reported higher payoffs the second time).</footnote>
<table><thead><tr><th></th><th>(1)</th><th>(2)</th></tr></thead><tbody><tr><td>SUB-ACT</td><td>Ref.</td><td>Ref.</td></tr><tr><td>COMP-ACT</td><td>-1.36***<br>(0.52)</td><td>-1.05**<br>(0.43)</td></tr><tr><td>COMP-PASS</td><td>-0.77<br>(0.50)</td><td>-0.75*<br>(0.39)</td></tr><tr><td>SUB-PASS</td><td>-0.70<br>(0.56)</td><td>-0.55<br>(0.44)</td></tr><tr><td>Belief</td><td>-0.47***<br>(0.17)</td><td>-0.50***<br>(0.17)</td></tr><tr><td>Belief × COMP-ACT</td><td>0.96***<br>(0.25)</td><td>0.97***<br>(0.25)</td></tr><tr><td>Belief × COMP-PASS</td><td>1.07***<br>(0.25)</td><td>1.11***<br>(0.26)</td></tr><tr><td>Belief × SUB-PASS</td><td>-0.14<br>(0.23)</td><td>-0.13<br>(0.24)</td></tr><tr><td>Social desirability</td><td></td><td>0.04<br>(0.06)</td></tr><tr><td>Male</td><td></td><td>0.25<br>(0.31)</td></tr><tr><td>Age</td><td></td><td>-0.39***<br>(0.14)</td></tr><tr><td>Experience</td><td></td><td>0.96***<br>(0.13)</td></tr><tr><td>Risk taking</td><td></td><td>0.00<br>(0.08)</td></tr><tr><td>Constant</td><td>5.55***<br>(0.36)</td><td>11.77***<br>(2.98)</td></tr><tr><td>Observations</td><td>656</td><td>656</td></tr><tr><td>Right-cens obs.</td><td>232</td><td>232</td></tr><tr><td>Left-cens obs.</td><td>170</td><td>170</td></tr><tr><td>Pseudo R2</td><td>0.020</td><td>0.092</td></tr><tr><td>Log-likelihood</td><td>-964.760</td><td>-893.342</td></tr></tbody></table>

Notes: *$p < 0.1$, **$p < 0.05$, ***$p < 0.01$. Tobit regressions with clustered standard errors (in parentheses) at the subject level. “Belief” is centered to avoid multicollinearity problems (Marquardt, 1980).

<caption>Table D1: Determinants of lying behavior in the second stage</caption>
ACT and COMP-PASS ($p \ge 0.591$ in both models). Interestingly, the strength of the relationship between behavior and beliefs is the same in COMP-ACT and SUB-ACT ($|\beta_{Belief}| = |\beta_{Belief} + \beta_{Belief \times COMP-ACT}|, p \ge 0.873$).

In Table D2, we inspect the robustness of the findings about brazen and non-brazen subjects in a regression framework (see Section 5.3), mirroring our analysis in Table D1. The dependent variable is the report of a treated subject for a given belief. In Model 1, the independent variables are treatment dummies (with SUB-ACT as the reference category), the belief faced by the subject in a given situation, and a dummy that identifies brazen subjects. We also include pairwise and triple interaction terms between these variables. In Model 2, we add controls for individual characteristics (age, gender, previous experience in lab experiments, risk attitude, and social desirability).<fnref n="39" /> We use Tobit regressions with standard errors clustered at the subject level.

Focusing on non-brazen subjects, the negative and significant coefficients of the treatment dummies COMP-ACT, COMP-PASS and SUB-PASS indicate that the intercept in SUB-ACT is significantly higher. Interestingly and in line with our predictions, non-brazen subjects lie less in *Passive*, but only in *Substitutes* (the coefficients of COMP-ACT and COMP-PASS are not statistically different; $p \ge 0.643$ in both models).

Turning to brazen subjects, we find that they lie significantly more than non-brazen subjects, as indicated by the positive and statistically significant coefficient of the variable “Brazen”. They also react more to changes in beliefs. In SUB-ACT, the relationship between reports and beliefs is negative and highly significant ($\beta_{Belief} + \beta_{Belief \times Brazen} < 0$, $p \le 0.014$ in both models). The *Passive* condition does not significantly modify this relationship (see the insignificant coefficient on “SUB-PASS × Brazen × Belief”). In both COMP-ACT and COMP-PASS, brazen subjects increase their report more compared to non-brazen subjects when beliefs increase (see the positive and significant coefficients on “COMP-ACT × Brazen × Belief” and “COMP-PASS × Brazen × Belief”).

<footnote n="39">³⁹For these variables, we replicate the previous findings reported in Table D1.</footnote>
<table><thead><tr><th></th><th>(1)</th><th>(2)</th></tr></thead><tbody><tr><td>COMP-ACT</td><td>-0.99**<br>(0.44)</td><td>-1.08***<br>(0.40)</td></tr><tr><td>COMP-PASS</td><td>-0.86**<br>(0.39)</td><td>-0.90***<br>(0.33)</td></tr><tr><td>SUB-PASS</td><td>-1.40***<br>(0.50)</td><td>-1.23***<br>(0.42)</td></tr><tr><td>Belief</td><td>-0.26*<br>(0.15)</td><td>-0.26*<br>(0.15)</td></tr><tr><td>Belief × COMP-ACT</td><td>0.60**<br>(0.24)</td><td>0.58**<br>(0.24)</td></tr><tr><td>Belief × COMP-PASS</td><td>0.63**<br>(0.26)</td><td>0.63**<br>(0.26)</td></tr><tr><td>Belief × SUB-PASS</td><td>-0.16<br>(0.27)</td><td>-0.17<br>(0.27)</td></tr><tr><td>Brazen</td><td>2.37***<br>(0.59)</td><td>1.56***<br>(0.56)</td></tr><tr><td>Belief × Brazen</td><td>-0.55<br>(0.36)</td><td>-0.57<br>(0.36)</td></tr><tr><td>Brazen × COMP-ACT</td><td>1.08<br>(0.91)</td><td>1.63*<br>(0.88)</td></tr><tr><td>Brazen × COMP-PASS</td><td>0.80<br>(0.84)</td><td>0.86<br>(0.76)</td></tr><tr><td>Brazen × SUB-PASS</td><td>1.50<br>(0.93)</td><td>1.56*<br>(0.82)</td></tr><tr><td>COMP-ACT × Brazen × Belief</td><td>1.37***<br>(0.48)</td><td>1.38***<br>(0.48)</td></tr><tr><td>COMP-PASS × Brazen × Belief</td><td>1.23**<br>(0.50)</td><td>1.26**<br>(0.49)</td></tr><tr><td>SUB-PASS × Brazen × Belief</td><td>-0.02<br>(0.50)</td><td>-0.04<br>(0.51)</td></tr><tr><td>Controls for individual characteristics</td><td>No</td><td>Yes</td></tr><tr><td>Observations</td><td>656</td><td>656</td></tr><tr><td>Right-cens obs.</td><td>232</td><td>232</td></tr><tr><td>Left-cens obs.</td><td>170</td><td>170</td></tr><tr><td>Pseudo R2</td><td>0.141</td><td>0.170</td></tr><tr><td>Log-likelihood</td><td>-845.590</td><td>-816.334</td></tr></tbody></table>

Notes: *p* < 0.1, **p* < 0.05, ***p* < 0.01. Tobit regressions with clustered standard errors (in parentheses) at the subject level. Belief is centered to avoid multicollinearity problems (Marquardt, 1980).

