ISSN (Print) 0473-453X

Discussion Paper No. 1146

ISSN (Online) 2435-0982

INTELLIGENCE PROMOTES COOPERATION
IN LONG-TERM INTERACTION:
EXPERIMENTAL EVIDENCE IN INFINITELYREPEATED PUBLIC GOODS GAMES
Tetsuya Kawamura
Tiffany Tsz Kwan Tse

October 2021

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Intelligence promotes cooperation in
long-term interaction: Experimental evidence
in infinitely repeated public goods games
Tetsuya Kawamura1 and Tiffany Tsz Kwan Tse2*
1* Department of Economics, Tezukayama University,

Tezukayama, Nara, 6318501, Japan.
2 Institute of Social and Economic Research, Osaka University,

Ibaraki, Osaka, 5670047, Japan.

*Corresponding author(s). E-mail(s): tiffany.ttk@gmail.com;
Contributing authors: kawamuratetsuya2027@gmail.com;
Abstract
A growing body of literature in experimental economics examines how
cognitive ability affects cooperation in social dilemma settings. We contribute to the existing literature by studying this relationship in amore complex and strategic environment when the number of partners increases in an infinitely repeated public goods game. We designed
four treatments with different continuation probability under two conditions: whether cooperation can be sustained as risk dominance ornot. We asked participants to decide whether to cooperate in every
period in the first five rounds. They were further asked to decide
if they should elicit their strategy at the beginning of each supergame using the strategy method in the last five rounds. We foundthat participants with greater cognitive abilities cooperated more (less)when cooperation could(not) be sustained as risk dominance. A similar trend was observed in the frequency of fully cooperative strategies.
We also found that participants with greater cognitive abilities employedlenient and forgiving strategies more frequently when the continuation
probability was far higher than the risk dominant threshold level.
Keywords: cognitive ability, infinitely repeated game, public goods game,risk dominance, strategy method
JEL Classification: C72 , C73 , C91 , C92

1

2Intelligence promotes cooperation in long-term interaction...

1 Introduction
How does the intelligence of participants affect decision-making in strategicinteractions? It may depend on the number of equilibria of the game andwhether the interaction is intertemporal. Experimental evidence (see BrañasGarza et al. (2012), Carpenter et al. (2013), and Gill and Prowse (2016)
for p-beauty game experiments; Kawamura and Ogawa (2019) for recipient
behavior in ultimatum game experiments; and Barreda-Tarrazona et al. (2017)
for prisoner’s dilemma (PD) game experiments) suggests that more intelligent individuals will exhibit behavior close to the theoretical prediction in the
one-shot game, with a single sub-game perfect Nash equilibrium (SPE).
When a game is repeated and the strategic interaction is intertemporal,
even if the game has a unique SPE, the relationship between intelligence andbehavior is complicated. Al-Ubaydli et al. (2016) and Barreda-Tarrazona et al.
(2017) found no significant relationship between participants’ intelligence andcooperation rates in finitely repeated PD game experiments.
When the game has multiple SPEs, the relationship between participants’
intelligence and behavior becomes more complicated. Jones (2008) found apositive relationship between participants’ intelligence and cooperation rate.
Proto et al. (2019) established that intelligence has a large and positive longrun effect on cooperative behavior in an infinitely repeated PD game.
Can the same trend of more intelligent individuals becoming more cooperative in long-term interactions in a more complex strategic environment be
achieved when the number of partners increases in an infinitely repeated public
goods (PG) game? This study is an attempt to answer this question.
The rich experimental literature on infinitely repeated PD games provides important attributes for studying infinitely repeated PG games. Thesestudies investigate cooperative behavior in infinitely repeated PD games fromthe following aspects: equilibrium selection (Blonski et al., 2011), the shadowof the future (Dal Bó & Fréchette, 2011), strategy methods (Dal Bó &Fréchette, 2019; Romero & Rosokha, 2018), discounting and random termination (Fréchette & Sevgi, 2017), and the effects of intelligence and personal
characteristics (Dreber et al., 2014; Proto et al., 2019).1
Dal Bó and Fréchette (2011) found that increasing the continuation probability δ facilitates cooperation. Blonski et al. (2011) established that when thegrim trigger strategy (GRIM)2 is supported as a risk dominance equilibrium(RDE), cooperation is more easily achieved than when it is not an RDE. Protoet al. (2019) found that participants with high cognitive ability cooperate or
employ cooperative strategies more frequently when GRIM is an RDE.
Few experimental studies have investigated infinitely repeated PG games,
as most compare cooperative behavior in infinitely and finitely repeated games.
Palfrey and Rosenthal (1994) determined that the cooperation rate is higher
in an infinitely repeated PG game than in a one-shot PG game. Tan and Wei
1
In addition, some studies have examined the impact of monitoring (Aoyagi et al., 2019) andgroup matching methods (Duffy & Ochs, 2009) in infinitely repeated PD games.
2
Players using GRIM will cooperate if all partners cooperate; otherwise, they defect.

Intelligence promotes cooperation in long-term interaction...

3(2014) found no significant difference in the cooperation rate between finitely
and infinitely repeated PG games. Lugovsky et al. (2017) established that thecooperation rate is significantly higher in infinitely repeated settings than infinitely repeated settings in a four-person PG game. Sell and Wilson (1999)
compared the cooperation rate under multiple δ in infinitely repeated PG
games and found that the cooperation rate increases when δ increases, but
only in the treatment in which participants are required to employ the grim
trigger strategy. They designed treatments in which GRIM is supported as anSPE, but not as an RDE. To our knowledge, no study has explored cooperative
behavior when GRIM is supported as an RDE in infinitely repeated PG games.
The threshold discount factor for RDE is known to be a good predictor of
the cooperation trend in infinitely repeated PD game experiments. This study
examined whether higher intelligence allows for more efficient equilibria to bereached by processing richer information. The theoretical prediction from twoperson games was extended to n-person games (Carlsson & van Damme, 1993;
Kim, 1996)3 to design δ, so that we have one treatment for which δ is lower
than the risk-dominant threshold and two treatments for which δ is higher
than the risk-dominant threshold.
In an infinitely repeated PG game, the strategy space is broader than in
an infinitely repeated PD game. Unlike the PD game, punishing a player who
deviates from the equilibrium strategy in the PG game not only affects thepayoff of the punished player, but also affects the payoff of the other players
who did not deviate from the equilibrium strategy. To achieve mutual cooperation, participants have more chances to employ lenient and forgiving strategies.
To our knowledge, no existing study has explored strategies in an infinitely
repeated PG game. By employing the one-period-ahead strategy method presented in Dal Bó and Fréchette (2019)’s study , we explored the strategy in an
infinitely repeated PG game. We investigated not only the difference in cooperation rate, but also the difference in strategies between participants with highcognitive ability (HCA) and participants with low cognitive ability (LCA).
The remainder of this paper is organized as follows. In Section 2, we introduce the experimental design and procedure. In Section 3, we introduce themethodology employed. In Section 4, we propose our hypotheses based on
the two equilibrium concepts in infinitely repeated game theory: the SPE and
RDE. In Section 5, we present our experimental results. In Sections 6 and 7,
we discuss our findings and conclude the paper, respectively.

2 Experimental Design
2.1 Parameter settings
The group comprised of four players who played the PG game infinitely andrepeatedly. In the PG game, players make a binary choice regarding whether
to cooperate or not. We set the initial endowment to 10, and the marginal
3
Carlsson & van Damme (1993) and Kim (1996) explore Harsanyi and Selten (1988)’s notionof RDE in two-person to n-person games.

4Intelligence promotes cooperation in long-term interaction...

per capita return at 0.5. Here, xi denotes player i’s level of cooperation. The
payoff of player i is given by:
πi = 10 − xi + 0.5

4
X

xj

j=1

We set the continuation probability of all treatments above the threshold level in which GRIM is supported as an SPE. Therefore, we focused on
situations where both cooperative and non-cooperative equilibria exist in alltreatments. In an infinitely repeated PD game, whether GRIM is supported
as an RDE or not can be a good predictor of the cooperation trend, as in
the infinitely repeated PD game experiments. We investigated cooperative
behavior when GRIM is and is not supported as an RDE.
We conducted four treatments with δT 1 = 0.4 (Treatment 1, or T1), δT 2 =
0.6 (T2), δT 3 = 0.8 (T3), and δT 4 = 0.9 (T4), where GRIM is supported as
the SPE in all the treatments and is supported as an RDE in T3 and T4. The
threshold value of the continuation probability for GRIM to be supported as
RDE δRDE is 0.8, which is equal to δT 3 4 . We set δT 1 and δT 2 to be lower than
δRDE , and δT 4 was higher than δRDE .

2.2 Experimental Procedure
The experiments were conducted in the laboratory of the Center for Experimental Economics at Kansai University. We used the online bulletin boardof Kansai University to recruit participants who did not have any experience
with PG and PD game experiments. Experiments were conducted in elevensessions between July 2018 and July 2021. Each participant participated inonly one session.
Each session lasted about 120 (180) min in T1, T2 and T3 (T4) and was
conducted by the same experimenter. After the participants were randomly
assigned to their seats, they were asked to sign the consent form. After confirming that all participants had signed the consent form, the experimenterread them the instructions. Each participant received printed handouts of the
instructions and listened to the audio instructions. During this time the participants could ask any questions about the experiment. After the instructions,a three-question review test about the payoff calculation was conducted tocheck the participants’ understanding of the game. After all the participants
had answered every question correctly, the experiment began.
The experiment was implemented using a z-tree (Fischbacher, 2007). Eachsession consisted of 10 rounds (also called supergames), and in each round, participants repeatedly played a PG game with their fixed partners. The numberof periods in a round is determined by the δ of the corresponding treatment(0.4 in T1, 0.6 in T2, 0.8 in T3, and 0.9 in T4, respectively). At the end ofeach period, the experimenter drew one card from five cards, which consisted
4
The procedure for calculating the threshold value of continuation probability for GRIM to besupported as an RDE is shown in the Appendix A.

Intelligence promotes cooperation in long-term interaction...

5of three jokers (two jokers) [one joker] and two (three) [four] spade cards in
T1 (T2) [T3]. The experimenter drew one card from 10 cards, which consistedof one joker and nine spade cards in T4. When the experimenter drew a joker,
the round was finished, all members were randomly re-matched, and the next
round started with four new members. The process of drawing cards was shownon the screen at the front of the laboratory. Therefore, it was ensured that thecontinuation of every period by the given probability is common knowledge.
The decision-making methods in the first five rounds and the last fiverounds differed. Participants decide whether to cooperate in every period in
the first five rounds. We refer to this as the direct response method. In the last
five rounds, participants constructed their strategy for repeated PG games atthe beginning of each round by using a one-period-ahead strategy method.5
In the strategy method, participants were asked to decide whether to cooperate in all possible one-period-ahead histories and the first period. There areeight one-period-ahead histories (two levels of each player’s cooperation rate,
multiplied by four levels of the other players’ total cooperation rate in theprevious period). The nine questions of all possible one-period-ahead histories
and the first period were shown randomly. Participants could take notes about
their strategic choices after constructing their strategies. The strategies werethen played automatically. The participants could not change their strategies
during a round.
After 10 rounds of repeated PG games, participants answered 16 questions6from the Raven Progressive Matrices Test (Raven, 1936) in 10 minutes. The
maximum test score was 16. The total profit earned in all the rounds andperiods was exchanged at a rate of 3 JPY per point to control for the income
effect. The total payment was the sum of the participation fee (1,000 JPY)
and the earnings in the game.

3 Methodology
3.1 Strategy Classification
We used a one-period-ahead strategy method to investigate the types of strategies employed by the participants.7 Using this method, we can simplify andclarify the experimental results to determine the types of strategies that are
significantly related to the cooperation rate.
5
The strategy method for infinitely repeated games was introduced by Selten (1967). Vespa(2020) extended the strategy method into a one-period-ahead strategy method and Romero andRosokha (2018) introduced the constructing strategy method. There is still no evidence that
players employ strategies beyond two-period-ahead histories (or above) in infinitely repeated PG
games. Hence, to reduce players’ difficulty in eliciting strategies, we used the one-period-ahead
strategy method to investigate the one-period-ahead history strategies in an infinitely repeated
PG game following Dal Bó and Fréchette (2019) and Vespa (2020).
6
The 16 selected questions are commonly used in Japan and Europe (see Hanaki et al., 2016).
These 16 questions are selected from all 48 questions, arranged from easy to difficult.
7
We also used the strategy frequency estimation method (Dal Bó & Fréchette, 2011) to estimate
strategies under the direct response method. The results are reported in the Appendix C. We
thank Dal Bó and Fréchette (2011) and Bigoni et al. (2015) for providing their code for strategy
estimation.

6Intelligence promotes cooperation in long-term interaction...

