ISSN (Print) 0473-453X

Discussion Paper No. 1145

ISSN (Online) 2435-0982

OBSERVABILITY OF
PARTNERS’ PAST PLAY
AND COOPERATION:
EXPERIMENTAL EVIDENCE
Kenju Kamei
Hajime Kobayashi
Tiffany Tsz Kwan Tse

October 2021

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

Observability of Partners’ Past Play andCooperation: Experimental EvidencebyKenju Kamei1, Hajime Kobayashi2, Tiffany Tsz Kwan Tse3
1 Department of Economics and Finance, Durham University, Email: kenju.kamei@gmail.com.
2 Department of Economics, Kansai University, Email: kobayashihajime72@gmail.com.
3 Institute of Social and Economic Research, Osaka University, Email: tszkwantse@iser.osaka-u.ac.jp.
This version: October, 2021

Abstract: The observability of partners’ past play is known to theoretically improve cooperationin an infinitely repeated prisoner’s dilemma game under random matching. This paper presents
evidence from an incentivized experiment that reputational information per se may not improvecooperation. A structural estimation suggests that a certain percentage of players act according to
the “Always Defect” strategy, whether or not the reputational information is available. The
remaining players adopt available cooperative strategies: specifically, the tit-for-tat strategy
when reputational information is not available, and a strategy that conditions on the matched
partner’s past play when reputational information is available.
JEL classification: C92, C73, D70
Keywords: experiment, cooperation, infinitely repeated prisoner’s dilemma game, reputation
Acknowledgement: The authors thank Yuki Hamada for her help in conducting the experiment at
Osaka University. This project was funded by the Joint Usage and Research Grant program at
Kansai University, and the Japan Society for the Promotion of Science (KAKENHI Grant
Numbers JP18K01526 and JP20H05631).

1

1. Introduction
In research on repeated dilemmas, the effectiveness of reputation for sustaining
cooperation has received considerable attention both theoretically and experimentally. However,a fundamental, but as yet unsettled, question is whether reputational information itself
encourages cooperation in an infinitely repeated prisoner’s dilemma game under random
matching (“IRPD,” hereafter). This paper provides the first experiment that isolates the role ofinformation on partners’ past play in sustaining cooperation using a new design that satisfies thetheoretical condition specified by Takahashi (2010).
While prior experiments emphasized positive effects of information on the partner’s past
play in improving cooperation, the findings might have been driven by factors other thanrevealed information. First, Stahl (2013) demonstrated that the color-coded reputation
mechanism (Kandori, 1992) encourages cooperation. However, in Stahl’s experimental setting,the color depends on past play of the player and his/her opponent. Specifically, each player had acolor, either green (good) or purple (bad), where the green turns to purple if they defect on agreen opponent. When confronted with a purple opponent, the color green does not change even
if a player defects; this is similar to the “Standing” discussed in Nowak and Sigmund (1998).
Second, information created by voluntary reporting of opponents’ actions helps improvecooperation, if reporting is not costly and enough information is accumulated in the community(Camera and Casari, 2018; Kamei and Nesterov, 2020). However, the positive effect might bedue to endogeneity. Third, while non-anonymous public monitoring (Camera and Casari, 2009;
Kamei, 2017) may help boost cooperation, the positive effect could be due to the observable
identity information.
The present experiment is built on Takahashi (2010). Using a variant of Grim-trigger
strategy, Takahashi derives a theoretical condition to sustain cooperation as an outcome of strict
equilibrium when players are informed of their partners’ past play. An experiment treatment is
carefully designed to satisfy this condition. Another result derived by Takahashi is thatcooperation also holds as a belief-free equilibrium outcome if players are informed of not only
the partners’ past actions but also the partners’ past partners’ actions (i.e., interaction outcome,e.g., (C,C), rather than the partner’s action only, e.g., C).1 This paper further investigates how the1

This is not the same as the Nowak and Sigmund (1998)’s Standing.