<caption>Table D2: Determinants of lying behavior in the second stage for brazen and non-brazen subjects</caption>
## D.2 Hierarchical Clustering

Here, we provide more details about the hierarchical cluster analysis reported in Section 5.4. The procedure works as follows. Take two subjects from all treated subjects, say subject *i* and *j*. Let $R_i^b$ be the report of subject *i* given the belief *b* about the report of his/her counterpart (the untreated subject) in the second stage. We calculate the dissimilarity between subject *i* and *j* as the Manhattan distance $d(i, j) = \sum_{b=3}^{6} |R_i^b - R_j^b|$. We calculate this distance for each possible pair of subjects. This gives us a 164 × 164 matrix containing the dissimilarity measures for treated subjects in our sample. The algorithm then clusters subjects according to their degree of dissimilarity using Ward's method (Ward Jr, 1963). This method clusters subjects in such a way that the sum of squared errors within each cluster is minimized. We rely on the DudaHart $Je(2)/Je(1)$ index and the associated pseudo-T2 statistic (see Duda et al., 2001) to determine an appropriate number of clusters. Following this procedure, we isolate four distinct types.

We can calculate the Silhouette statistic (Rousseeuw, 1987) for each subject in each cluster and plot the distribution of this statistic to get an idea of how similar subjects are within each cluster. The Silhouette statistic of subject *i* is computed as:

$$s_i = \frac{b_i - a_i}{\max(a_i, b_i)}$$

with $-1 \le s_i \le 1$. $a_i$ captures the average dissimilarity between *i* and all other subjects within the same cluster. $b_i$ is the average dissimilarity between *i* and all subjects in the neighboring cluster (that is, the next best-fit cluster for *i*). If $s_i$ is close to 1, it means that *i* is appropriately clustered. In contrast, if $s_i$ is close to -1, it means that *i* would be more appropriately clustered in the neighboring cluster.

Figure D1 plots the Silhouette statistic for all subjects, sorting them according to their dissimilarity rank. For most subjects, the Silhouette statistic is positive. This indicates that they are appropriately grouped. Most subjects who display negative statistics belong
to the category “Others”, confirming that this is a residual category that contains more heterogeneous profiles. All in all, our cluster analysis generates a robust classification of subjects that we can confidently rely on for the analysis presented in the main paper.

<figure><img src="image_8.png" /></figure>

Notes: Strongly dishonest are in orange, Honest subjects are in green, Conditional dishonest subjects are in red, and Others are in blue.

<caption>Figure D1: Silhouette plot</caption>

## D.3 Regression analysis on maximal lying

Table D3 reports the estimates of two linear probability models, where the dependent variable is a dummy that takes the value 1 if a treated subject reported six heads, and zero otherwise.<fnref n="40" /> In Model 1, the independent variables are the treatment dummies (using SUB-ACT as the reference category), the belief faced by the subject in a given situation, and the interaction terms between the treatment dummies and the belief. In Model 2,

<footnote n="40">⁴⁰We also analyzed the data using logit models. The results are qualitatively the same. Logit models are more suitable to analyze binary choice data than linear probability models, but the interpretation of the interaction terms is more complicated.</footnote>
<table><thead><tr><th></th><th>(1)</th><th>(2)</th></tr></thead><tbody><tr><td>Belief</td><td>-0.05*<br>(0.03)</td><td>-0.05*<br>(0.03)</td></tr><tr><td>COMP-ACT</td><td>-0.20**<br>(0.08)</td><td>-0.15**<br>(0.07)</td></tr><tr><td>COMP-PASS</td><td>-0.12<br>(0.08)</td><td>-0.12*<br>(0.07)</td></tr><tr><td>SUB-PASS</td><td>-0.06<br>(0.09)</td><td>-0.03<br>(0.07)</td></tr><tr><td>Belief × COMP-ACT</td><td>0.11***<br>(0.04)</td><td>0.11***<br>(0.04)</td></tr><tr><td>Belief × COMP-PASS</td><td>0.12***<br>(0.04)</td><td>0.12***<br>(0.04)</td></tr><tr><td>Belief × SUB-PASS</td><td>-0.01<br>(0.04)</td><td>-0.01<br>(0.04)</td></tr><tr><td>Social desirability</td><td></td><td>0.00<br>(0.01)</td></tr><tr><td>Male</td><td></td><td>0.09*<br>(0.05)</td></tr><tr><td>Age</td><td></td><td>-0.06***<br>(0.02)</td></tr><tr><td>Experience</td><td></td><td>0.15***<br>(0.02)</td></tr><tr><td>Risk taking</td><td></td><td>-0.01<br>(0.01)</td></tr><tr><td>Constant</td><td>0.45***<br>(0.06)</td><td>1.50***<br>(0.46)</td></tr><tr><td>Observations</td><td>656</td><td>656</td></tr><tr><td>R-squared</td><td>0.040</td><td>0.217</td></tr><tr><td>Log-likelihood</td><td>-433.438</td><td>-366.661</td></tr></tbody></table>

Notes: *p* < 0.1, **p* < 0.05, ***p* < 0.01. Linear probability regressions with clustered standard errors (in parentheses) at the subject level. Belief is centered to avoid multicollinearity problems (Marquardt, 1980).

<caption>Table D3: Determinants of Maximal Lying in Stage 2</caption>
we also include controls for individual characteristics (age, gender, previous experience in lab experiments, risk attitude, and social desirability). Standard errors are clustered at the subject level. The results are in line with those reported in the main paper (see Table D1) with two distinctions. First, in the Substitutes treatments, the probability of lying to the full extent decreases in the belief, but only weakly significantly so. Second, there is some (weakly significant) evidence that male subjects are more likely to lie to the full extent than female subjects.

## D.4 Regression analysis without subjects who always lie to the full extent in all situations

In Table D4, we replicate the regression analysis of Table D1 but with the exclusion of subjects who always lie to the full extent in all situations. The results remain robust. Moreover, note that in Model (1) we find weakly significant evidence for a lower intercept in SUB-PASS compared to SUB-ACT.

## D.5 Separate regression analysis for the *Active* and *Passive* conditions

In Table D5, we test the robustness of the results reported in Table D1 by running separate regressions for the *Active* and *Passive* conditions. The first two columns (1 and 2) refer to the *Active* condition. The last two columns (3 and 4) refer to the *Passive* condition. The results are consistent with those reported in the main part of the paper. The only notable difference is in the coefficient of the Male dummy that turns out to be significant in *Passive*, suggesting that male subjects lie more than female subjects in that condition.
<table><thead><tr><th></th><th>(1)</th><th>(2)</th></tr></thead><tbody><tr><td>Belief</td><td>-0.47***<br>(0.16)</td><td>-0.49***<br>(0.16)</td></tr><tr><td>COMP-ACT</td><td>-1.15***<br>(0.38)</td><td>-1.00***<br>(0.32)</td></tr><tr><td>COMP-PASS</td><td>-0.80**<br>(0.34)</td><td>-0.84***<br>(0.28)</td></tr><tr><td>SUB-PASS</td><td>-0.74*<br>(0.43)</td><td>-0.57<br>(0.36)</td></tr><tr><td>Belief × COMP-ACT</td><td>0.95***<br>(0.25)</td><td>0.95***<br>(0.24)</td></tr><tr><td>Belief × COMP-PASS</td><td>1.09***<br>(0.25)</td><td>1.11***<br>(0.26)</td></tr><tr><td>Belief × SUB-PASS</td><td>-0.17<br>(0.23)</td><td>-0.16<br>(0.23)</td></tr><tr><td>Social desirability</td><td></td><td>0.04<br>(0.05)</td></tr><tr><td>Male</td><td></td><td>-0.02<br>(0.23)</td></tr><tr><td>Age</td><td></td><td>-0.16<br>(0.10)</td></tr><tr><td>Experience</td><td></td><td>0.61***<br>(0.10)</td></tr><tr><td>Risk taking</td><td></td><td>0.03<br>(0.06)</td></tr><tr><td>Constant</td><td>4.81***<br>(0.26)</td><td>6.81***<br>(2.32)</td></tr><tr><td>Observations</td><td>536</td><td>536</td></tr><tr><td>Right-cens obs.</td><td>112</td><td>112</td></tr><tr><td>Left-cens obs.</td><td>170</td><td>170</td></tr><tr><td>Pseudo R2</td><td>0.030</td><td>0.074</td></tr><tr><td>Log-likelihood</td><td>-802.091</td><td>-766.474</td></tr></tbody></table>

Notes: *p* < 0.1, **p* < 0.05, ***p* < 0.01. To-bit regressions with clustered standard errors (in parentheses) at the subject level. Belief is centered to avoid multicollinearity problems (Marquardt, 1980).