We considered 35 simplified strategies with a one-period-ahead history,
which includes 20 commonly studied strategies in infinitely repeated PD games(Fudenberg et al., 2012). The strategy dataset includes unconditional cooperation (UC), GRIM, other trigger types, Tit-for-Tat (TFT) types, exploitative
TFT (DTFT, also called suspicious TFT) types, false cooperator (C to All D),
false defector (D to All C), alternator (DC Alternative), and unconditional
defection (UD) strategies. Following Fudenberg et al. (2012), we classified thesestrategies into fully cooperative, fully non-cooperative, partially cooperative,
lenient, forgiving, and unforgiving strategies. Our definition of leniency differs
slightly from that of Fudenberg et al. (2012), who defined leniency based on apartner’s history. We call this “vertical leniency.” As there are three partners
in our infinitely repeated PG game, we consider a strategy to be lenient when
it can endure one or two partners’ defection in the previous period. We callthis “horizontal leniency.” A description of the strategy types is presented inTable 1.

3.2 Simulation
In the strategy method, participants construct their strategies before interacting with their partners, and they cannot change their strategies during
a round. Therefore, we expect that they construct strategies to respond toother participants in their session, but not their partners whom they do notknow when constructing their strategies. Therefore, we simulated all possiblegroup matching in each session and calculated the average cooperation rateof the constructed strategies. In each session and each round, we matched theparticipants to form all possible groups; for example, if the number of participants
was 16 in a session, the number of all possible group matching was

16
16!
=
4
4!(16−4)! = 1820. We used the same number of periods in each round ineach session, as in the experiments. Participants played a game fictitiously. We
then calculated the average cooperation rates of HCA and LCA participants.

4 Hypothesis
Proto et al. (2019) investigated the relationship between cognitive ability, as
measured by the Raven Progressive Matrices Test, and cooperation rate in an
infinitely repeated PD game when δ is strictly higher than δRDE . They foundthat HCA participants were more cooperative than LCA participants. Basedon the results of Proto et al. (2019), we expect that HCA participants more
frequently reach more efficient equilibria (i.e., RDE) than LCA participantsby maximizing their expected payoff by processing rich information. In ourdesign, UD risk dominates GRIM in T1 and T2, and GRIM risk dominates
UD in T3 and T4. We expect that the cooperation rate among HCA participants is higher (lower) than that of LCA participants when δ is higher (lower)
than δRDE . Thus, we propose the following hypotheses:
Hypothesis 1-1: The cooperation rate among HCA participants is lower thanIntelligence promotes cooperation in long-term interaction...

7

Table 1 Description of strategy types
Strategy

Description

UC
GRIM

UD

Players always cooperate.
Players cooperate if all partners cooperate; otherwise, theydefect.
Players cooperate in the first period and continue cooperating
if at least X partners cooperated in the previous period; otherwise, they defect forever.
Players cooperate if all partners cooperated in the previous
period.
Players cooperate in the first period, and they cooperate in thecurrent period if the players cooperate and at least X partners
cooperated in the previous period. They also cooperate in thecurrent period if the players defect and at least Y partners
cooperated in the previous period.
Players defect in the first period. They cooperate if all partners
cooperated in the previous period.
Players defect in the first period, and they cooperate in thecurrent period if the players cooperate and at least X partners
cooperated in the previous period. They also cooperate in thecurrent period if the players defect and at least Y partners
cooperated in the previous period.
Players defect first and then cooperate forever.
Players cooperate first and then defect forever.
Players start with defection and then alternate between cooperation and defection.
Players always defect.

Strategy Types

Description

Fully cooperative

The strategies obtain full cooperation when players who
employ the same type of strategies are matched with eachother.
The strategies obtain a mixture of cooperation and defection when players who employ the same type of strategies arematched with each other.
The strategies obtain full defection when players who employ
the same type of strategies are matched with each other.
These are fully cooperative strategies that are slower to resort
to punishment. They include all fully cooperative strategies,
except UC, GRIM, and TFT; In the UC strategy, a player
cooperates infinitely, while in the GRIM and TFT, a player
cooperates infinitely only when all partners contribute fully.
These are fully cooperative strategies that are fast to forgive.
They include all cooperative TFT types.
These are fully cooperative strategies that never forgive. They
include all cooperative trigger types.

TriggerX

TFT
TFTcXdY

DTFT
DTFTcXdY

D to All C
C to All D
DC alternative

Partially cooperative

Fully non-cooperative
Lenient

Forgiving
Unforgivingthat of LCA participants in T1.
Hypothesis 1-2: The cooperation rate among HCA participants is lower thanthat of LCA participants in T2.

8Intelligence promotes cooperation in long-term interaction...

Hypothesis 1-3: The cooperation rate among HCA participants is higher thanthat of LCA participants in T3.
Hypothesis 1-4: The cooperation rate among HCA participants is higher thanthat of LCA participants in T4.
Dal Bó and Fréchette (2011; 2019) revealed that when δ is set to exceed
δRDE , the frequency of fully cooperative strategies increases. Proto et al.
(2019) suggested that HCA participants employ cooperative strategies more
frequently, whereas LCA participants employ UD more frequently when δ is
set to exceed δRDE . We expect that fully cooperative strategies are employed
more frequently by HCA participants than LCA participants when GRIM is
supported as an RDE. When δ is set to be smaller than δRDE , UD is RDE;
hence, HCA participants employ cooperative strategies less frequently than
LCA participants. Thus, we propose the following hypotheses:
Hypothesis 2-1: The frequency of fully cooperative strategies among HCA
participants is lower than that of LCA participants in T1.
Hypothesis 2-2: The frequency of fully cooperative strategies among HCA
participants is lower than that of LCA participants in T2.
Hypothesis 2-3: The frequency of fully cooperative strategies among HCA
participants is higher than that of LCA participants in T3.
Hypothesis 2-4: The frequency of fully cooperative strategies among HCA
participants is higher than that of LCA participants in T4.
Romero and Rosokha (2018) found that a large proportion of cooperative strategies are lenient and forgiving when δ exceeds δRDE . Dal Bó andFréchette (2011) showed that the frequency of TFT (i.e., a forgiving strategy)
increases when δ exceeds δRDE . We expect the same trend of leniency andforgiving in infinitely repeated PG games. We expect HCA participants toemploy lenient and forgiving strategies more frequently than LCA participants when δ exceeds δRDE . We may expect to observe the reverse trend
when δ is smaller than δRDE . Thus, we propose the following hypotheses:
Hypothesis 3-1: The frequency of forgiving strategies among HCA participants is lower than that of LCA participants in T1.
Hypothesis 3-2: The frequency of forgiving strategies among HCA participants is lower than that of LCA participants in T2.
Hypothesis 3-3: The frequency of forgiving strategies among HCA participants is higher than that of LCA participants in T3.

Intelligence promotes cooperation in long-term interaction...

9

Hypothesis 3-4: The frequency of forgiving strategies among HCA participants is higher than that of LCA participants in T4.
Hypothesis 4-1: The frequency of lenient strategies among HCA participants
is lower than that of LCA participants in T1.
Hypothesis 4-2: The frequency of lenient strategies among HCA participants
is lower than that of LCA participants in T2.
Hypothesis 4-3: The frequency of lenient strategies among HCA participants
is higher than that of LCA participants in T3.
Hypothesis 4-4: The frequency of lenient strategies among HCA participants
is higher than that of LCA participants in T4.

5 Experimental Results
A total of 172 participants participated in our experiment, consisting of elevensessions. The average payment was 1,568 JPY in T1, 1,904 JPY in T2, 3,029
JPY in T3, and 4,128 JPY in T4. Each session lasted for two hours in T1, T2
and T3, and three hours in T4. On average, there were 1.5 periods per roundin T1, 2.5 periods per round in T2, 6 periods per round in T3, and 9 periods
per round in T4. Table 2 presents a summary of the experiments.
Table 2 Summary of the experiments

Number of sessions
Number of participants
Theaveragenumberofrounds1
The average number of periods
per round
Average payment (JPY)
Exchange rate (JPY/point)
Raven score
Male
Age
Economics or business students

Treatment 1

Treatment 2

Treatment 3

Treatment 4

3
48
10

3
40
10

3
44
10

2
40
9.5

1.5

2.5

6

9

1568
3
11.25
56.25%
21.0218.333%

1904
3
10.975
42.5%
19.95
27.5%

3029
3
11.54556.818%20.77320.455%

4128
3
11.1
57.5%
20
32.5%

1 Due to time constraint, we conducted nine rounds in one session in Treatment 3.

To check the balance of cognitive ability among the four treatments, we
conducted a one-way ANOVA to compare average Raven scores: 11.25 in T1,
10.975 in T2, 11.545 in T3, and 11.1 in T4, with no significant difference(p = 0.775). We considered participants who had Raven scores above the mean

10Intelligence promotes cooperation in long-term interaction...

as HCA participants and those who had Raven scores below or equal to themean as LCA participants. There were 28, 14, 26, and 22 participants whose
Raven scores were above 11 in T1, T2, T3 and T4, respectively. Meanwhile, 20,
26, 18, and 18 participants had Raven scores below or equal to 11 in T1, T2,
T3 and T4, respectively. Figure 1 shows the distribution of the Raven scorefor each treatment.
Fig. 1 The distribution of the Raven score in each treatment

We have also checked the balance of gender, age, and economics or business students among the four treatments by conducting a one-way ANOVA.
We found a 1% significant difference among treatments on age and a 5 % significant difference among treatment on economics or business students, but nosignificant difference on male (p = 0.474).
In the analysis of average cooperation rate and the frequency of strategy types, we control demographic characteristics including gender, age, andeconomics or business students.

5.1 Average Cooperation Rate
Figure 2 shows the average cooperation rate (%) across rounds between HCA
participants and LCA participants. We report two types of results: average
cooperation rate in period 1 only and all periods. Participants make decision
under direct response method from round 1 to 5 and strategy method fromround 6 to 10. In treatment 1, HCA participants always cooperated less than
LCA participants for both period 1 and all periods. In treatment 2, the average
cooperation rate between HCA participants and LCA participants was similar
across rounds. In treatment 3, HCA participants cooperated more than LCA
participants in period 1 after round 2. HCA participants cooperated more than
LCA participants in all periods from round 2 to round 5 and then behaved

Intelligence promotes cooperation in long-term interaction...

11

similarly from round 6. In treatment 4, HCA participants always cooperated
more than LCA participants in period 1 after round 2. However, HCA participants sometimes cooperated more and sometimes less than LCA participantsin all periods across rounds.
Fig. 2 Average cooperation rate across rounds between HCA participants and LCA participants

We examined our hypothesis that HCA participants are more (less) likely
to cooperate than LCA participants in T3 and T4 (T1 and T2) in period 1 andall periods, in which participants behave according to RDE. We examined ourhypothesis by reporting two types of results: experimental results under the
direct response method (rounds 1 to 5) and simulation results using strategy
method observation.8
Figure 3 shows the predicted average cooperation rate (%) between HCA
and LCA participants under the direct response method (rounds 1 to 5), andstrategy method (simulation) in (a) Treatment 1, (b) Treatment 2, (c) Treatment 3 and (d) Treatment 4. We provide the results of period 1 only and all
periods. For each pairwise comparison between HCA and LCA participantsin each treatment, we report the results of logistic regression of cooperation
rate, with HCA participants as the dummy independent variable, controllingfor demographic variables, including age, gender, and economics major.9 We
report robust standard errors clustered by group. We define a p-value less thanor equal to 0.05, which is typically ≤ 0.05, as statistically significant. We report
the predicted average cooperation rate (predicted probabilities) presented by
8
We report the results of experimental data from strategy method (round 6 to 10) in Table A12
in Appendix D.
9We also conducted the unconditional logistic regression of cooperation rate, with HCA participants as the dummy independent variable, without controlling for demographic variables androbust standard errors clustered by group. The results are shown in Table A18 and Table A20 inAppendix E.

12Intelligence promotes cooperation in long-term interaction...

rectangular bars and standard errors of the predicted average cooperation ratepresented by error bars.10
Fig. 3 Predicted Average Cooperation Rate (%) between HCA and LCA participants under
the direct response method and strategy method (simulation) in (a) Treatment 1, (b) Treatment 2, (c) Treatment 3, and (d) Treatment 4(a) Treatment 1(b) Treatment 2(c) Treatment 3(d) Treatment 4

Notes:Predicted average cooperation rates and p-values are calculated based on logistic
regression of cooperation rate, with HCA participants as dummy independent variable,
controlling for demographic characteristics (including age, gender, and economics major), withrobust standard errors clustered by group. *, **, and *** indicate significance at the 0.10, 0.05,
and 0.01 levels, respectively. n.s. means the difference is not statistically significant at 0.1. See
Table A11 and Table A13 in Appendix D.

(a) Treatment 1
Under the direct response method, the predicted average cooperation rateof HCA participants was always lower than that of LCA participants for both
period 1 (HCA: 24% and LCA: 40%) and all periods (HCA: 21% and LCA:
41%). These differences were not statistically significant. Under the strategy
method (simulation), the predicted average cooperation rate of HCA participants was always lower than that of LCA participants for both period 1 (HCA:
18% and LCA: 36%) and all periods (HCA: 17% and LCA: 33%). These differences between the HCA and LCA participants were statistically significant.
Thus, Hypothesis 1-1 was supported.
(b) Treatment 2
Under the direct response method, the predicted average cooperation rateof HCA participants was lower than that of LCA participants for both period
1 (HCA: 26% and LCA: 33%) and all periods (HCA: 23% and LCA: 30%), and10

All regression results are shown in Table A11 and A13 in Appendix D.