<caption>Table D4: Determinants of Lying Behavior in Stage 2 (restricted sample)</caption>
<table><thead><tr><th rowspan="2"></th><th colspan="2">Active</th><th colspan="2">Passive</th></tr><tr><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th></tr></thead><tbody><tr><td>Belief</td><td>-0.46***<br>(0.16)</td><td>-0.50***<br>(0.17)</td><td>-0.64***<br>(0.18)</td><td>-0.65***<br>(0.18)</td></tr><tr><td>COMP-ACT</td><td>-1.30***<br>(0.50)</td><td>-0.97**<br>(0.40)</td><td></td><td></td></tr><tr><td>Belief × COMP-ACT</td><td>0.92***<br>(0.25)</td><td>0.95***<br>(0.25)</td><td></td><td></td></tr><tr><td>COMP-PASS</td><td></td><td></td><td>-0.07<br>(0.59)</td><td>-0.21<br>(0.49)</td></tr><tr><td>Belief × COMP-PASS</td><td></td><td></td><td>1.26***<br>(0.27)</td><td>1.27***<br>(0.27)</td></tr><tr><td>Social desirability</td><td></td><td>-0.03<br>(0.10)</td><td></td><td>0.07<br>(0.08)</td></tr><tr><td>Male</td><td></td><td>-0.51<br>(0.41)</td><td></td><td>1.08**<br>(0.47)</td></tr><tr><td>Age</td><td></td><td>-0.36**<br>(0.17)</td><td></td><td>-0.50**<br>(0.22)</td></tr><tr><td>Experience</td><td></td><td>0.96***<br>(0.17)</td><td></td><td>1.01***<br>(0.18)</td></tr><tr><td>Risk taking</td><td></td><td>0.01<br>(0.12)</td><td></td><td>0.08<br>(0.11)</td></tr><tr><td>Constant</td><td>5.51***<br>(0.36)</td><td>12.12***<br>(3.87)</td><td>4.87***<br>(0.46)</td><td>12.29***<br>(4.45)</td></tr><tr><td>Observations</td><td>332</td><td>332</td><td>324</td><td>324</td></tr><tr><td>Right-cens obs.</td><td>116</td><td>116</td><td>116</td><td>116</td></tr><tr><td>Left-cens obs.</td><td>82</td><td>82</td><td>88</td><td>88</td></tr><tr><td>Pseudo R2</td><td>0.026</td><td>0.095</td><td>0.0130</td><td>0.105</td></tr><tr><td>Log-likelihood</td><td>-488.383</td><td>-453.871</td><td>-475.695</td><td>-431.489</td></tr></tbody></table>

Notes: *p* < 0.1, **p* < 0.05, ***p* < 0.01. Tobit regressions with clustered standard errors (in parentheses) at the subject level. Belief is centered to avoid multicollinearity problems (Marquardt, 1980).

<caption>Table D5: Determinants of Lying Behavior in Stage 2</caption>
## D.6 Alternative specifications of beliefs

In our main analysis, we use the information we provide to subjects as a measure of their beliefs. To make beliefs across subjects more comparable, we also told them that 90% of subjects in a previous experiment reported in the second stage either the same number of heads as in the first stage or a number that was one higher or lower. In the Online Appendix A, we show that this manipulation worked as intended.

In this section, we show that our results are robust to alternative ways of specifying beliefs. One option is to assume that subjects have rational expectations, that is, they form, on average, correct beliefs about the behavior of the counterpart based on the information provided. We replicate our main analysis using the actual average report of the untreated subjects in the second stage for each possible report in the first stage as a treated subject's belief. For example, in the situation where treated subjects are told that their counterpart reported four heads in the first stage, instead of assigning “4” to the belief variable, we calculate the average report in the second stage of all untreated subjects who reported four heads in the first stage. The average report is computed for each incentive condition separately. We then perform the same regression analysis of Table D1. We report this analysis in the third and fourth columns of Table D6. In the first two columns, we display the results of Table D1 for comparison.

Another option is to use the average stated beliefs of the subjects who participated in the manipulation check, with the idea that subjects should have roughly equal beliefs in the main experiment. For example, in the situation where subjects are told that their counterpart reported five heads in the first stage, we replaced “5” with the corresponding average stated belief of the subjects who participated in the manipulation check (that is, their average belief regarding the second stage report of untreated subjects who reported five heads in the first stage). The average report is computed for each incentive condition separately. We report the results of this analysis in the last two columns of Table D6. The
table shows that our results are robust to different ways of specifying subjects' beliefs.

<table><thead><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th><th>(6)</th></tr></thead><tbody><tr><td>Belief</td><td>-0.47***<br>(0.17)</td><td>-0.50***<br>(0.17)</td><td>-0.44***<br>(0.16)</td><td>-0.47***<br>(0.16)</td><td>-0.47***<br>(0.17)</td><td>-0.50***<br>(0.17)</td></tr><tr><td>COMP-ACT</td><td>-1.36***<br>(0.52)</td><td>-1.05**<br>(0.43)</td><td>-1.24**<br>(0.52)</td><td>-0.93**<br>(0.43)</td><td>-1.61***<br>(0.53)</td><td>-1.31**<br>(0.44)</td></tr><tr><td>COMP-PASS</td><td>-0.77<br>(0.50)</td><td>-0.75*<br>(0.39)</td><td>-0.77<br>(0.49)</td><td>-0.75*<br>(0.40)</td><td>-1.13**<br>(0.49)</td><td>-1.13***<br>(0.40)</td></tr><tr><td>SUB-PASS</td><td>-0.70<br>(0.56)</td><td>-0.55<br>(0.44)</td><td>-0.58<br>(0.56)</td><td>-0.42<br>(0.44)</td><td>-0.52<br>(0.57)</td><td>-0.36<br>(0.45)</td></tr><tr><td>Belief × COMP-ACT</td><td>0.96***<br>(0.25)</td><td>0.97***<br>(0.25)</td><td>0.86***<br>(0.23)</td><td>0.87***<br>(0.22)</td><td>0.95***<br>(0.25)</td><td>0.96***<br>(0.25)</td></tr><tr><td>Belief × COMP-PASS</td><td>1.07***<br>(0.25)</td><td>1.11***<br>(0.26)</td><td>0.83***<br>(0.25)</td><td>0.89***<br>(0.25)</td><td>1.06***<br>(0.26)</td><td>1.10***<br>(0.26)</td></tr><tr><td>Belief × SUB-PASS</td><td>-0.14<br>(0.23)</td><td>-0.13<br>(0.24)</td><td>-0.15<br>(0.24)</td><td>-0.14<br>(0.24)</td><td>-0.13<br>(0.23)</td><td>-0.13<br>(0.24)</td></tr><tr><td>Social desirability</td><td></td><td>0.04<br>(0.06)</td><td></td><td>0.04<br>(0.06)</td><td></td><td>0.04<br>(0.06)</td></tr><tr><td>Male</td><td></td><td>0.25<br>(0.31)</td><td></td><td>0.25<br>(0.31)</td><td></td><td>0.25<br>(0.31)</td></tr><tr><td>Age</td><td></td><td>-0.39***<br>(0.14)</td><td></td><td>-0.39***<br>(0.14)</td><td></td><td>-0.39***<br>(0.14)</td></tr><tr><td>Experience</td><td></td><td>0.96***<br>(0.13)</td><td></td><td>0.97***<br>(0.13)</td><td></td><td>0.97***<br>(0.13)</td></tr><tr><td>Risk taking</td><td></td><td>0.00<br>(0.08)</td><td></td><td>0.00<br>(0.08)</td><td></td><td>0.00<br>(0.08)</td></tr><tr><td>Constant</td><td>5.55***<br>(0.36)</td><td>11.77***<br>(2.98)</td><td>5.46***<br>(0.36)</td><td>11.66***<br>(2.98)</td><td>5.55***<br>(0.36)</td><td>11.77***<br>(2.98)</td></tr><tr><td>Observations</td><td>656</td><td>656</td><td>656</td><td>656</td><td>656</td><td>656</td></tr><tr><td>Right-cens obs.</td><td>232</td><td>232</td><td>232</td><td>232</td><td>232</td><td>232</td></tr><tr><td>Left-cens obs.</td><td>170</td><td>170</td><td>170</td><td>170</td><td>170</td><td>170</td></tr><tr><td>Pseudo R2</td><td>0.020</td><td>0.092</td><td>0.015</td><td>0.087</td><td>0.015</td><td>0.087</td></tr><tr><td>Log-likelihood</td><td>-964.760</td><td>-893.342</td><td>-968.743</td><td>-898.376</td><td>-965.085</td><td>-893.716</td></tr></tbody></table>

Notes: *p < 0.1, **p < 0.05, ***p < 0.01. Tobit regressions with clustered standard errors (in parentheses) at the subject level. Belief is centered to avoid multicollinearity problems (Marquardt, 1980).

<caption>Table D6: Determinants of Lying Behavior in Stage 2</caption>
## D.7 Social preferences and group dishonesty

The final questionnaire of the experiment includes an incentivized measure of distribu-
tional preferences taken from Kerschbamer (2015). To measure these preferences, we ask
subjects to make 10 binary choices about how to distribute money between themselves
and another subject. Table D7 lists the 10 allocation choices. For each participant, a
decision is randomly selected to determine the payment for this task.

Following (Kerschbamer, 2015)'s procedure to classify the subjects, we identify five
types of subjects: altruistic, inequality averse, equality averse, spiteful, and selfish. Figure
D2 provides an overview of this classification (the code to generate this figure is taken
from Galeotti and Zizzo, 2018).

Most subjects have altruistic preferences (72.87%). 11.89% of the subjects can be classified as inequality averse, while 7.62% as equality averse. Spiteful types account for only 3.96% of the subjects. 3.66% subjects did not pass the consistency check and are classified as inconsistent. Selfish subjects are a weak manifestation of the other types (i.e., altruistic, inequality averse, equality averse, and spiteful subjects) and represent 46.04% of all participants.

<table><caption>Table D7: Allocation Choices in the Kerschbamer (2015)'s Task</caption><thead><tr><th colspan="2">Right allocation</th><th colspan="2">Left allocation</th></tr><tr><th>Your gain</th><th>Other person's gain</th><th>Your gain</th><th>Other person's gain</th></tr></thead><tbody><tr><td>€0.80</td><td>€1.30</td><td>€1.00</td><td>€1.00</td></tr><tr><td>€0.90</td><td>€1.30</td><td>€1.00</td><td>€1.00</td></tr><tr><td>€1.00</td><td>€1.30</td><td>€1.00</td><td>€1.00</td></tr><tr><td>€1.10</td><td>€1.30</td><td>€1.00</td><td>€1.00</td></tr><tr><td>€1.20</td><td>€1.30</td><td>€1.00</td><td>€1.00</td></tr><tr><td>€0.80</td><td>€0.70</td><td>€1.00</td><td>€1.00</td></tr><tr><td>€0.90</td><td>€0.70</td><td>€1.00</td><td>€1.00</td></tr><tr><td>€1.00</td><td>€0.70</td><td>€1.00</td><td>€1.00</td></tr><tr><td>€1.10</td><td>€0.70</td><td>€1.00</td><td>€1.00</td></tr><tr><td>€1.20</td><td>€0.70</td><td>€1.00</td><td>€1.00</td></tr></tbody></table>
<figure><img src="image_9.png" /><figcaption>Figure D2: Distributional types based on the Kerschbamer (2015)'s task

*Notes*: Observations are jittered; inconsistent subjects (N=12) are not included in the figure.</figcaption></figure>

In the remainder of the analysis, we will focus only on selfish and strongly altruistic types. We exclude (in)equality averse subjects, spiteful subjects, and inconsistent subjects. (In)equality-averse preferences cannot explain the behavior in the coin-flip task because subjects always receive the same payoff within a pair. Hence, focusing on (in)equality averse subjects is not particularly interesting. Spiteful and inconsistent subjects are too few to be analyzed with sufficient precision.

In Stage 1, selfish subjects report a slightly higher number of heads than altruistic subjects, but the difference is not statistically significant (Mann-Whitney tests: 4.68 vs. 4.52 in Complements, *p* = 0.397; 4.92 vs. 4.69 in Substitutes, *p* = 0.160).<sup>41</sup>

We next examine whether the behavior of selfish and altruistic types differs in Stage 2. We performed a regression analysis similar to the one reported in Table D1, but

<footnote n="41"><sup>41</sup>Both types of subjects report a higher number of heads than what is expected under truthful reporting (Wilcoxon signed-rank tests, *p* < 0.001).</footnote>
with the inclusion of a dummy for altruistic subjects and interaction terms between
this dummy and the other variables (except the demographic controls). The results are
reported in Table D8. We find that selfish and altruistic subjects do not differ much in
the way they respond to changes in beliefs across treatments. That is, both types of
subjects increase (decrease) their report as a function of their beliefs in the *Substitutes*
(*Complements*) condition. However, we find that altruistic subjects lie less than selfish
subjects in COMP-ACT (the coefficient of “Altruistic × COMP-ACT” is negative and
significant) compared to the other treatments.<fnref n="42" />