Intelligence promotes cooperation in long-term interaction...

13

these differences were not statistically significant. Under the strategy method(simulation), the predicted average cooperation rate of HCA participants was
lower than that of LCA participants for both period 1 (HCA: 21% and LCA:
22%) and all periods (HCA: 15% and LCA: 19%), and these differences were
statistically significant.11 Thus, Hypothesis 1-2 was not supported in direct
response method, but supported in strategy method (simulation).
(c) Treatment 3
Under the direct response method, the predicted average cooperation rateof HCA participants was higher than that of LCA participants in both period
1 (HCA: 45% and LCA: 40%) and all periods (HCA: 30% and LCA: 26%).
These differences were not statistically significant. Under the strategy method(simulation), the predicted average cooperation rate of HCA participants was
similar to that of LCA participants in both period 1 (HCA: 42.3% and LCA
41.8%) and all periods (HCA:22% and LCA: 21%). These differences were notstatistically significant.12 Thus, Hypothesis 1-3 was not supported.
(d) Treatment 4
Under the direct response method (rounds 1 to 5), the predicted average
cooperation rate of HCA participants was higher than that of LCA participantsin both period 1 (HCA: 49% and LCA: 39%) and all periods (HCA: 28% and
LCA: 19%), and these differences were not statistically significant in period
1, but statistically significant in all periods.13 Under the strategy method(simulation), the predicted average cooperation rate of HCA participants washigher than that of LCA participants in both period 1 (HCA: 44% and LCA:
27%) and all periods (HCA: 15% and LCA: 14%), and these differences were
statistically significant. Thus, Hypothesis 1-4 was supported, except in period
1 in direct response method.

5.2 Strategy analysis
We examined our hypothesis that HCA participants more (less) frequently
employ fully cooperative, forgiving, and lenient strategies than LCA participants in T3 and T4 (T1 and T2), in which participants behave according
to RDE. We report the predicted frequency of strategies using the strategy
method (rounds 6 to 10).
Figure 4 shows the predicted frequency (%) of the (a) fully cooperative
strategy, (b) forgiving strategy, and (c) lenient strategy between HCA and LCA
11
In the results of unconditional logistic regression (i.e., without controlling demographic variables), in strategy method (simulation) in Treatment 2, the average cooperation rate of HCA
participants and LCA participants were not statistically significant in period 1 (HCA: 21% and
LCA: 22%) and all periods (HCA: 17% and LCA: 17%).
12
In the results of unconditional logistic regression (i.e., without controlling demographic variables), in strategy method (simulation) in Treatment 3, the average cooperation rate of HCA
participants is higher than that of LCA participants in both period 1 (HCA: 44% and LCA:39%)
and all periods (HCA: 22% and LCA: 20%) with statistically significant.
13
In the results of unconditional logistic regression (i.e., without controlling demographic variables), in strategy method (simulation) in Treatment 4, the average cooperation rate of HCA
participants and LCA participants were not statistically significant in period 1 (HCA: 46% and
LCA: 41%) and all periods (HCA: 27% and LCA: 19%).

14

Intelligence promotes cooperation in long-term interaction...

participants. For each pairwise comparison between HCA and LCA participants in each treatment, we report the results of logistic regression of strategy
types, with HCA participants as the dummy independent variable, controllingfor demographic variables, including age, gender, and economics major.14 We
report robust standard error. We report the predicted frequency (predictedprobabilities) presented by rectangular bars and standard errors of predictedfrequency presented by error bars.15
Fig. 4 The predicted frequency (%) of (a) fully cooperative strategy, (b) forgiving strategy,and (c) lenient strategy between HCA and LCA participants under strategy method in eachtreatment(a) Fully cooperative strategy(b) Forgiving strategy(c) Lenient strategy
Notes:Predicted frequency and p-values are calculated based on logistic regression of strategy
types, with HCA participants as dummy independent variable, controlling for demographic
characteristics (including age, gender, and economics major), with robust standard errors. *, **,and *** indicate significance at the 0.10, 0.05, and 0.01 level, respectively. See Table A14 to A16
in Appendix D.

(a) Fully cooperative strategy
In Treatment 1, the predicted frequency of the fully cooperative strategy
among HCA participants was 14% lower than that of LCA participants (31%),
and these differences were statistically significant. Thus, Hypothesis 2-1 was
supported. In Treatment 2, the predicted frequency of the fully cooperative
strategy among HCA participants was 6% lower than that of LCA participants(18%), and these differences were not statistically significant. Thus, Hypothesis 2-2 was not supported. In Treatment 3, the predicted frequency of the14
We also conducted the unconditional logistic regression of strategy types, with HCA participants as the dummy independent variable, without controlling for demographic variables androbust standard errors. The results are shown in Table A21 to A23 in Appendix E.
15
All regression results are shown in Table A14 to A16 in Appendix D.

Intelligence promotes cooperation in long-term interaction...

15

fully cooperative strategy among HCA was 21% and that of LCA participants
was 26%, with no statistically significant differences. Thus, Hypothesis 2-3
was not supported. In Treatment 4, the predicted frequency of the fully cooperative strategy among HCA participants was 32% higher than that of LCA
participants (17%) and these differences were statistically significant.16 Thus,
Hypothesis 2-4 was supported.
(b) Forgiving strategy
In Treatment 1, the predicted frequency of the forgiving strategy among
HCA participants was 15% lower than that of LCA participants (19%), without
statistically significant differences. Thus, Hypothesis 3-1 was not supported.
In Treatment 2, the predicted frequency of the forgiving strategy among HCA
participants was 6% lower than that of LCA participants (15%), without statistically significant differences. Thus, Hypothesis 3-2 was not supported. In
Treatment 3, the predicted frequency of the forgiving strategy among HCA
was 17% lower than that of LCA participants (19%), without statistically significant differences. Thus, Hypothesis 3-3 was not supported. In Treatment 4,
the predicted frequency of the forgiving strategy among HCA participants was
25% higher than that among LCA participants (11%), and these differenceswere statistically significant. Thus, Hypothesis 3-4 was supported.
(c) Lenient strategy
In Treatment 1, the predicted frequency of the lenient strategy among
HCA participants was 14% lower than that of LCA participants (19%), withno statistically significant difference. Thus, Hypothesis 4-1 was not supported.
In Treatment 2, the predicted frequency of the lenient strategy among HCA
participants was 7% lower than that of LCA participants (13%), with no statistically significant difference. Thus, Hypothesis 4-2 was not supported. In
Treatment 3, the predicted frequency of the lenient strategy among HCA participants was 16%, which is lower than the 21% for LCA participants, with nostatistically significant difference. Thus, Hypothesis 4-3 was not supported. In
Treatment 4, the frequency of the lenient strategy among HCA participants
was 26% higher than that of LCA participants (13%), and these differenceswere statistically significant. Thus, Hypothesis 4-4 was supported.

6 Discussion
In the theoretical prediction, GRIM risk dominates UD when δ ≥ δRDE . In
our experiment, we set δT 3 = 0.8, which is δRDE . We expect HCA participants
to reach more efficient equilibria (i.e., RDE) more frequently than LCA participants by maximizing their expected payoff, which is achieved by processing
rich information. However, at δT 3 = δRDE , the expected payoff employing
GRIM is the same as that employing UD. Thus, we focus on the comparison
between T1 and T4, or T2 and T4 for investigating the effect of continuation
16
In the results of unconditional logistic regression (i.e., without controlling demographic variables), in Treatment 4, the frequency of fully cooperative strategies among HCA participants and
LCA participants was not statistically significant (HCA: 31% and LCA: 18%).

16

Intelligence promotes cooperation in long-term interaction...

probability (i.e., whether GRIM is supported as the RDE or not) on behaviors
among treatments for each type of participant.
Focusing on the direct response method, the cooperation rate of HCA participants in period 1 and all periods increased as the expected payoff of GRIM
exceeded that of UD from Treatment 1 to 4 (p < 0.01 for period 1 and p < 0.05
for all periods; see Table A17 in Appendix D) and from Treatment 2 to 4
(p < 0.01 for period 1 and p=0.859 for all periods; see Table A17 in Appendix
D). This implies that HCA participants cooperated more in T4 than in T1 or
T2 in period 1, in order to maximize their expected payoff.
However , the cooperation rate of LCA participants in the direct response
method remained unchanged in period 1 and decreased in all periods from
Treatment 1 to 4 (p = 0.271 for period 1 and p < 0.01 for all periods; see Table
A17 in Appendix D) and 2 to 4 (p = 0.490 for period 1 and p=0.025 for all
periods, see Table A17 in Appendix D). This implies that LCA participantstended to cooperate in period 1 due to similar frequencies in T1, T2, andT4, but defected more in all periods in T4 than they did in T1 or T2. As
the frequency of fully non-cooperative strategies was more than 50% among
HCA participants and LCA participants in all treatments (see Table A10 inAppendix C), the level of cooperation did not evolve if there was a large
fraction of fully non-cooperative strategies. The average number of periods perround was higher in T4 than in T1 and T2. Therefore, the high frequency offully non-cooperative strategies decreased the cooperation rate in all periods
in T4, as compared to that in T1 and T2.
In the direct response method, we found that hypotheses 1-1 and 1-4 were
supported, and hypotheses 1-2 and 1-3 were not supported. The backgroundfor these results was built up in two aspects: 1) LCA participants cooperated more than HCA participants with statistical significance (p < 0.01 forperiod 1 and all periods) in T1. 2) LCA participants decreased cooperationand HCA participants increased cooperation as δ increased and exceeded δRDE
(see Table A17 in Appendix D). Because the trend of cooperation rate wasreversed between HCA and LCA participants as δ increased, the statisticallysignificant difference in the cooperation rate in T1 was rendered insignificant
from T1 to T2 and T3. Moreover, the cooperation rate of HCA participants
exceeded that of LCA participants from T1 to T4.
We found that Hypotheses 2-1 and 2-4 were supported but Hypotheses 2-2
and 2-3 were not. We confirmed these results by examining the differences inthe trend of the fully cooperative strategies between HCA and LCA participants. HCA participants employed fully cooperative strategies from Treatment
1 to 4 (p < 0.01, see Table A17 in Appendix D) and 2 to 4 (p < 0.01, see Table
A17 in Appendix D) more frequently. However, the frequency of fully cooperative strategies employed by LCA participants was not statistically different
between Treatments 1 and 4 (p = 0.056, see Table A17 in Appendix D) and
Treatment 2 and 4 (p = 0.385, see Table A17 in Appendix D).
Similar to the trends in the cooperation rate between HCA and LCA participants, the reversed trends in the frequency of fully cooperative strategies

Intelligence promotes cooperation in long-term interaction...

17

between the two groups of participants, along with LCA participants employing fully cooperative strategies more frequently than HCA participants in T1,
builds up the background for the results testing Hypotheses 2-1 to 2-4. The
difference in the frequency of fully cooperative strategies between the two
types of participants was diminished came closer as δ increased from T1 to
T3, and HCA participants turned to employ fully cooperative strategies more
frequently than LCA participants in T4.
Our experimental results suggested the lag effects of the continuation probability (i.e., whether GRIM is supported as the RDE) on the cooperation rate
and the frequency of fully cooperative strategies. HCA participants did notchange their strategy from fully non-cooperative strategies, including UD, tofully cooperative strategies including GRIM and TFT as soon as δ exceededδRDE or the expected payoff of GRIM exceeded that of UD. Instead, HCA
participants gradually switched from fully non-cooperative strategies to fully
cooperative strategies. These changes in the strategy profiles of HCA participants caused the cooperation rate to gradually increase as δ increased.
However, LCA participants tended to maintain the initial relatively high cooperation rate, as δ increased, by maintaining the initial strategy profiles in T1.
Thus, our hypotheses were supported in T1 and T4, where δ was far away from
δRDE , but not supported in T2 and T3, where δ was relatively closer to δRDE .

7 Conclusion
In this study, we designed an infinitely repeated PG game experiment under
different δ. We designed two treatments for which the continuation probability
was lower than the δRDE and two treatments in which the continuation probability was higher than the δRDE . We investigated the differences in cooperation
rates and strategies between HCA and LCA participants.
We found that 1) the average cooperation rate of HCA participants was
statistically significantly lower than that of LCA participants in T1. 2) The
average cooperation rate of HCA participants was statistically significantly
lower than that of LCA participants in T2 in the simulation results with strategy method, but not in direct response method. 3) The average cooperation
rate of HCA participants was not statistically significantly different from thatof LCA participants in T3, which continuation probability was the same as theδRDE , 4) the average cooperation rate of HCA participants was statisticallysignificantly higher than that of LCA participants in T4, 5) the frequency offully cooperative strategies for HCA participants was statistically lower thanthat for LCA participants in T1, but not different in T2, 6) the frequency offully cooperative strategies for HCA participants was statistically higher thanthat for LCA participants in T4, but not different in T3, and 7) the frequencyof lenient and forgiving strategies for HCA participants was statistically higher
than that for LCA participants, but only in T4; they were not different inother treatments.