<footnote n="42">⁴²There is also some weak evidence that they lie less in SUB-PASS than SUB-ACT and COMP-PASS (the coefficient of Altruistic × SUB-PASS is negative but only weakly significant in Model (1), which suggests caution in interpreting this result).</footnote>
<table><thead><tr><th></th><th>(1)</th><th>(2)</th></tr></thead><tbody><tr><td>Belief</td><td>-0.62**<br>(0.29)</td><td>-0.64**<br>(0.29)</td></tr><tr><td>COMP-ACT</td><td>-0.59<br>(0.76)</td><td>-0.02<br>(0.67)</td></tr><tr><td>COMP-PASS</td><td>-0.76<br>(0.71)</td><td>-0.93<br>(0.61)</td></tr><tr><td>SUB-PASS</td><td>0.28<br>(0.93)</td><td>0.36<br>(0.77)</td></tr><tr><td>Belief × COMP-ACT</td><td>1.03***<br>(0.39)</td><td>1.05***<br>(0.39)</td></tr><tr><td>Belief × COMP-PASS</td><td>1.25***<br>(0.38)</td><td>1.28***<br>(0.38)</td></tr><tr><td>Belief × SUB-PASS</td><td>-0.07<br>(0.37)</td><td>-0.10<br>(0.38)</td></tr><tr><td>Altruistic</td><td>-0.34<br>(0.82)</td><td>0.00<br>(0.65)</td></tr><tr><td>Altruistic × Belief</td><td>0.22<br>(0.39)</td><td>0.18<br>(0.40)</td></tr><tr><td>COMP-ACT × Altruistic</td><td>-1.74<br>(1.14)</td><td>-2.03**<br>(0.99)</td></tr><tr><td>COMP-PASS × Altruistic</td><td>-0.08<br>(1.14)</td><td>0.59<br>(0.99)</td></tr><tr><td>SUB-PASS × Altruistic</td><td>-2.19*<br>(1.27)</td><td>-1.75<br>(1.07)</td></tr><tr><td>COMP-ACT × Altruistic × Belief</td><td>-0.37<br>(0.52)</td><td>-0.35<br>(0.52)</td></tr><tr><td>COMP-PASS × Altruistic × Belief</td><td>-0.41<br>(0.57)</td><td>-0.39<br>(0.57)</td></tr><tr><td>SUB-PASS × Altruistic × Belief</td><td>-0.40<br>(0.56)</td><td>-0.31<br>(0.57)</td></tr><tr><td>Social desirability</td><td></td><td>0.03<br>(0.07)</td></tr><tr><td>Male</td><td></td><td>0.25<br>(0.36)</td></tr><tr><td>Age</td><td></td><td>-0.48***<br>(0.15)</td></tr><tr><td>Experience</td><td></td><td>0.93***<br>(0.14)</td></tr><tr><td>Risk taking</td><td></td><td>0.06<br>(0.10)</td></tr><tr><td>Constant</td><td>5.85***<br>(0.53)</td><td>13.31***<br>(3.27)</td></tr><tr><td>Observations</td><td>556</td><td>556</td></tr><tr><td>Right-cens obs.</td><td>206</td><td>206</td></tr><tr><td>Left-cens obs.</td><td>142</td><td>142</td></tr><tr><td>Pseudo R-squared</td><td>0.046</td><td>0.113</td></tr><tr><td>Log-likelihood</td><td>-788.596</td><td>-732.971</td></tr></tbody></table>

Notes: *p* < 0.1, **p* < 0.05, ***p* < 0.01. Tobit regressions with clustered standard errors (in parentheses) at the subject level. Belief is centered to avoid multicollinearity problems (Marquardt, 1980). Subjects classified as equality averse, inequality averse, spiteful, or inconsistent are excluded.

<caption>Table D8: Determinants of Lying Behavior in Stage 2</caption>
# E Instructions

*THE INSTRUCTIONS ARE TRANSLATED IN ENGLISH FROM FRENCH*

## E.1 Main experiment

*Instructions for first stage were handed out at the beginning of the experiment (Instructions for Active and Passive treatment are the same here)*

### General instructions

Welcome and thank you for taking part in this experiment.

You will receive 5 euros for showing up on time (participation fee). During the course of the experiment, you may earn additional money based on your decisions, the decisions of other participants and chance. It is therefore essential that you read these instructions carefully and understand them. You will make your decisions alone and in private.

Please take a moment to turn off your phone before you begin. Please do not communicate with other participants in the room. If you have any questions during the experiment, press the red button on the left of your desk and we'll come and answer you privately.

Today's experiment is divided into two parts, followed by a questionnaire. At the beginning of each part, you will receive the corresponding instructions. The instructions are the same for all participants. At the end of the experiment, a part will be drawn by the computer program and you will be paid according to the earnings made in this part. In addition, you can earn extra money by answering some of the questions in the final questionnaire. During the experiment, your decisions may be shown to other participants. However, all your decisions will remain anonymous, and at no time will your identity be revealed to another participant. Similarly, you will never know the identity of other participants.
## Instructions : Part 1

In this part, you'll be asked to flip a coin several times.

### Where is the coin?

On your table, there's a coin in a cup. Open the lid. Take the coin out of the cup and inspect it. As you'll see, there are only two possible outcomes: TAILS or HEADS. The TAILS side of the coin refers to the side of the coin that shows the coin's value; the HEADS side of the coin refers to the side of the coin that shows the image (see below). The probability of flipping heads or tails is 50%. Put the coin back into the cup and close the lid. The lid has an opening. If you look through this opening, you'll see the top of the coin.

<figure><img src="image_10.png" /></figure>

### How does the coin flip work in this experiment?

When you're asked to flip a coin, pick up the cup, shake it a few times, then place it back on the table in front of you. Then look through the opening in the lid and report the result of the coin flip by entering it into the computer.

Now, please try it a few times to see how it works and make sure you've understood the procedure.

### Pairing and roles

You will be randomly paired with another participant. You and this other participant will be called *co-participants*.
One of you will be randomly assigned the role of **YELLOW co-participant** and the other the role of **BLUE co-participant**. You won't know your role until the end of the instructions in Part 1.

Whatever your role, you'll be asked to flip a coin six times and report the total number of heads you've observed.

## Earnings

Your earnings depend on your report and that of your co-participant, as illustrated in the table below. The table reads as follows. The rows (yellow boxes) show the possible number of heads that the YELLOW co-participant could report from the six coin flips. The columns (blue boxes) show the possible number of heads that the BLUE co-participant could report. The earnings of each co-participant are displayed in euros in the table and depend on the combination of the two reports. Note that the winnings of the two co-participants are identical in each box.

Please note that you will be informed of your earnings from Part 1 at the end of the experiment. At that time, you will also be informed of your co-participant's report. Similarly, your co-participant will be informed of your report.

<table><caption>Table D1: *Complements* treatment</caption><thead><tr><th rowspan="2"></th><th rowspan="2"></th><th colspan="4">Report of the BLUE co-participant:</th></tr><tr><th>6 heads</th><th>5 heads</th><th>4 heads</th><th>3 heads<br>or less</th></tr></thead><tbody><tr><th rowspan="4" scope="rowgroup">Report of the YELLOW<br>co-participant:</th><th scope="row">6 heads</th><td>6 €</td><td>5 €</td><td>4 €</td><td>3 €</td></tr><tr><th scope="row">5 heads</th><td>5 €</td><td>5 €</td><td>4 €</td><td>3 €</td></tr><tr><th scope="row">4 heads</th><td>4 €</td><td>4 €</td><td>4 €</td><td>3 €</td></tr><tr><th scope="row">3 heads<br>or less</th><td>3 €</td><td>3 €</td><td>3 €</td><td>3 €</td></tr></tbody></table>
<table><caption>Table D2: *Substitutes* treatment</caption><thead><tr><th colspan="2"></th><th colspan="4">Report of the BLUE co-participant:</th></tr><tr><th colspan="2"></th><th>6 heads</th><th>5 heads</th><th>4 heads</th><th>3 heads<br>or less</th></tr></thead><tbody><tr><th rowspan="4">Report of the YELLOW<br>co-participant:</th><th>6 heads</th><td>6 €</td><td>6 €</td><td>6 €</td><td>6 €</td></tr><tr><th>5 heads</th><td>6 €</td><td>5 €</td><td>5 €</td><td>5 €</td></tr><tr><th>4 heads</th><td>6 €</td><td>5 €</td><td>4 €</td><td>4 €</td></tr><tr><th>3 heads<br>or less</th><td>6 €</td><td>5 €</td><td>4 €</td><td>3 €</td></tr></tbody></table>

*Before proceeding to the Coin Flip task, subjects were asked to calculate the payments for three different, randomly generated pairs of reports. They could only proceed if they entered the correct answer.*

*Instructions for second stage were handed out after the first stage.*

*Instructions for Active treatment:*

**Instructions : Part 2**

In this part, you will be randomly paired with a new co-participant. This participant will not be the same as the one you were paired with in Part 1.

One of you will be randomly assigned the role of **VIOLET co-participant** and the other the role of **ORANGE co-participant**. You will not know your role until the end of these instructions.

Regardless of your role, you'll be asked to flip the coin several times, and report the total number of heads observed.

Below, you'll find instructions for the VIOLET and ORANGE co-participants, and learn how the earnings are determined.
## Instructions for the VIOLET co-participant

If you are the VIOLET co-participant, you will be confronted with 4 different situations. In each situation, you will be informed of the number of heads your current co-participant (i.e. the ORANGE co-participant) has reported in Part 1.

However, in only one situation is the information provided real, i.e. it concerns your current co-participant. In the other three situations, the information provided is set by the computer at random or selected by the experimenter on the basis of the behavior of participants who have taken part in previous sessions of this experiment.

In each situation, you will flip a coin six times, and report the total number of heads you have observed (as in Part 1).

Your earnings will be determined by your report in the real situation, and by the report of co-participant ORANGE. As you do not know in advance which situation is the real one, it is possible that any of the 4 situations will be used to calculate your earnings in Part 2. It is therefore in your best interest to treat each situation as if it was real.

## Instructions for the ORANGE co-participant

If you are the ORANGE co-participant, you will not receive any information about your current co-participant (i.e. the VIOLET co-participant).

You'll flip the coin six times and report the total number of heads you observe (as in Part 1).

Your earnings will be determined by your report and the report of the VIOLET co-participant in the real situation.

### Earnings

Your earnings depend on your report and that of your co-participant, as illustrated in the table below. The table reads as follows. The rows (VIOLET boxes) indicate the possible number of heads that the VIOLET co-participant could report from the six coin flips. Remember that only his report in the real situation will be taken into
**account.** The columns (ORANGE boxes) show the possible number of heads that the ORANGE co-participant could report. The earnings of each co-participant are displayed in euros in the table and depend on the combination of the two reports. Note that the earnings are the same as in Part 1, and are identical in each box for both co-participants.

Please note that you will be informed of your earnings in Part 2 at the end of the experiment. At that point, you will also be informed of your co-participant's report. Similarly, your co-participant will be informed of your report.

<table><caption>Table D3: *Complements* treatment</caption><thead><tr><th colspan="2"></th><th colspan="4">Report of the BLUE co-participant:</th></tr><tr><th colspan="2"></th><th>6 heads</th><th>5 heads</th><th>4 heads</th><th>3 heads<br>or less</th></tr></thead><tbody><tr><th rowspan="3" scope="rowgroup">Report of the YELLOW<br>co-participant:</th><th scope="row">6 heads</th><td>6 €</td><td>5 €</td><td>4 €</td><td>3 €</td></tr><tr><th scope="row">5 heads</th><td>5 €</td><td>5 €</td><td>4 €</td><td>3 €</td></tr><tr><th scope="row">4 heads</th><td>4 €</td><td>4 €</td><td>4 €</td><td>3 €</td></tr><tr><th colspan="2"></th><th>3 heads<br>or less</th><td>3 €</td><td>3 €</td><td>3 €</td><td>3 €</td></tr></tbody></table>

<table><caption>Table D4: *Substitutes* treatment</caption><thead><tr><th colspan="2"></th><th colspan="4">Report of the BLUE co-participant:</th></tr><tr><th colspan="2"></th><th>6 heads</th><th>5 heads</th><th>4 heads</th><th>3 heads<br>or less</th></tr></thead><tbody><tr><th rowspan="3" scope="rowgroup">Report of the YELLOW<br>co-participant:</th><th scope="row">6 heads</th><td>6 €</td><td>6 €</td><td>6 €</td><td>6 €</td></tr><tr><th scope="row">5 heads</th><td>6 €</td><td>5 €</td><td>5 €</td><td>5 €</td></tr><tr><th scope="row">4 heads</th><td>6 €</td><td>5 €</td><td>4 €</td><td>4 €</td></tr><tr><th colspan="2"></th><th>3 heads<br>or less</th><td>6 €</td><td>5 €</td><td>4 €</td><td>3 €</td></tr></tbody></table>
To summarize:

* If you are the VIOLET co-participant:

- In each situation, you will be informed of the number of stacks your current co-participant (i.e. the ORANGE co-participant) reported in Part 1.

- Only one of these situations will contain the actual information about your current co-participant. In the other 3 situations, the information provided is set by the computer at random or selected by the experimenter based on the behavior of participants who have taken part in previous sessions of this experiment.

- In each situation, you will flip a coin six times and report the total number of piles you have observed (as in Part 1).

* If you are the ORANGE co-participant:

- You will receive no information about your current co-participant (i.e. the VIOLET co-participant).

- You will flip the coin six times, and that one time, and report the total number of heads observed (as in Part 1).

* The earnings will be determined by the report of the VIOLET co-participant in the real situation and by the report of the ORANGE co-participant.

*Instructions for Passive treatment:*

**Instructions : Part 2**

In this part, you will be randomly paired with a new co-participant. This participant will not be the same as the one you were paired with in Part 1.
One of you will be randomly assigned the role of **VIOLET co-participant** and the
other the role of **ORANGE co-participant**. You will not know your role until the end
of these instructions.

Only the VIOLET co-participant will be asked to flip the coin several times and report
the total number of heads observed. The ORANGE co-participant will not flip a coin.
He will be assigned the report of a participant who took part in a previous session, as
explained in the instructions below.

Below, you'll find instructions for the VIOLET and ORANGE co-participants, and
learn how the earnings are determined.

***Instructions for the VIOLET co-participant***

If you are the VIOLET co-participant, you will be confronted with 4 different situations. In each situation, you will be informed of the number of heads your current co-participant (i.e. the ORANGE co-participant) has reported in Part 1.

However, in only one situation is the information provided real, i.e. it concerns your
current co-participant. In the other three situations, the information provided is set by
the computer at random or selected by the experimenter on the basis of the behavior of
participants who have taken part in previous sessions of this experiment.

In each situation, you will flip a coin six times, and report the total number of heads
you have observed (as in Part 1).

Your earnings will be determined by your report in the real situation, and by the
report assigned to the ORANGE co-participant. Since you do not know in advance what
the real situation is, it is possible that any of the 4 situations will be used to calculate
your earnings in Part 2. So it's in your best interest to treat each situation as if it
were real. Below, we'll explain the procedure used to assign the report to the ORANGE
co-participant.

***Instructions for the ORANGE co-participant***
If you are the ORANGE co-participant, you will not receive any information about
your current co-participant (i.e. the VIOLET co-participant).

You will not flip the coin or make an active report in Part 2. Your report will be
determined by the following procedure.

* We have collected reports from ORANGE co-participants in previous sessions who, unlike you, flipped the coin six times in Part 2, and reported the total number of heads they observed.

* The computer will randomly select one of these ORANGE co-participants who reported exactly the same number of heads as you in Part 1, i.e. 6 heads, 5 heads, 4 heads or 3 heads or less.

* Your report in Part 2 will be equal to what that ORANGE co-participant reported in Part 2.

Your earnings will be determined by the report assigned to you by the computer and
by the VIOLET co-participant's report in the real situation.