18Intelligence promotes cooperation in long-term interaction...

In the future, we aim to follow Proto et al. (2019)’s experimental design toseparate HCA and LCA participants to play the infinitely repeated PG game.
HCA participants will only match with HCA partners, and LCA participants
will only match with LCA partners. We would like to confirm whether mutual
cooperation can be maintained when the group players are all HCA participants and when the GRIM is supported as an RDE. It will also be interesting
to conduct experiments with the different types of strategy methods. In thestrategy methods, participants choose their strategy from a strategy set consisting of UD, GRIM, lenient Trigger, TFT, and lenient TFT strategies. By
doing so, we can directly test the theoretical prediction on RDE condition.
This enables us to investigate the relationship between the cognitive abilitiesof participants and the types of strategies employed: cooperative/defective,
lenient/not lenient, and forgiving/unforgiving strategies, with great depth.

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22Intelligence promotes cooperation in long-term interaction...

Supplementary information. Supplementary material is available at journal’s website
Acknowledgments. We would like to thank the editor, the co-editor, andthe anonymous referees. We are grateful to Takanori Ida, Kazuhito Ogawa,
Hajime Kobayashi, Tadashi Sekiguchi, Hisaki Kono, Yohei Mitani, Masaki
Aoyagi, Nobuyuki Hanaki and Masao Ogaki, as well as the participants at
the International Workshop for Lab and Field Experiments and the 21stExperimental Social Sciences Conference, Kansai University for their helpful conversations and comments. We thank the Kansai University Center
for Experimental Economics for the use of experimental laboratories andparticipant recruiting system. Research support was provided by Japan Society for the Promotion of Science KAKENHI Grant Numbers (JP17J03485,
JP20H05631). The experiment reported in this paper is approved by Research
Ethic Committee at The Research Institute for Socionetwork Strategies(RISS), Kansai University.

Declarations• Funding
We gratefully acknowledge the financial support from Japan Society
for the Promotion of Science KAKENHI Grant Numbers (JP17J03485,
JP20H05631).
• Conflict of interest/Competing interests
The authors declare that they have no conflict of interest.
• Ethics approval
The experiment reported in this paper is approved by Research Ethic Committee at The Research Institute for Socionetwork Strategies (RISS), Kansai
University.
• Consent to participate
All participants signed the consent form to agree to participate thisexperiments.
• Consent for publication
All participants signed the consent form to agree to publish the experimental
data under the condition of anonymity.
• Availability of data and materials
Supplementary material is available at journal’s website.
• Code availability
Code used in analysis is available at journal’s website• Authors’ contributions
The authors contributed equally to this work.

NOT FOR PUBLICATION

Online Supplementary Appendix to:
Kawamura and Tse:1 “Intelligence promotes cooperation in long-term interaction: Experimental evidence ininfinitely repeated public goods games”

Tables of Contents
Appendix A: Calculation of the risk dominant threshold
Appendix B: Description of a strategic plan
Appendix C: Strategy analysis results
Appendix D: Regression Results for figures
Appendix E: Analyses of experimental results unconditional on personal characteristics
Appendix F: The frequency of unconditional defection strategy between HCA participants and LCA
participants
Appendix G: Average payoff between HCA participants and LCA participants
Appendix H: Experimental instruction

Kawamura: Tezukayama University (kawamuratetsuya2027@gmail.com),Tse: Osaka University(tiffany.ttk@gmail.com)
11

A. Calculation of the risk dominant threshold
Carlsson and van Damme (1993) and Kim (1996) explore Harsanyi and Selten (1988)’s notion of risk
dominance in two-person to n-person games. Using Kim’s method of calculating the expected payoff, weshow the expected payoff using UD and GRIM under the same probability to find the possible RDE strategies
that can minimize strategic risk.
We consider a game with these two pure SPE strategies (UD and GRIM)2. The possible situations for agiven individual are thus all the combinations of that individual playing GRIM or UD against three partners,
with k partners playing GRIM and (3-k) partners playing UD, for any 0 ≤ k ≤3. We denote the payoff when aplayer plays GRIM against k partners playing GRIM by 𝛼𝑘 and the payoff when a player plays UD against kpartners playing GRIM by 𝛽𝑘 .
There are four possible events: all three partners choose UD, one partner chooses GRIM and two partners
choose UD, two partners choose GRIM and one partner chooses UD, and all three partners choose GRIM.
Each partner chooses GRIM with probability 𝑦𝐺𝑟𝑖𝑚 and UD with probability 𝑦𝑈𝐷 , where 𝑦𝑈𝐷 = 1 − 𝑦𝐺𝑟𝑖𝑚 .
To simplify, following Dal Bó and Fréchette (2011), we assume that each partner chooses GRIM and UD withthe same probability, where 𝑦𝐺𝑅𝐼𝑀 =11
and 𝑦𝑈𝐷 = . The probability of a given player facing with k
2
2

players employing GRIM and 3-k players employing UD is given in the following formula:
1 𝑘
1 3−𝑘
1
3
3
3
𝑘
3−𝑘
(𝑦
)
(𝑦
)
Probability = ( ) × 𝐺𝑟𝑖𝑚 × 𝑈𝐷
= ( )×( ) ×( )= ( )×( )
𝑘
𝑘
𝑘
2
2
8
3
( ) indicates the combined probability of selecting k partners choosing GRIM from all three partners.
𝑘(𝑦𝐺𝑟𝑖𝑚 )𝑘 indicates the combined probability of the multiple individual probabilities of k partners employing
GRIM. (𝑦𝑈𝐷 )3−𝑘 indicates the combined probability of the multiple individual probabilities of (3-k) partners
employing UD. Table A1 shows the expected payoff using UD and GRIM against the three partners.

To prove that GRIM is supported as the SPE, we need to show that no subject has an incentive to deviate fromthe equilibrium path. On the equilibrium path, if player i follows GRIM, his/her payoff is given by 𝜋𝑖 (𝐺𝑅𝐼𝑀) =1
20(0.5 ∑4𝑖=1 10) =. While if he/she deviates, he/she receives a one-shot gain followed by lower future
2

1−𝛿

1−𝛿

𝛿

10𝛿

payoffs: 𝜋𝑖 (𝐷|𝐺𝑅𝐼𝑀) = (10 + 0.5 ∑𝑖≠𝑗 10) + 1−𝛿 10 = 25 + 1−𝛿. Thus, a player has no incentive to deviate fromthe equilibrium path when 𝜋𝑖 (𝐺𝑅𝐼𝑀) ≥ 𝜋𝑖 (𝐷|𝐺𝑅𝐼𝑀). Therefore, the threshold value of probability continuation1
which GRIM is supported as SPE δSPE is 3.
2

Table A1. Expected payoff using the possible SPE strategies (UD and GRIM)
Partners
Player i
GRIM

3UD

1GRIM+2UD

10𝛿
1−𝛿

10 +

10𝛿
1−𝛿

15 +

10𝛿
1−𝛿

5+

10
1−𝛿

UD

1
8

Probability

3
8

2GRIM+1UD

3GRIM

15 +

10𝛿
1−𝛿

20
1−𝛿

20 +

10𝛿
1−𝛿

25 +

3
8

10𝛿
1−𝛿

1
8

GRIM risk dominates UD if
3

3

𝑘=0

𝑘=0

3 1
3 1
𝜋𝐺𝑅𝐼𝑀 = ∑ ( ) ( ) 𝛼𝑘 ≥ ∑ ( ) ( ) 𝛽𝑘 = 𝜋𝑈𝐷
𝑘 8
𝑘 8
1
10𝛿
3
10𝛿
3
10𝛿
1 20
(5 +
) + (10 +) + (15 +
)+ (
)≥
8
1−𝛿
8
1−𝛿
8
1−𝛿
8 1−𝛿
1 10
3
10𝛿
3
10𝛿
1
10𝛿
≥ (
) + (15 +) + (20 +) + (25 +
)
8 1−𝛿
8
1−𝛿
8
1−𝛿
8
1−𝛿
δ𝑅𝐷𝐸 ≥

4
5

B. Description of a strategic plan
Table A2. Description of a strategic plan
ChoiceOwn Contribution at t-1

Partners’ Contribution at t-1

What is your contribution at t?

1

0

0

0 or 10?

20

100 or 10?

30

20

0 or 10?

4030

0 or 10?

5

100

0 or 10?

6

10

10

0 or 10?

7

10

20

0 or 10?

3

8

10

30

9

0 or 10?

First Period

0 or 10?

C. Strategy analysis results
1. Strategy Method (Round 6-10)
Table A3. Summary of strategies used by HCA participants in the strategy method stage
Treatment 1

Treatment 2

Treatment 3

Treatment 4

Strategy

Freq.

Strategy

Freq.

Strategy

Freq.

Strategy

Freq.

TFT

1

TFTc1d1

1

UC

1

UC

4

TFTc1d2

11

TFTc1d2

2

GRIM

4

GRIM

1

TFTc2d2

1

TFTc2d2

1

Trigger 2

2

Trigger 1

1

TFTc2d3

3

TFTc2d3

1

TFT

2

Trigger 2

1

TFTc3d2

1

C to All D1

TFTc1d1

2

TFT

1

C to All D

4

DTFT

1

TFTc1d2

4

TFTc1d1

4

DTFT

4

DTFTc2d3

7

TFTc2d01

TFTc1d2

6

DTFTc1d2

8

UD

31

TFTc2d3

5

TFTc2d1

1

DTFTc1d3

1

Unclassified

25

TFTc3d0

1

TFTc2d2

4

DTFTc2d2

10

Obs.

70

TFTc3d2

1

TFTc2d3

4

DTFTc2d3

14

C to All D

2

C to All D

4

UD

62

DTFT

2

D to All C

1

Unclassified

20

DTFTc1d3

1

DTFT

5

Obs.

140

DTFTc2d2

2

DTFTc1d2

3

DTFTc2d3

2

DTFTc2d2

2

DTFTc3d2

2

DTFTc2d3

2

UD

60

UD

32

Unclassified

36

Unclassified

25

Obs.

130

Obs.

101

4

a: The unit of observation is the decision making in every round in the strategy-method stage.
b: The total number of observations is the number of HCA/LCA participants× the number of rounds understrategy method (Round 6 to 10).

Table A4. Summary of strategies used by LCA participants in the strategy method stage
Treatment 1

Treatment 2

Treatment 3

Treatment 4

Strategy

Freq.

Strategy

Freq.

Strategy

Freq.

Strategy

Freq.

UC

9

UC

5

UC

1

UC

2

GRIM

2

Trigger2

4

GRIM

2

GRIM

2

Trigger 1

1

TFTc1d1

5

Trigger 2

2

Trigger 2

1

Trigger 2

1

TFTc1d2

4

TFT

1

TFTc1d1

1

TFT

2

TFTc2d3

4

TFTc1d2

4

TFTc1d2

4

TFTc1d1

1

C to All D1

TFTc1d3

1

TFTc2d2

1

TFTc1d2

6

DTFT

2

TFTc2d2

3

TFTc2d3

2

TFTc1d3

2

DTFTc1d1

1

TFTc2d3

3

TFTc3d0

1

TFTc2d3

1

DTFTc1d2

3

C to All D

1

C to All D

1

DTFT

1

DTFTc2d2

1

DTFTc0d2

1

DTFT

2

DTFTc1d2

2

DTFTc2d3

11

DTFTc1d2

1

DTFTc1d2

5

DTFTc2d3

5

UD

50

DTFTc2d3

6

DTFTc1d3

3

DTFTc3d1

1

Unclassified

39

UD

45

DTFTc2d2

1

DTFTc3d2

2

Obs.

130

Unclassified

19

DTFTc2d3

4

UD

37

Obs.

90

UD

40

Unclassified

27

Unclassified

13

Obs.

100

Obs.

83

a: The unit of observation is the decision making in every round in the strategy-method stage.

5

b: The total number of observations is the number of HCA/LCA participants× the number of rounds understrategy method (Round 6 to 10).

Table A5. Summary of frequency (%) of strategy types in strategy method stage
HCA participants

LCA participants

Strategy Types

T1

T2

T3

T4

T1

T2

T3

T4

Fully cooperative

14.286

7.143

23.07730.69330

16.92323.33318.072

UC

0

0

0.769

3.960

9.000

3.846

1.111

2.410

Lenient

13.571

7.143

17.69224.75217

13.07718.88913.253Forgiving

14.286

7.143

17.69223.7621713.84617.77812.048

Unforgiving

0

0

4.615

2.970

4

3.077

4.444

3.614

Partially cooperative

520

13.07712.871

15

9.231

6.667

9.639

Fully non-cooperative

80.71472.85763.84656.43655

73.84670

72.289UD

44.28644.28646.15431.68337

38.46250

48.193

Obs.