## Earnings

Your earnings depend on your report and that of your co-participant, as illustrated
in the table below. The table reads as follows. The rows (VIOLET boxes) indicate the
possible number of heads that the VIOLET co-participant could report from the six coin
flips. **Remember that only his report in the real situation will be taken into account.** The columns (ORANGE boxes) indicate the possible number of heads that could be assigned to the ORANGE co-participant. The earnings of each co-participant are displayed in euros in the table and depend on the combination of the two reports. Note that the earnings are the same as in Part 1, and are identical in each box for both co-participants.
Please note that you will be informed of your earnings in Part 2 at the end of the experiment. At that point, you will also be informed of your co-participant's report. Similarly, your co-participant will be informed of your report.

<table><caption>Table D5: *Complements* treatment</caption><thead><tr><th rowspan="2"></th><th rowspan="2"></th><th colspan="4">Report of the BLUE co-participant:</th></tr><tr><th>6 heads</th><th>5 heads</th><th>4 heads</th><th>3 heads<br>or less</th></tr></thead><tbody><tr><th rowspan="2">Report of the YELLOW</th><th>6 heads</th><td>6 €</td><td>5 €</td><td>4 €</td><td>3 €</td></tr><tr><th>5 heads</th><td>5 €</td><td>5 €</td><td>4 €</td><td>3 €</td></tr><tr><th rowspan="2">co-participant:</th><th>4 heads</th><td>4 €</td><td>4 €</td><td>4 €</td><td>3 €</td></tr><tr><th>3 heads<br>or less</th><td>3 €</td><td>3 €</td><td>3 €</td><td>3 €</td></tr></tbody></table>

<table><caption>Table D6: *Substitutes* treatment</caption><thead><tr><th rowspan="2"></th><th rowspan="2"></th><th colspan="4">Report of the BLUE co-participant:</th></tr><tr><th>6 heads</th><th>5 heads</th><th>4 heads</th><th>3 heads<br>or less</th></tr></thead><tbody><tr><th rowspan="2">Report of the YELLOW</th><th>6 heads</th><td>6 €</td><td>6 €</td><td>6 €</td><td>6 €</td></tr><tr><th>5 heads</th><td>6 €</td><td>5 €</td><td>5 €</td><td>5 €</td></tr><tr><th rowspan="2">co-participant:</th><th>4 heads</th><td>6 €</td><td>5 €</td><td>4 €</td><td>4 €</td></tr><tr><th>3 heads<br>or less</th><td>6 €</td><td>5 €</td><td>4 €</td><td>3 €</td></tr></tbody></table>

To summarize:

* If you are the VIOLET co-participant:
- In each situation, you will be informed of the number of stacks your current co-participant (i.e. the ORANGE co-participant) reported in Part 1.

- Only one of these situations will contain the actual information about your current co-participant. In the other 3 situations, the information provided is set by the computer at random or selected by the experimenter based on the behavior of participants who have taken part in previous sessions of this experiment.

- In each situation, you will flip a coin six times and report the total number of piles you have observed (as in Part 1).

* If you are the ORANGE co-participant:

- You will not receive any information about your current co-participant (i.e. the VIOLET co-participant).

- You will not flip the coin or make an active report in Part 2. Your report will be equal to the Part 2 report of a previous ORANGE co-participant who reported exactly the same number of heads as you did in Part 1, i.e. 6 heads, 5 heads, 4 heads or 3 heads or less.

* The earnings will be determined by the report of the VIOLET co-participant in the real situation and by the report assigned to the ORANGE co-participant.

*Before proceeding to the Coin Flip task, subjects were asked to calculate the payments for three different, randomly generated pairs of reports. They could only proceed if they entered the correct answer. They were also asked to answer the following questions:*

* The VIOLET co-participant will be confronted with 4 different situations. Only one of these situations will contain the real information about what his current co-participant (ORANGE co-participant) reported in Part 1. TRUE or FALSE
* The VIOLET co-participant will know in advance what the real situation is. TRUE or FALSE

* Only the report of the VIOLET co-participant in the real situation and that of the ORANGE co-participant will count for the calculation of earnings. TRUE or FALSE

* The ORANGE co-participant will be informed of the number of heads the VIOLET co-participant has reported in Part 1. TRUE or FALSE

* (Only Passive treatment) The ORANGE co-participant flips a coin six times and indicates the number of heads he has observed. TRUE or FALSE

Below is a picture of one of the cups participants used to play the Coin Flip task.

<figure><img src="image_11.png" /></figure>
## E.2 Manipulation check

### General instructions

Welcome and thank you for participating in this experiment.

Please take a moment to turn off your phone before you begin. Please do not communicate with other participants in the room. If you have any questions during the experiment, press the red button on the left of your desk and we will come and answer you privately.

In today's experiment, you'll be asked to guess the behavior of other participants, who have taken part in a previous experiment in this laboratory (henceforth the "target experiment"). You will earn a fixed sum of 7 euros for your participation and for carefully reading the instructions. You can earn an additional sum of money if you accurately guess the behavior of the participants in the target experiment. It is therefore essential that you carefully read these instructions and understand them.

In the following instructions, we will describe the instructions the participants received during the target experiment. The target experiment was divided into two parts (Part 1 and Part 2). At the start of each part, participants received the corresponding instructions. The instructions were the same for all participants. At the end of the target experiment, the earnings from one part were randomly selected for the payment of the participants. All decisions were anonymous.

**Your task:** Your task is to guess what the participants did in Part 2 of the target experiment, based on their behavior in Part 1.

### Instructions: target experiment

In both parts of the target experiment, participants had to flip a coin several times and report the result. They were seated in the same cubicles you are currently occupying and made their decisions alone and in private.

*How did the coin flip work in the target experiment?*
Participants had a coin in a cup on their table, like the one you have on your table.

Please take a few seconds to inspect the cup. Open the lid. Take the coin out of the cup and examine it. As you'll see, there are only two possible outcomes: TAILS or HEADS. The TAILS of the coin refers to the side of the coin that shows the coin's value; the HEADS side of the coin refers to the side of the coin that shows the image (see below). The probability of flipping heads or tails is 50%. Put the coin back into the cup and close the lid. The lid has an opening. If you look through this opening, you will see the top of the coin.

When participants in the target experiment were asked to flip a coin, they had to pick up the cup, shake it a few times and place it back on the table in front of them. They then had to look through the opening in the lid and report the result of the coin flip by entering it into the computer.

Now, please try doing this yourself a few times to see how it works and to make sure you understand how the participants in the target experiment flipped a coin.

<figure><img src="image_12.png" /></figure>

## Instructions : Part 1

### Matching and roles

In the first part of the target experiment, participants were randomly paired with another participant.
In each pair, one participant was randomly assigned the role of YELLOW co-participant and the other the role of BLUE co-participant.

Regardless of their role, each was asked to flip the coin six times and report the total number of heads they had observed.

## Earnings

The earnings of the two co-participants in each pair depend on their reports, as illustrated in the table below. The table can be read as follows. The rows (yellow boxes) show the possible number of heads that the YELLOW co-player could report from the six coin flips. The columns (blue boxes) show the possible number of heads that the BLUE co-participant could report. Each co-participant's earnings are displayed in euros in the table and depend on the combination of the two reports. Note that the earnings of both co-participants are identical in each box.

Participants were informed of their earnings from Part 1 at the end of the experiment. At that point, they were also informed of their co-participant's report.