140

70

130

101

100

130

90

83

a: T1 for treatment 1. T2 for treatment 2. T3 for treatment 3. T4 for treatment 4.
b: The unit of observation is the decision making in every round in the strategy-method stage.
c: The total number of observations is the number of HCA/LCA participants× the number of rounds understrategy method (Round 6 to 10).

2. Direct Response Method (Round 1- 5)
We employ the strategy frequency estimation method, following Dal Bó and Fréchette (2011) andFudenberg et al. (2012), to estimate the subjects’ strategies in the first five rounds under direct-response
method.3

We thank Guillaume Fréchette for kindly providing the original code for strategy estimation. We also thank Maria
Bigoni for kindly providing the modified code for strategy estimation.
6
3

The method works on the history of play as follows. First, we generate the simulated action sequence byfollowing the constructed strategy set which 35 simplified strategies considered in Table 1 in section 3.1. We
compare a subject’s actual action sequence against the simulated action sequence generated by a given
strategy from constructed strategy set sk. Then, strategy sk correctly matches the subject’s action sequence C
times and does not match the sequence E times. Therefore, the probability that player i employs strategy k isgiven by𝑃𝑖 (𝑠 𝑘 ) = ∏ ∏ 𝛽 𝐶 (1 − 𝛽)𝐸𝑟𝑜𝑢𝑛𝑑 𝑝𝑒𝑟𝑖𝑜𝑑βis the probability of correctly matching actions from the constructed strategy set and actions from the1
2

subjects. In each period, the subject plays according to the chosen strategy with probability βϵ( , 1)and1

makes a mistake with probability (1-β). When β is close to 2, choices are almost random, and when it is close
to 1, choices are almost perfectly predicted. In addition, the likelihood function is given byℒ(𝛽, 𝜙) =∑𝑖∈𝑆𝑢𝑏𝑗𝑒𝑐𝑡𝑠

ln (

∑

𝜙 𝑘 𝑃𝑖 (𝑠 𝑘 ))𝑘∈𝑆𝑡𝑟𝑎𝑡𝑒𝑔𝑖𝑒𝑠

𝜙 𝑘 is the frequency of strategy k.
For each treatment, we draw 100 random samples to calculate bootstrapped standard errors. Firstly, we
generate random samples using the following two ways. For the analysis of the entire sample, we take all
subjects in a given treatment and draw them at random with replacement until the random sample has as many
subjects as in the treatment. For the analysis of the HCA/LCA participants subsample, we take all subjects
from each subsample in a given treatment and draw them at random with replacement until the random sample
has as many subjects as in the corresponding cognitive ability group in the treatment. Secondly, we estimate
the strategy frequency for each random sample. Finally, we calculate the bootstrapped standard error.

Table A6. Estimation of strategies used in treatment 1(data from the direct-response-method stage)
HCA participants

LCA participants

7Strategy

Freq. (%)

Bootstrapped

p-value

Strategy

Freq. (%)

SEa

Bootstrapped

p-value

SE

TFT

3.506

0.017

0.019

UC

18.702

0.110

0.045

TFTc2d3

3.507

0.017

0.019

TFTc3d2

7.377

0.056

0.093

TFTc1d3

3.506

0.017

0.019

TFTc1d2

7.365

0.055

0.092

DTFT1

9.851

0.079

0.106

DTFT2

62.004

0.242

0.005

DTFTc2d3

7.555

0.066

0.127

DTFTc3d0

1.517

0.019

0.217

DTFTc1d3

7.498

0.066

0.128

DTFTc1d0

1.517

0.019

0.217

DTFT

7.442

0.066

0.130

DTFTc2d0

1.517

0.019

0.217

DTFTc0d3

7.498

0.066

0.128

γ

72.426

0.088

0.000

UD

49.632

0.256

0.026

β

79.911γ

53.485

0.061

0.000

β

86.642: The table reports the estimated frequency of each strategy in the population. We show the strategies withestimated frequency larger than 1%.
b: The parameter γ is used in estimation with1

β = 1+exp(−1 ).
⁄γTable A7. Estimation of strategies used in treatment 2(data from the direct-response-method stage)
HCA participants
Strategy

Freq. (%)

Bootstrapped

LCA participants
p-value

Strategy

Freq. (%)

SE

Bootstrapped

p-valueSE

TFTc1d1

7.145

0.090

0.213

UC

5.4939

0.035

0.059

DC alternative

6.804

0.000

0.000

Trigger2

6.7704

0.083

0.209

DTFT

39.426

0.199

0.024

TFTc1d1

3.2768

0.037

0.188

DTFTc1d1

7.202

0.078

0.179

DTFTc2d2

21.673

0.127

0.043

DTFTc1d3

9.890

0.061

0.053

DTFTc3d1

1.9531

0.013

0.068

8

a

DTFTc0d3

9.889

0.061

0.053

DTFTc2d1

1.9531

0.013

0.068

DTFTc2d3

9.824

0.061

0.054

DTFTc0d1

1.9527

0.013

0.068

UD

9.817

0.061

0.054

UD

56.927

0.250

0.011

γ

54.191

0.073

0.000

γ

62.225

0.056

0.000

β

86.358β83.300: The table reports the estimated frequency of each strategy in the population. We show the strategies withestimated frequency larger than 1%.
b: The parameter γ is used in estimation with

β=

1

.

1+exp(−1⁄γ)

Table A8. Estimation of strategies used in treatment 3 (data from the direct-response-method stage)
HCA participants
Strategy

Freq. (%)

Bootstrapped

LCA participants
p-value

Strategy

Freq. (%)

SE

Bootstrapped

p-valueSE

Trigger1

20.565

0.113

0.034

Trigger2

6.793

0.058

0.123

Trigger2

2.662

0.046

0.283

TFT2

19.199

0.126

0.063

TFTc1d1

18.788

0.065

0.002

TFT1

5.474

0.071

0.222

TFT

3.190

0.042

0.222

DTFT1

5.152

0.072

0.236

DC alternative

1.377

0.000

0.000

C to All D

4.511

0.049

0.180

DTFT

8.446

0.100

0.199

UD

58.870

0.157

0.000

DTFTc3d2

2.663

0.024

0.129

γ

56.506

0.095

0.000

DTFTc1d0

2.663

0.024

0.129

β

85.442

DTFTc0d2

2.663

0.024

0.129

UD

36.983

0.197

0.030

γ

68.832

0.092

0.000

β

81.0439a: The table reports the estimated frequency of each strategy in the population. We show the strategies withestimated frequency larger than 1%.
b1: The parameter γ is used in estimation with β = 1+exp(−1 ).
⁄γTable A9. Estimation of strategies used in treatment 4 (data from the direct-response-method stage)
HCA participants
Strategy

Freq. (%)

LCA participants

Bootstrapped

p-value

Strategy

Freq. (%)

BootstrappedSEap-valueSEUC

12.983

0.092

0.078

Trigger1

20.423

0.107

0.028

Grim

6.879

0.057

0.114

Trigger2

9.386

0.081

0.123

Trigger1

3.681

0.104

0.361

TFT2

13.209

0.084

0.058

TFT1

13.838

0.075

0.032

DTFT1

4.833

0.043

0.133

TFT2

5.116

0.068

0.224

UD

51.193

0.154

0.000

TFTc1d2

3.454

0.025

0.084

γ

46.942

0.073

0.000

TFTc3d2

3.448

0.025

0.083

β

89.381

UD

50.601

0.199

0.005

γ

54.082

0.074

0.000

β

86.401: The table reports the estimated frequency of each strategy in the population. We show the strategies withestimated frequency larger than 1%.
b: The parameter γ is used in estimation with

β=

1

.

1+exp(−1⁄γ)

Table A10. Summary of estimated frequency (%) of strategy types in direct response method by using SFEM
Strategy Types

Fully cooperative

HCA participants

LCA participants

T1

T2

T3

T4

T1

T2

T3

T4

10.5197.145

45.20549.39933.44415.54131.46643.018

10

UC

0

0

0

12.98318.702

5.494

0

0

Lenient

7.013

7.145

42.01529.53714.74210.04731.46643.018Forgiving

10.5197.145

21.97825.85614.742

3.277

24.67313.209Unforgiving

0023.227

10.560

0

6.770

6.793

29.809Partially cooperative

0

6.804

1.377

0

0

0

4.511

0

Fully non-cooperative

89.47686.04853.41850.60166.55584.45964.02256.026

UD

49.6329.817

36.98350.601056.92758.87051.193

Obs.

28

14

26

22

20

26

18

18

a: T1 indicates treatment 1. T2 indicates treatment 2. T3 indicates treatment 3. T4 indicates treatment 4.
b: The unit of observation is the number of HCA participants and LCA participants in each treatment.

D. Regression results for figures

Table A11. Odds ratio estimates of logistic regression of HCA dummy and demographic characteristics on first
period cooperation and all periods cooperation in direct response method (Round 1 to 5) with robust standard
error clustered by group
(1)

(2)
(3)
Direct Response Method(Round 1 to 5)
First Period Cooperation
T2
T3

(4)

(5)

T4

T1

(6)
(7)
Direct Response Method(Round 1 to 5)
All Period Cooperation
T2
T3

VARIABLES

T1

HCA dummy-0.766***(0.246)-0.120(0.083)0.066(0.289)-0.462(0.576)2.125(1.744)-0.354(0.431)
0.037(0.145)0.485(0.399)-0.706*(0.402)-1.512(2.942)0.228(0.312)0.204***(0.070)0.420(0.324)-0.387(0.435)-4.850***(1.548)0.473(0.293)0.344***(0.104)-0.097(0.287)-1.145***(0.343)-6.989***(2.020)-0.969***(0.238)-0.036(0.074)0.024(0.254)-0.784(0.514)0.427(1.570)-0.392(0.330)0.001(0.118)0.667**(0.308)-0.329(0.295)-1.063(2.377)

240

200

220

200

400

464

Age
Male
Economics
Constant

Observations

(8)

T4

0.165
0.530**(0.214)(0.228)0.104**
0.287***(0.051)(0.061)0.379*-0.263(0.220)(0.239)-0.379-0.615**(0.236)(0.303)-3.344*** -6.955***(1.143)(1.360)
1,256

1,776

11

Clusters
Wald chi2
Prob > chi2
Pseudo R2

60
12.332
0.015
0.030

50
5.467
0.243
0.022

55
21.417
0.000
0.055

50
22.516
0.000
0.091

60
19.3620.001
0.043

Predicted first period cooperation rate
HCA
participants
LCA
participants

0.241(0.032)0.404(0.044)0.256(0.061)
0.327(0.043)0.448(0.047)0.397(0.052)0.489(0.050))0.387(0.042)

50
7.568
0.109
0.017

55
24.605
0.000
0.025

50
35.7500.000
0.056

Predicted all period cooperation rate
0.209
(0.029)0.409(0.052)0.228(0.049)0.302(0.039)0.297(0.037)0.264(0.034)0.276(0.039)0.187(0.033)a: HCA dummy = 1 for HCA participants and 0 for LCA participants. Male =1 for male and 0 for female.
Economics =1 for students from economics and management major and 0 for otherwise. b: The unit ofobservation is the decision making in period 1 in every round. The total number of observations is the number ofsubjects × number of rounds. c: The robust standard errors cluster by group are in parentheses. *** p < 0.01, ** p
< 0.05, and * p < 0.1

Table A12. Odds ratio estimates of logistic regression of HCA dummy and demographic characteristics on first
period cooperation and all periods cooperation in strategy method (Round 6 to 10) with robust standard error
clustered by group
(1)

(2)
(3)
Strategy Method(Round 6 to 10)
First period cooperation
T2
T3

(4)

(5)

T4

T1

(6)
(7)
Strategy Method(Round 6 to 10)
All period cooperation
T2
T3

(8)

VARIABLES

T1

HCA dummy-0.944***(0.349)-0.057(0.092)0.281(0.361)-2.162*(1.110)0.570(1.897)-0.615(0.385)0.101(0.159)0.715*(0.414)0.158(0.381)-3.447(3.210)0.288(0.295)0.100(0.076)0.553(0.358)-0.480(0.427)-3.306**(1.636)1.045***(0.327)0.156*(0.090)0.752**(0.381)-0.869**(0.381)-4.642**(1.822)-1.239***(0.355)-0.053(0.087)0.363(0.338)-2.524**(1.150)0.441(1.823)-0.482(0.517)0.017(0.139)0.880**(0.404)-0.007(0.335)-2.273(2.775)0.141-0.363(0.277)(0.473)0.320***
0.476***(0.078)(0.129)0.167-0.567(0.400)(0.417)0.522-0.132(0.641)(0.451)-9.072*** -11.239***(1.719)(2.511)240
60
11.212
0.024
0.060

200
50
3.881
0.422
0.017

220
55
9.779
0.044
0.041

184
46
22.027
0.000
0.091

320
60
15.983
0.003
0.089

532
50
7.161
0.128
0.020

1,232
55
19.586
0.001
0.048

Age
Male
Economics
Constant

Observations
Clusters
Wald chi2
Prob > chi2
Pseudo R2

Predicted first period cooperation rate

T4

1,792
46
14.7970.005
0.076

Predicted all period cooperation rate

12

HCA
participants
LCA
participants

0.182(0.035)0.358(0.051)

0.162(0.039)0.260(0.037)

0.336(0.039)0.278(0.045)0.431(0.047)0.224(0.042)0.140(0.027)0.352(0.057)0.123(0.033)0.183(0.041)

0.112(0.022)0.099(0.025)0.089(0.020)0.121(0.041)a: HCA dummy = 1 for subjects belong to HCA participants and 0 for LCA participants. Male =1 for male and 0
for female. Economics =1 for students from economics and management major and 0 for otherwise. b: The unit ofobservation is the decision making in period 1 in every round. The total number of observations is the number ofsubjects × number of rounds. c: The robust standard errors cluster by group are in parentheses. *** p < 0.01, ** p
< 0.05, and * p < 0.1

Table A13. Odds ratio estimates of logistic regression of HCA dummy and demographic characteristics on first
period cooperation and all periods cooperation in strategy method (Simulation) with robust standard error
clustered by group
(1)

(2)
(3)
Strategy Method(Simulation)
First period cooperation
T2
T3

(4)

(5)

T4

T1

(6)
(7)
Strategy Method(Simulation)
All period cooperation
T2
T3

(8)

VARIABLES

T1

HCA dummy-0.944***(0.016)-0.057***(0.004)0.281***(0.016)-2.162***(0.050)0.570***(0.083)-0.112*** 0.021*
0.768*** -0.888*** -0.263***
0.003(0.027)(0.013)(0.009)(0.016)(0.030)(0.014)0.077*** 0.085***-0.000-0.048*** 0.109*** 0.161***(0.008)(0.003)(0.004)(0.004)(0.007)(0.003)0.115*** 1.004*** 0.278*** 0.263*** 0.448*** 0.581***(0.028)(0.013)(0.010)(0.015)(0.028)(0.013)-0.259*** -0.061*** -0.989*** -2.495*** -0.305*** 0.284***(0.026)(0.017)(0.011)(0.051)(0.027)(0.020)-2.783*** -2.743*** -0.939*** 0.284*** -3.806*** -5.119***(0.155)(0.065)(0.074)(0.079)(0.153)(0.076)0.083***(0.010)-0.018***(0.005)-0.300***(0.011)-0.807***(0.014)-1.076***(0.094)109,200
27300
5768.71
0.000
0.060

56,20014050
309.560.000
0.004

2,773,568
60410
3811.93
0.000
0.017

Age
Male
Economics
Constant

Observations
Clusters
Wald chi2
Prob > chi2
Pseudo R2

116,700
29175
8801.68
0.000
0.053

241,640
60410
20508.26
0.000
0.056

Predicted first period cooperation rate
HCA
participants
LCA
participants

0.182(0.002)0.358(0.002)0.205(0.003)0.224(0.002)0.423(0.002)0.418(0.002)0.436(0.001)
0.271(0.001)

145,600
27300
5643.65
0.000
0.062

148,100
14050
785.360.000
0.0097

460,560
29175
4555.24
0.000
0.028

T4

Predicted all period cooperation rate
0.173
(0.002)0.332(0.002)0.150(0.003)0.187(0.002)0.215(0.002)0.215(0.002)0.144(0.001)0.154(0.001)13

a: HCA dummy = 1 for HCA participants and 0 for LCA participants. Male =1 for male and 0 for female.

Economics =1 for students from economics and management major and 0 for otherwise. b: The unit ofobservation is the decision making in period 1 in every round. The total number of observations is the number ofsubjects × number of rounds. c: The robust standard errors cluster by group are in parentheses. *** p < 0.01, ** p
< 0.05, and * p < 0.1

Table A14. Odds ratio estimates of logistic regression of HCA dummy and demographic characteristics on the
fully cooperative strategy in strategy method stage, with robust standard error
(1)

(2)
(3)
Fully cooperative strategy dummy
T2
T3

(4)

VARIABLES

T1

HCA dummy-1.055***(0.341)
0.012(0.093)0.585(0.370)-1.902*(1.085)-1.286(1.929)-1.202*(0.624)-0.123(0.198)0.672(0.467)0.790*(0.435)0.362(3.916)-0.308(0.364)0.125(0.085)0.939**(0.393)-0.502(0.528)-4.157**(1.832)0.880**(0.386)0.310***(0.109)0.475(0.438)-0.651(0.450)-7.956***(2.104)240
13.573
0.009
0.069

200
9.315
0.054
0.064

220
11.103
0.025
0.058

184
19.406
0.001
0.094

Age
Male
Economics
Constant

Observations
Wald chi2
Prob > chi2
Pseudo R2

T4

Predicted Frequency
HCA participants
LCA participants

0.139 (0.029)
0.310 (0.045)

0.064 (0.031)
0.180 (0.036)

0.213 (0.035)
0.265 (0.049)

0.322 (0.046)
0.175 (0.040)

a: Fully cooperative strategy dummy = 1 for fully cooperative strategy and 0 for other strategies. HCA dummy = 1

for HCA participants and 0 for LCA participants. Male =1 for male and 0 for female. Economics =1 for students
from economics and management major and 0 for otherwise. b: The unit of observation is the elicited strategy inevery round. The total number of observations is the number of subjects × number of rounds. c: The robust
standard errors are in parentheses. *** p < 0.01, ** p < 0.05, and * p < 0.1

Table A15. Odds ratio estimates of logistic regression of HCA dummy and demographic characteristics on theforgiving strategy in strategy method stage, with robust standard error
(1)

(2)
(3)
Forgiving strategy dummy

(4)

14

VARIABLES

T1

T2

T3

T4

HCA dummy-0.266(0.369)0.047(0.089)0.216(0.383)
N/A-0.192(0.399)0.119(0.092)0.518(0.422)-0.568(0.593)-4.138**(1.971)0.970**(0.426)0.150(0.121)0.424(0.491)-0.616(0.513)-5.180**(2.283)

220
5.835
0.212
0.033

184
10.3860.034
0.058

Constant-2.566(1.845)-1.074(0.661)-0.169(0.232)
1.015**(0.508)1.165**(0.467)0.710(4.560)Observations
Wald chi2
Prob > chi2
Pseudo R2

220
1.099
0.777
0.006

200
11.844
0.019
0.094

Age
Male
Economics

Predicted Frequency
HCA participants
LCA participants

0.153 (0.032)
0.190 (0.042)

0.061 (0.030)
0.151 (0.033)

0.167 (0.033)
0.194 (0.044)

0.249 (0.044)
0.114 (0.034)

a: Forgiving strategy dummy = 1 for forgiving strategy and 0 for other strategies. HCA dummy = 1 for HCA

participants and 0 for LCA participants. Male =1 for male and 0 for female. Economics =1 for students from
economics and management major and 0 for otherwise. b: The unit of observation is the elicited strategy in every
round. The total number of observations is the number of subjects × number of rounds. c: The robust standard
errors are in parentheses. *** p < 0.01, ** p < 0.05, and * p < 0.1

Table A16. Odds ratio estimates of logistic regression of HCA dummy and demographic characteristics on thelenient strategy in strategy method stage, with robust standard error(1)
VARIABLES

T1

HCA dummy

Economics-0.345(0.375)0.042(0.092)0.449(0.405)
N/A

Constant-2.597

Age
Male

(2)
(3)
Lenient strategy dummy
T2
T3-0.677(0.644)-0.157(0.209)0.276(0.516)0.596(0.475)0.906-0.332(0.404)0.080(0.099)0.757*(0.441)-0.577(0.588)-3.381(4)
T4
0.898**(0.416)0.157(0.117)0.379(0.469)-0.520(0.495)-5.186**15

Observations
Wald chi2
Prob > chi2
Pseudo R2(1.890)(4.109)(2.093)(2.224)

220
2.328
0.507
0.013

200
4.949
0.293
0.032

220
6.649
0.156
0.040

184
9.564
0.048
0.052

Predicted Frequency
HCA participants
LCA participants

0.144 (0.031)
0.192 (0.042)

0.072 (0.035)
0.131 (0.032)

0.164 (0.033)
0.212 (0.047)

0.258 (0.045)
0.127 (0.036)

a: Lenient strategy dummy =1 for lenient strategy and 0 for other strategies. HCA dummy = 1 for HCA
participants and 0 for LCA participants. Male =1 for male and 0 for female. Economics =1 for students from
economics and management major and 0 for otherwise. b: The unit of observation is the elicited strategy in every
round. The total number of observations is the number of subjects × number of rounds. c: The robust standard
errors are in parentheses. *** p < 0.01, ** p < 0.05, and * p < 0.1

Table A17. Odds ratio estimates of logistic regression of treatment dummy and demographic characteristics oncooperation in period 1 and all periods among HCA participants and LCA participants in direct response method(Round 1 to 5) with robust standard error clustered by group; and the fully cooperative strategy among HCA
participants and LCA participants in strategy method (Round 6 to 10) with robust standard error
(1)
(2)
(1)
(2)
HCA
LCA
HCA
LCA
DirectDirectDirectDirectResponse
Response
Response
Response
MethodMethodMethodMethod(Round 1 to 5) (Round 1 to 5) (Round 1 to 5) (Round 1 to 5)
Cooperation
Cooperation
Cooperation
Cooperation
Period 1
Period 1
All periods
All periods(Default:
Treatment 1)
Treatment 2
Treatment 3
Treatment 4
Age
Male
Economics

0.453(0.327)1.079***(0.271)1.326***(0.282)0.074(0.050)-0.041(0.208)-0.748***0.114(0.287)0.090(0.298)0.326(0.296)
0.249***(0.084)
0.391*(0.227)-0.747**0.576*(0.329)0.633**(0.251)0.635**(0.272)0.168***(0.045)-0.126(0.175)-0.437*-0.209(0.287)-0.584**(0.271)-0.970***(0.347)0.130**(0.066)0.455*(0.240)-0.482**(3)
HCA
Strategy
Method(Round 6 to
10)
Fully
cooperative
strategy(4)
LCA
Strategy
Method(Round 6 to
10)
Fully
cooperative
strategy-0.645(0.533)0.630*(0.327)1.361***(0.353)0.163***(0.059)0.439(0.286)-0.499-0.419(0.349)-0.227(0.336)-0.779*(0.408)0.034(0.092)0.952***(0.281)-0.14616

Constant(0.259)-2.639**(1.104)(0.297)-5.798***(1.759)(0.256)-4.769***(0.993)(0.228)-3.305**(1.412)(0.351)-5.496***(1.311)(0.316)-2.075(1.957)

Observations
Clusters
Wald chi2
Prob > chi2
Pseudo R2

450
201
37.035
0.000
0.052

410
199
24.096
0.001
0.052

2,124
201
32.290
0.000
0.030

1,772
199
30.014
0.000
0.040

441

403

27.0680.000
0.077

19.0340.004
0.050

Predicted Frequency
T1
T2
T3
T4
T1=T2
T1=T3
T1=T4
T2=T3
T2=T4
T3=T4

0.223 (0.032)
0.309 (0.054)
0.451 (0.049)
0.511 (0.049)

0.339 (0.041)
0.363 (0.044)
0.358 (0.049)
0.409 (0.048)

0.182 (0.027)
0.280 (0.053)
0.291 (0.036)
0.292 (0.040)

0.367 (0.048)
0.321 (0.042)
0.248 (0.033)
0.184 (0.037)

0.132 (0.028)
0.074 (0.032)
0.218 (0.035)
0.360 (0.050)

0.277 (0.044)
0.204 (0.039)
0.236 (0.044)
0.154 (0.040)

Prob > chi2

Prob > chi2

Prob > chi2

Prob > chi2

Prob > chi2

Prob > chi2

0.166
0.000
0.000
0.058
0.008
0.401

0.693
0.762
0.271
0.940
0.490
0.470

0.080
0.012
0.020
0.861
0.859
0.993

0.467
0.031
0.005
0.159
0.025
0.237

0.226
0.054
0.000
0.014
0.000
0.025

0.230
0.499
0.056
0.594
0.385
0.194

a: Treatment 1 dummy = 1 for treatment 1 and 0 for others. Treatment 2 dummy = 1 for treatment 2 and 0 forothers. Treatment 3 dummy = 1 for treatment 3 and 0 for others. Treatment 4 dummy = 1 for treatment 4 and 0
for others. The default treatment is treatment 1. Male =1 for male and 0 for female. Economics =1 for students
from economics and management major and 0 for otherwise. b: The unit of observation is the decision making inall periods in every round. The total number of observations is the number of subjects × number of rounds ×
number of periods. c: The robust standard errors cluster by group are in parentheses. *** p < 0.01, ** p < 0.05,
and * p < 0.1

E. Analyses of experimental results unconditional on personal characteristics
Table A18. Odds ratio estimates of logistic regression of HCA dummy on first period cooperation and all periods
cooperation in direct response method (Round 1 to 5) with robust standard error clustered by group
(1)

(2)
(3)
Direct Response Method(Round 1 to 5)
First Period Cooperation
T2
T3

VARIABLES

T1

HCA dummy-0.732***

0.000

0.345

(4)

(5)

T4

T1

0.214

-0.932***(6)(7)
Direct Response Method(Round 1 to 5)
All Period Cooperation
T2
T3
0.010

0.293

(8)

T4
0.452*

17

Constant(0.235)-0.405**(0.177)(0.342)-0.847***(0.193)(0.292)-0.499**(0.222)(0.276)-0.359*(0.207)(0.229)-0.386*(0.208)(0.308)(0.188)(0.244)-0.979*** -1.104*** -1.447***(0.177)(0.169)(0.227)

Observations
Clusters
Wald chi2
Prob > chi2
Pseudo R2

240
60.000
9.702
0.002
0.023

200
50.000
0.000
1.000
0.000

220
55.000
1.393
0.238
0.005

200
50.000
0.598
0.439
0.002

400
60.00016.590
0.000
0.036

464
50.000
0.001
0.974
0.000

First period cooperation rate
HCA
participants
LCA
participants

0.243(0.036)0.400(0.049)0.300(0.055)0.300(0.040)0.462(0.044)0.378(0.051)

1,256
55.000
2.438
0.118
0.003

1,776
50.000
3.421
0.064
0.008

All period cooperation rate
0.464
(0.048)0.411(0.052)0.211(0.027)0.405(0.038)0.275(0.035)0.273(0.026)0.308(0.017)0.249(0.019)0.270(0.014)0.190(0.014)

a: HCA dummy = 1 for HCA participants and 0 for LCA participants. Male =1 for male and 0 for female.