<table><caption>Table D7: *Complements* treatment</caption><thead><tr><th rowspan="2"></th><th rowspan="2"></th><th colspan="4">Report of the BLUE co-participant:</th></tr><tr><th>6 heads</th><th>5 heads</th><th>4 heads</th><th>3 heads<br>or less</th></tr></thead><tbody><tr><th rowspan="4">Report of the YELLOW<br>co-participant:</th><th>6 heads</th><td>6 €</td><td>5 €</td><td>4 €</td><td>3 €</td></tr><tr><th>5 heads</th><td>5 €</td><td>5 €</td><td>4 €</td><td>3 €</td></tr><tr><th>4 heads</th><td>4 €</td><td>4 €</td><td>4 €</td><td>3 €</td></tr><tr><th>3 heads<br>or less</th><td>3 €</td><td>3 €</td><td>3 €</td><td>3 €</td></tr></tbody></table>
<table><caption>Table D8: *Substitutes* treatment</caption><thead><tr><th rowspan="2"></th><th rowspan="2"></th><th colspan="4">Report of the BLUE co-participant:</th></tr><tr><th>6 heads</th><th>5 heads</th><th>4 heads</th><th>3 heads<br>or less</th></tr></thead><tbody><tr><td rowspan="4">Report of the YELLOW co-participant:</td><td>6 heads</td><td>6 €</td><td>6 €</td><td>6 €</td><td>6 €</td></tr><tr><td>5 heads</td><td>6 €</td><td>5 €</td><td>5 €</td><td>5 €</td></tr><tr><td>4 heads</td><td>6 €</td><td>5 €</td><td>4 €</td><td>4 €</td></tr><tr><td>3 heads<br>or less</td><td>6 €</td><td>5 €</td><td>4 €</td><td>3 €</td></tr></tbody></table>

*Before proceeding to the instruction of Stage 2, subjects were asked to calculate the payments for three different, randomly generated pairs of reports. They could only proceed if they entered the correct answer.*

## Instructions : Part 2

In the second part of the target experiment, participants were randomly matched into new pairs. Their partner was not the same co-participant who had been matched with them in Part 1.

In each pair, one of the two co-participants was randomly assigned the role of **VIOLET co-participant** and the other the role of **ORANGE co-participant**.

Regardless of their role, each was asked to flip a coin several times and report the total number of heads they had observed.

### VIOLET co-participant

The **VIOLET co-participant** was confronted with 4 different situations. In each situation, he was informed of the number of batteries his current co-participant (i.e. the ORANGE co-participant) had reported in Part 1.
However, in only one situation was the information provided real, i.e. it concerned his current co-participant. In the other 3 situations, the information provided was either randomly set by the computer or selected by the experimenter on the basis of the behavior of participants who had taken part in previous sessions of the target experiment.

In each situation, the VIOLET co-participant flipped the coin six times and reported the total number of heads he observed (as in Part 1).

The VIOLET co-participant's earnings were based on his report in the real situation and the ORANGE co-participant's report.

## ORANGE co-participant

The ORANGE co-participant received no information about his current co-participant (i.e. the VIOLET co-participant).

He flipped the coin six times, and that once, and reported the total number of heads he observed (as in Part 1).

The ORANGE co-participant's earnings were based on his report and that of the VIOLET co-participant in the real situation.

## Earnings

The earnings of the two co-participants in each pair depend on their reports, as illustrated in the table below. The table reads as follows. The rows (VIOLET boxes) show the possible number of heads that the VIOLET co-participant could report from the six coin flips. Remember that only his report in the real situation was taken into account. The columns (ORANGE boxes) show the possible number of heads that the ORANGE co-participant could report. The earnings of each co-participant are displayed in euros in the table and depend on the combination of the two reports. Note that the earnings are the same as in Part 1, and are identical in each box for both co-participants.

Participants were informed of their earnings in Part 2 at the end of the experiment. At that point, they were also informed of their co-participant's report.
<table><caption>Table D9: *Complements* treatment</caption><thead><tr><th colspan="2"></th><th colspan="4">Report of the BLUE co-participant:</th></tr><tr><th colspan="2"></th><th>6 heads</th><th>5 heads</th><th>4 heads</th><th>3 heads<br>or less</th></tr></thead><tbody><tr><th rowspan="3" scope="rowgroup">Report of the YELLOW<br>co-participant:</th><th scope="row">6 heads</th><td>6 €</td><td>5 €</td><td>4 €</td><td>3 €</td></tr><tr><th scope="row">5 heads</th><td>5 €</td><td>5 €</td><td>4 €</td><td>3 €</td></tr><tr><th scope="row">4 heads</th><td>4 €</td><td>4 €</td><td>4 €</td><td>3 €</td></tr><tr><th colspan="2"></th><th>3 heads<br>or less</th><td>3 €</td><td>3 €</td><td>3 €</td><td>3 €</td></tr></tbody></table>

<table><caption>Table D10: *Substitutes* treatment</caption><thead><tr><th colspan="2"></th><th colspan="4">Report of the BLUE co-participant:</th></tr><tr><th colspan="2"></th><th>6 heads</th><th>5 heads</th><th>4 heads</th><th>3 heads<br>or less</th></tr></thead><tbody><tr><th rowspan="3" scope="rowgroup">Report of the YELLOW<br>co-participant:</th><th scope="row">6 heads</th><td>6 €</td><td>6 €</td><td>6 €</td><td>6 €</td></tr><tr><th scope="row">5 heads</th><td>6 €</td><td>5 €</td><td>5 €</td><td>5 €</td></tr><tr><th scope="row">4 heads</th><td>6 €</td><td>5 €</td><td>4 €</td><td>4 €</td></tr><tr><th colspan="2"></th><th>3 heads<br>or less</th><td>6 €</td><td>5 €</td><td>4 €</td><td>3 €</td></tr></tbody></table>

To summarize:

* In Part 1 of the target experiment:

- participants were randomly paired and assigned to the role of YELLOW co-participant or BLUE co-participant;
- each of them flipped a coin six times and reported the number of heads they observed.

* In Part 2 of the target experiment:

- participants were randomly matched with a new participant and assigned to the role of VIOLET co-participant or ORANGE co-participant;

- the VIOLET co-participant flipped a coin six times in four different situations and indicated how many heads he had observed in each situation. Only the situation containing the actual information about his current co-participant was used to determine earnings.

- The ORANGE co-participant flipped a coin six times and reported how many heads he had observed.

* The way the reports were combined to determine earnings was exactly the same in Part 1 and Part 2.

*Before proceeding to the instructions regarding the belief elicitation, subjects were asked to calculate the payments for three different, randomly generated pairs of reports. They could only proceed if they entered the correct answer.*

**Instructions: your task**

Your task is to guess how many heads four ORANGE co-participants who took part in the target experiment reported in Part 2. These four ORANGE co-participants are chosen at random, except that they all reported a different number of heads in Part 1.

You will be informed of the number of heads each of these ORANGE co-participants reported in Part 1, and you will be asked to guess their report in Part 2. At the end of the experiment, the computer will randomly select one of your guesses and determine your payout.
To help you make your guess, you should know that in the target experiment, at least 90% of ORANGE co-participants reported the same number of heads in Part 2 as in Part 1, or a number of heads 1 higher or lower than in Part 1.

## Earnings

If your guess is correct, i.e. if the number you guess matches the number of heads reported by the ORANGE co-participant in Part 2, you will get 6 euros. Otherwise, you will get 0 euros.

For example, imagine that, in the guess that determines your earnings, you enter 4 heads. If the ORANGE co-participant for whom you made the guess reported 4 heads in Part 2, you will get 6 euros. If the ORANGE co-participant for whom you made the guess reported a number of heads other than 4 in Part 2, you will get 0 euros.