Economics =1 for students from economics and management major and 0 for otherwise. b: The unit ofobservation is the decision making in period 1 in every round. The total number of observations is the number ofsubjects × number of rounds. c: The robust standard errors cluster by group are in parentheses. *** p < 0.01, ** p
< 0.05, and * p < 0.1

Table A19. Odds ratio estimates of logistic regression of HCA dummy on first period cooperation and all periods
cooperation in strategy method (Round 6 to 10) with robust standard error clustered by group(1)

VARIABLESHCA dummy
Constant

Observations
Clusters
Wald chi2
Prob > chi2
Pseudo R2

T1

(2)
(3)
Strategy Method(Round 6 to 10)
First period cooperation
T2
T3

(4)

(5)

T4

T1

(8)

T4

-0.859**-0.182
0.467*
0.767*** -1.144***
0.035
0.016
-0.299(0.334)(0.340)(0.275)(0.278)(0.338)(0.342)(0.395)(0.493)-0.619*** -1.204*** -1.069*** -1.147*** -0.648** -1.701*** -2.138*** -2.002***(0.222)(0.180)(0.221)(0.227)(0.256)(0.225)(0.367)(0.416)240
60.000
6.606
0.010
0.030

200
50.000
0.287
0.592
0.001

220
55.000
2.874
0.090
0.009

184
46.000
7.585
0.006
0.024

320
60.00011.4310.001
0.052

First period cooperation rate
HCA
participants(6)(7)
Strategy Method(Round 6 to 10)
All period cooperation
T2
T3

0.186
(0.033)0.2(0.048)0.354(0.042)532
50.000
0.011
0.918
0.000

1,232
55.000
0.002
0.969
0.000

1,792
46.000
0.366
0.545
0.003

All period cooperation rate
0.406
(0.049)0.143(0.026)0.159(0.026)0.107(0.012)0.091(0.009)18

LCA
participants

0.35(0.048)0.231(0.037)0.256(0.046)0.241(0.047)0.344(0.042)0.154(0.020)0.105(0.136)0.119(0.011)

a: HCA dummy = 1 for HCA participants and 0 for LCA participants. Male =1 for male and 0 for female.

Economics =1 for students from economics and management major and 0 for otherwise. b: The unit ofobservation is the decision making in period 1 in every round. The total number of observations is the number ofsubjects × number of rounds. c: The robust standard errors cluster by group are in parentheses. *** p < 0.01, ** p
< 0.05, and * p < 0.1

Table A20. Odds ratio estimates of logistic regression of HCA dummy on first period cooperation and all periods
cooperation in strategy method (Simulation) with robust standard error clustered by group(1)

VARIABLESHCA dummy
Constant

Observations
Clusters
Wald chi2
Prob > chi2
Pseudo R2

T1

(2)
(3)
Strategy Method(Simulation)
First period cooperation
T2
T3

(4)

(5)

T4

T1

(8)

T4

-0.859***-0.0240.218*** 0.702*** -0.807*** 0.034*
0.125*** 0.097***(0.015)(0.020)(0.012)(0.008)(0.016)(0.020)(0.014)(0.010)-0.619*** -1.275*** -0.463*** -0.976*** -0.735*** -1.588*** -1.377*** -1.790***(0.010)(0.012)(0.010)(0.006)(0.010)(0.014)(0.015)(0.010)109,200
27300
3326.01
0.000
0.030

56,200
14050
1.38
0.240
0.000

116,700
29175
322.650.000
0.002

241,640
60410
7017.64
0.000
0.021

145,600
27300
2622.39
0.000
0.026

First period cooperation rate
HCA
participants
LCA
participants(6)(7)
Strategy Method(Simulation)
All period cooperation
T2
T3

0.186
(0.002)0.350(0.002)0.214(0.003)0.218(0.002)0.439(0.002)0.386(0.002)

148,100
14050
2.97
0.085
0.000

460,560
29175
81.90
0.000
0.001

2,773,568
60410
88.26
0.000
0.000

All period cooperation rate
0.432
(0.001)
0.274(0.001)0.176(0.001)
0.324(0.002)0.174(0.002)0.170(0.001)0.222(0.001)0.201(0.001)0.155(0.000)0.143(0.000)a: HCA dummy = 1 for HCA participants and 0 for LCA participants. Male =1 for male and 0 for female.

Economics =1 for students from economics and management major and 0 for otherwise. b: The unit ofobservation is the decision making in period 1 in every round. The total number of observations is the number ofsubjects × number of rounds. c: The robust standard errors cluster by group are in parentheses. *** p < 0.01, ** p
< 0.05, and * p < 0.1

Table A21. Odds ratio estimates of logistic regression of HCA dummy on the fully cooperative strategy instrategy method stage, with robust standard error

19

(1)

(2)
(3)
Fully cooperative strategy
T2
T3

(4)

VARIABLES

T1

HCA dummy-0.944***(0.326)-0.847***(0.219)-0.974*(0.521)-1.591***(0.234)-0.014(0.325)-1.190***(0.250)0.697*(0.359)-1.511***(0.286)

240
8.384
0.004
0.035

200
3.494
0.062
0.026

220
0.002
0.965
0.000

184
3.777
0.052
0.019

0.231 (0.037)
0.233 (0.045)

0.307 (0.046)
0.181 (0.042)

Constant

Observations
Wald chi2
Prob > chi2
Pseudo R2

T4

Frequency
HCA participants
LCA participants

0.143 (0.030)
0.300 (0.046)

0.071 (0.031)
0.169 (0.033)

a: HCA dummy = 1 for HCA participants and 0 for LCA participants. Male =1 for male and 0 for female.

Economics =1 for students from economics and management major and 0 for otherwise. b: The unit ofobservation is the elicited strategy in every round. The total number of observations is the number of subjects ×
number of rounds. c: The robust standard errors are in parentheses. *** p < 0.01, ** p < 0.05, and * p < 0.1

Table A22. Odds ratio estimates of logistic regression of HCA dummy on the forgiving strategy in strategy
method stage, with robust standard error
(1)

(2)

(3)

(4)

Forgiving strategy
VARIABLES

T1

T2

T3

T4

HCA dummy-0.206(0.360)-1.586***(0.267)-0.737(0.530)-1.828***(0.255)-0.006(0.360)-1.531***(0.276)0.822**(0.411)-1.988***(0.338)

240
0.327
0.567
0.002

200
1.930
0.165
0.015

220
0.000
0.987
0.000

184
3.993
0.046
0.024

0.177 (0.034)
0.178 (0.041)

0.238 (0.043)
0.120 (0.036)

Constant

Observations
Wald chi2
Prob > chi2
Pseudo R2

Frequency
HCA participants
LCA participants

0.143 (0.030)
0.170 (0.038)

0.071 (0.031)
0.138 (0.030)

a: HCA dummy = 1 for HCA participants and 0 for LCA participants. Male =1 for male and 0 for female.

20

Economics =1 for students from economics and management major and 0 for otherwise. b: The unit ofobservation is the elicited strategy in every round. The total number of observations is the number of subjects ×
number of rounds. c: The robust standard errors are in parentheses. *** p < 0.01, ** p < 0.05, and * p < 0.1

Table A23. Odds ratio estimates of logistic regression of HCA dummy on the lenient strategy in strategy method
stage, with robust standard error
(1)

(2)

(3)

(4)

Lenient strategy
VARIABLES

T1

T2

T3

T4

HCA dummy-0.266(0.364)-1.586***(0.267)-0.671(0.533)-1.894***(0.261)-0.080(0.355)-1.457***(0.270)0.767*(0.399)-1.879***(0.325)

240
0.534
0.465
0.003

200
1.582
0.209
0.013

220
0.051
0.821
0.000

184
3.703
0.054
0.022

0.177 (0.034)
0.189 (0.041)

0.248 (0.043)
0.133 (0.037)

Constant

Observations
Wald chi2
Prob > chi2
Pseudo R2

Frequency
HCA participants
LCA participants

0.136 (0.029)
0.170 (0.038)

0.071 (0.031)
0.131 (0.030)

a: HCA dummy = 1 for HCA participants and 0 for LCA participants. Male =1 for male and 0 for female.

Economics =1 for students from economics and management major and 0 for otherwise. b: The unit ofobservation is the elicited strategy in every round. The total number of observations is the number of subjects ×
number of rounds. c: The robust standard errors are in parentheses. *** p < 0.01, ** p < 0.05, and * p < 0.1

21

F. The frequency of unconditional defection strategy between HCA participants and LCA participants
Table A24. Odds ratio estimates of logistic regression of HCA dummy and demographic characteristics on theunconditional strategy in strategy method stage, with robust standard error
(1)

(2)
(3)
Unconditional defection
T2
T3

(4)

VARIABLES

T1

HCA dummy

0.376(0.277)-0.012(0.089)-0.109(0.293)1.642***(0.550)-0.392(1.866)1.006**(0.402)0.011(0.149)-1.161***(0.380)0.851**(0.342)-0.725(2.985)-0.0791(0.288)-0.029(0.071)-0.158(0.300)0.272(0.374)0.595(1.538)-0.834**(0.324)0.064(0.088)-0.380(0.316)0.452(0.330)-1.210(1.772)

240
12.83
0.012
0.038

200
14.34
0.006
0.063

220
1.952
0.745
0.007

184
9.100
0.059
0.037

Age
Male
Economics
Constant

Observations
Wald chi2
Prob > chi2
Pseudo R2

T4

Predicted Frequency
HCA participants
LCA participants

0.448 (0.040)
0.362 (0.048)

0.553 (0.066)
0.335 (0.038)

0.469 (0.045)
0.489 (0.054)

0.305 (0.046)
0.498 (0.054)

a: HCA dummy = 1 for HCA participants and 0 for LCA participants. Male =1 for male and 0 for female.

Economics =1 for students from economics and management major and 0 for otherwise. b: The unit ofobservation is the elicited strategy in every round. The total number of observations is the number of subjects ×
number of rounds. c: The robust standard errors are in parentheses. *** p < 0.01, ** p < 0.05, and * p < 0.1

Table A25. Odds ratio estimates of logistic regression of HCA dummy on the unconditional defection strategy instrategy method stage, with robust standard error(1)
VARIABLES

T1

HCA dummy

0.303(0.269)-0.532**(0.208)Constant(2)(3)
Unconditional defection
T2
T3
0.240
(0.301)-0.470***(0.181)-0.154(0.275)-0(0.211)(4)
T4-0.696**(0.307)-0.0723(0.220)22

Observations
Wald chi2
Prob > chi2
Pseudo R2

240
1.269
0.260
0.00394

200
0.636
0.425
0.00236

220
0.314
0.575
0.00104

184
5.126
0.02360.0212

0.462 (0.044)
0.5 (0.053)

0.317 (0.046)
0.482 (0.055)

Frequency
HCA participants
LCA participants

0.443 (0.042)
0.37 (0.048)

0.443 (0.060)
0.385 (0.043)

a: HCA dummy = 1 for HCA participants and 0 for LCA participants. Male =1 for male and 0 for female.
Economics =1 for students from economics and management major and 0 for otherwise. b: The unit ofobservation is the elicited strategy in every round. The total number of observations is the number of subjects ×
number of rounds. c: The robust standard errors are in parentheses. *** p < 0.01, ** p < 0.05, and * p < 0.1

23

G. Average payoff between HCA participants and LCA participants
Table A26. OLS regression of HCA dummy and demographic characteristics on payoff in direct response method (Round 1 to 5), strategy method (Round 6 to 10)
and strategy method (simulation) with robust standard error clustered by group
(1)

(2)
(3)
Direct Response Method(Round 1 to 5)
Payoff
T2
T3

(4)

(5)

T4

T1

(6)
(7)
Strategy Method(Round 6 to 10)
Payoff
T2
T3

(8)

(9)

T4

T1

(10)
(11)
Strategy Method(Simulation)
Payoff
T2
T3

VARIABLES

T1

HCA dummy

0.783(0.514)0.227(0.170)-0.232

1.431**(0.558)-0.272(0.208)-1.245**-0.057(0.481)0.214*(0.111)-0.271-0.811*(0.460)-0.220*(0.127)
0.119

0.447
(0.506)-0.246*(0.132)-0.089-0.253(0.663)-0.069(0.177)-0.4090.255(0.332)0.231**(0.106)0.561-0.219(0.363)-0.065(0.164)0.362

0.930***(0.027)0.081***(0.007)-0.375***0.074*(0.041)-0.091***(0.011)-0.309***

400
60
0.958
0.437
0.013

464
50
4.113
0.006
0.042

1,256
55
1.821
0.138
0.009

1,776
50
1.476
0.224
0.019

320
60
1.741
0.153
0.018

532
50.000
1.109
0.363
0.011

1,232
55
2.253
0.075
0.027

1,792
46
0.657
0.625
0.008

145,600
27300
491.000.000
0.019

148,100
14050
131.15
0.000
0.007

Age
Male

Economics
Constant

Observations
Clusters
F
Prob > F
R2

(12)

T4

0.289*** 0.153***(0.022)(0.014)0.153***-0.008(0.006)(0.005)0.077***
0.154***(0.403)(0.523)(0.416)(0.487)(0.557)(0.524)(0.432)(0.364)(0.027)(0.039)(0.022)(0.014)0.102
1.452**-0.107-0.196
0.997
0.481
0.206
0.376
1.389*** 0.586*** 0.358*** 0.137***(0.607)(0.555)(0.452)(0.471)(1.056)(0.411)(0.531)(0.363)(0.044)(0.033)(0.031)(0.016)
7.817** 17.779*** 8.628*** 17.198*** 17.112*** 13.087*** 5.837** 12.113*** 10.194*** 13.527*** 8.758*** 11.482***(3.608)(4.204)(2.468)(2.784)(2.808)(3.545)(2.225)(3.263)(0.155)(0.224)(0.136)(0.106)Predicted average payoff

Predicted average payoff

460,560
29175
192.490.000
0.006

2,773,568
60410
59.24
0.000
0.001

Predicted average payoff

24

HCA
participants
LCA
participants

13.254(0.366)12.471(0.366)13.675(0.531)
12.244(0.325)12.820(0.374)12.876(0.395)11.978(0.370)12.789(0.460)12.433(0.430)11.986(0.366)

11.400(0.512)11.653(0.283)11.169(0.269)10.915(0.255)10.938(0.304)11.157(0.309)12.747(0.019)11.817(0.020)11.761(0.031)
11.687(0.022)

12.251(0.017)11.962(0.022)

11.567(0.013)
11.414(0.013)a: HCA dummy = 1 for HCA participants and 0 for LCA participants. Male =1 for male and 0 for female. Economics =1 for students from economics andmanagement major and 0 for otherwise. b: The unit of observation is the decision making in all periods in every round. The total number of observations is thenumber of subjects × number of rounds × number of periods. c: The robust standard errors cluster by group are in parentheses. *** p < 0.01, ** p < 0.05, and * p <0.1

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H. Experimental instruction
Sample of Experimental Instruction for treatment 4 (in Japanese)
経済実験説明書

実験にご参加いただきありがとうございます。これから、経済実験を行います。説明書をよく読み、内容を完全に理解して参加ください。何か不明な点があれば、すぐに手を上げスタッフにお知らせください。

1. 配布資料席に着いたら、A4 用紙の紙が 5 種類あることを確認して下さい。
1. 実験参加同意書 2. 実験説明書
3. 画面説明書 4. 記録用紙

5.領収書

2. 実験の報酬について
実験の報酬は 2 つの部分からなります。１つは参加報酬です。参加報酬として皆様全員に 1000 円をお支払いします。もう 1 つは成果報酬です。成果報酬は実験の結果によって決まります。
3. グループの決まり方➢ ゲーム開始時に、グループがランダムに決まります。全てのグループは 4 人の参加者からなります。グループ番号がコンピュータ
画面に表示されます。
➢ 各ラウンドで、グループは同じです。あなたは、グループのメンバーが誰なのかを知ることはできません。
➢ 実験は 10 ラウンドからなります。この実験は、前半 5 ラウンドと後半 5 ラウンドで意思決定の仕方が異なりますが、グループの決まり方とピリオドの決まり方は同じです。
➢ 各ラウンドの開始時点で、全てのグループはランダムに組みなおされます。従って、あなたはもう一度同じメンバーとグループを組むかもしれませんし、まったく新しいメンバーとグループを組むかもしれません。
➢ グループ番号を確認したら、次の意思決定に進んでください。
4. 各ラウンドでのピリオドの決まり方
実験は１０ラウンドからなります。
➢ 各ラウンドが何ピリオド続くのかは、実験者がくじで決めます。
➢ 実験者は各ピリオド終了時に、10 枚のカードから 1 枚を引きます。
➢ 10 枚のカードは、スペード（♠)が 9 枚、ジョーカーが 1 枚です。
➢ ピリオド終了時に、実験者がこの 10 枚のカードから 1 枚をランダムに引きます。
➢ 実験者が引いたカードが、スペード（♠)だった場合、次のピリオドに進みます。
➢ 実験者がジョーカーを引いた場合、ピリオドは終了し、次のラウンドに進みます。
➢ 従って、各ピリオドは 90%(=9/10)で続き、10%(=1/10)で終了します。
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5-1. 意思決定（前半パート）
はじめに、1〜５ラウンドの前半パートでの意思決定を説明します。
各参加者は、各ピリオドのはじめに初期保有ポイントとして 10 ポイントを与えられます。10 ポイ
ントから、グループの公共財に全額拠出するまたは拠出しないから選んで下さい。
5-2. 意思決定（後半パート）➢ 次に、6〜10 ラウンドの後半ラウンドでの意思決定について説明します。後半ラウンドのはじめに、各ラウンドにおける意思決定の方針を定めます。後半ラウンドでは、あなたの定めた行動方
針によって、公共財に全額拠出するまたは拠出しないが決定されます。
➢ 具体的には、9 問の質問に回答することで、あなたの行動方針が定まります。各設問は、①第１ピリオドで公共財に全額拠出するか否か（全１問）、②1 期前にあなたの選択（拠出する、拠出しない）及びグループの拠出額(0, 10, 20, 30、40)に応じて、今期あなたは公共財に拠出するか否か（全 8 問）です。
➢ 各設問はランダムな順番で画面に表示されます。全てに回答して下さい。
➢ 全ての質問（合計 9 問）の回答が終わると、あなたの選んだ方針を確認する画面が表示されます。自分の選んだ方針を記録用紙にメモしてください。
➢ 後半ラウンドでは、行動方針が定まった後は、その方針に基づいて自動的にゲームがプレイされ、あなたは各ピリオドで結果を確認するだけです。
➢ 各ラウンドのはじめに、同じ 9 の質問が表示されます。過去のラウンドと同じ方針を採用する
場合、記録用紙を見ながら前のラウンドと同じ回答を入力してください。
6. 利得の決まり方
あなたはグループの総拠出額を知ることができます。
あなたのポイントは、グループの総拠出額によって決まります。あるピリオドのあなたの利得は以下の式で計算されます。
あるピリオドにおけるあなたのポイント＝10－自分の拠出額＋0.5×(グループの総拠出額)
例えば、あなたが 10 ポイントを全額拠出し、グループの総拠出額が 40 ポイントの場合を考えましょう。このピリオドのあなたの利得は以下のようになります。
このピリオドのあなたのポイント＝(10－10)+0.5×40＝0+20＝2027例えば、あなたが拠出しない、グループの総拠出額が 0 ポイントの場合を考えましょう。このピリオドのあなたの利得は以下のようになります。
このピリオドのあなたのポイント＝(10－0)+0.5×0＝10+0＝10
7. 報酬額あなたの最終ポイントは、10 ラウンドの合計ポイントで計算されます。1 ポイント=3 円で計算され、参加報酬 1000 円と合計してあなたへの報酬額が決定されます。
あなたの報酬額
＝￥１０００＋ 10 ラウンドの合計ポイント×￥3
以上

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Sample of Experiment Instructions for Treatment 4 (translated in English)

Economic Experiment Instructions

Thank you for participating in our experiment. We will conduct an economic experiment. Please read the
instructions carefully and make sure you understand the content fully. If you have any questions, please raise
your hand immediately and let the staff know.

1. Handouts
When you get to your seat, make sure you have five handouts:
1. Experiment Participation Agreement 2. Experiment Instructions 3. Screen Instructions 4. Record Form 5.
Receipt
2. How to decide the profit
The profit for the participants consists of two parts. The first is the participation payment. We will pay
JPY 1,000 to all of you for your participation. The second is the experiment payment. The result of theexperiment determines the amount to be paid.
3. How to set up a group➢ At the start of the game, the group is randomly determined. All groups
consist of four participants. Your group number appears on the computer
screen.
➢ For each round, the group is the same. You won’t know who the othergroup members are.
➢ The experiment consists of 10 rounds. This experiment is different in thefirst five rounds and the last five rounds, but the way groups are formed isthe same.
➢ At the beginning of each round, all groups are randomly regrouped. Therefore, you may join the same
members again, or you may go with entirely new members.
➢ Once you have verified the group number, proceed to the next decision.
4. How to set the number of periods in each roundThe experiment consists of 10 rounds.
➢ The experimenter decides how many periods each round lasts.
➢ At the end of each period, the experimenter draws one from ten cards.
➢ There are nine spades (♠) and one Joker.
➢ At the end of the period, the experimenter randomly draws one of these ten cards.
➢ If the card drawn by the experimenter was a spade (♠), go to the next period.
➢ If the card drawn by the experimenter was a Joker, the period ends and proceeds to the next round.
29➢Therefore, each period is followed by 90% (=9/10) and ends at 10% (=1/10).

5-1. Decision making (First Five Rounds)
First, let’s consider the decision making from Round 1 to Round 5. Each participant is given 10 points as theinitial endowment at the beginning of each period. Please choose from 10 points to fully contribute or notcontribute to the group’s public goods.
5-2. Decision-Making (Last Five Rounds)➢ Next, we'll talk about the decision-making from Round 6 to Round 10. At the beginning of each round, youwill be asked to create a strategic plan. Your strategic plan will determine whether you will fully contributeor not contribute to public goods.
➢ Specifically, you will be asked to answer the following nine questions to frame your strategic plan:(1) Will you contribute fully to public goods in the first period? (There is a total of 1 question.).
(2) Depending on your choice (contribution, no contribution) and the group’s contribution (0, 10, 20, 30,40) in the previous period, will you contribute fully to public goods in this current period? (There is a totalof 8 questions.).
➢ Each question is displayed on the screen in random order. Please answer all questions.
➢ After answering all of the questions (9 questions in total), you will be prompted to review your chosen
strategic plan. Make a note of your choice on the record form.
➢ Once you decide upon your strategic plan, the game is automatically played, based on that strategic plan,and you only need to read the results for each period.
➢ At the beginning of each round, you’ll see the same nine questions. If you want to adopt the same strategy
as in the past rounds, check the record form and enter the same choice as the previous round.
6. How to determine the gain
You can know the total contribution of your group. Your points are determined by the total contribution ofyour group. The following equation calculates your point for a period:Your point in a period= 10 – My contribution + 0.5 × (total contribution of the group)
For example, consider a case where you fully contribute, and your group contributes 40 points in total. Your
profit in this period:Your point of this period = (10 – 10) + 0.5 × 40 = 0 + 20 = 2030

Consider a case when you do not contribute, and your group contributes 0 points in total. Your profit in thisperiod:Your point of this period = (10 – 0) + 0.5 × 0 = 10 + 0 = 10
7. Total Profit
Your final point is calculated at an overall point of 10 rounds. It is calculated at 1 point = JPY 3, and your total
profit amount is determined with the participation fee of JPY 1000.
Your total profit = JPY 1000 + total points in 10 rounds × JPY 3

References

Carlsson, H., & Van Damme, E. (1993). Equilibrium Selection in Stag Hunt Games. Frontiers of game theory,
237.
Dal Bó, P., & Fréchette, G. R. (2011). The evolution of cooperation in infinitely repeated games:
Experimental evidence. American Economic Review, 101(1), 411-29.
Fudenberg, D., Rand, D.G., Dreber, A. (2012). Slow to anger and fast to forgive: Cooperation in an uncertain
world. American Economic Review, 102 (2), 720–49.
Harsanyi, J. C., & Selten, R. (1988). A general theory of equilibrium selection in games. MIT Press Books, 1.
Kim, Y. (1996). Equilibrium selection inn-person coordination games. Games and Economic Behavior, 15 (2),203–227.

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