2

additional information affects cooperation.
The experimental results show that reputational information alone does not boost
cooperation. This suggests that the positive effects of reputation seen in earlier studies (Camera
and Casari, 2009; Stahl, 2013, Kamei, 2017; Kamei and Nesterov, 2020) may be due to factors
other than the information about partners’ past play.
2. Experimental Design
The IRPD is designed using a random termination rule. There are three treatments,
namely the “Baseline,” “Reputation,” and “Reputation-H” (“Reputation with Higher-orderinformation”) treatments, implemented using a between-subjects design.
2.1. Common Features
Subjects play IRPD (supergame) as many times as possible for at least 60 minutes. At theonset of each supergame, subjects are randomly assigned to a group of four; and the groupcomposition remains the same for the entire supergame. In each round, subjects are randomly
matched with another in their group and play the prisoner’s dilemma game (Figure 1). The
payoff matrix is obtained by converting from a normalized payoff matrix with g = 1/3, and l =2/3. At the end of the round, subjects are informed of their own interaction outcome.
The continuation probability is set at 14/15, the rationale for which will be explained in
Section 2.2. The number of supergames is not predetermined (Dal Bó and Fréchette, 2011).
Operationally, an integer between 1 and 15 is randomly drawn for a session in each round. If theinteger drawn is 15 exactly (less than 15), the current supergame is over (continues). The
experiment ends once the number 15 is drawn for the first time after 60 minutes of play.
Figure 1: Payoff Matrix
Cooperate

DefectCooperate30, 305, 35

Defect35, 5

15, 15

Cooperate

DefectCooperateb + a, b + a

lb + a, (1 + g)b + a

Defect(1 + g)b + a, lb + aa, a(a) The present experiment(b) Normalized matrix

Note: Takahashi (2010) used the standard normalization: a = 0 and b = 1.

3

2.2. Treatments
In the Baseline treatment, subjects interact with each other under random matching
without knowing their partners’ past play. Camera and Casari (2009) shows that cooperation
holds as an equilibrium outcome in this setup according to the Grim-trigger strategy if G > 0.443.
In the Reputation (Reputation-H) treatment, each subject is informed of their partner’s
past actions ((a) past actions and (b) past partners’ actions) for the most recent five rounds within
the current supergame before choosing an action. Reputational information does not carry overfrom supergame to supergame.
Using the so-called “pairwise Grim-trigger” strategy, Takahashi (2010) demonstrates thatcooperation is sustained as an equilibrium outcome if G ≥ g(1+l)/[(1+g)l] = 0.625 and T ≥ 2 (T:the history length) when subjects are aware of their partner’s past actions. Further, under theindifference condition, he provides a belief-free equilibrium condition for cooperation when they
are additionally aware of their partner’s past partners’ actions: G ≥ max{g/(1+g), l/(1+l)} = 0.400,
and only the history in the last round suffices. Under the belief-free equilibrium, players are
indifferent between Cooperate and Defect at all histories. Therefore, they have weak incentivesof mixing over Cooperate and Defect at all histories. Table 1 provides the summary ofequilibrium conditions.
Table 1: Equilibrium Conditions
Baseline

Reputation

Reputation-H

Strict equilibriumɁ ൐ ͲǤͶͶ͵Ɂ ൐ ͲǤ͸ʹͷ#1

Ɂ ൐ ͲǤ͸ʹͷ#1

Belief-free equilibrium

does not exist

does not existɁ ൐ ͲǤͶͲͲ

Note: #1 Based on the pairwise Grim-trigger strategy.

According to Proposition 5 of Takahashi (2010), the continuum-population equilibrium
holds in a model with finite players without changing the condition for the existence ofequilibrium. Hence, the equilibrium conditions in Takahashi (2010) can directly be applied to thesetup with a group size of four here.
Since the present experiment is designed to study whether cooperation evolves with
reputational information in a manner consistent with Takahashi (2010), the continuation
probability of 14/15 was selected to satisfy G ≥ 0.625. The length of history information was set
4

at 5 since it must be greater than 1 (the theory predicts the same behavior provided that T ≥ 2).
This means that the condition of G ≥ 0.443 in the Baseline treatment is also met, implying thatthe theory does not predict which performs better, the Baseline or the two reputation treatments.
Table 1 suggests that, with G = 14/15, a belief-free equilibrium exists in the Reputation-H
treatment. Breitmoser (2015) argues that subjects use mixed strategies in IRPDs. If this tendency
holds in the present experiment, the cooperation rate will be higher in the Reputation-H than in
the Reputation treatment since no belief-free equilibrium exists in the Reputation treatment.
3. Results
Section 3.1 reports the cooperation rate by treatment, after which Section 3.2 summarizes
results from a structural estimation of subjects’ strategy choices. See Appendix A for theexperimental procedure.
3.1. Cooperation Rates
Subjects selected cooperation around 50-60% of the time on average in all three treatments(Table 2). The cooperation rates were not significantly different among the treatments.
Figure 2 reports the across-supergame trends of cooperation rates. There are stable, andgradually increasing, trends in all treatments. A regression analysis confirms that while thecooperation rate is decreasing over time within a given supergame, subjects gradually learn tocooperate from supergame to supergame, whether or not they are aware of their partners’ past play
(Table B.3).
Result 1: Reputational information did not improve cooperation.
Table 2: Cooperation Rates
Round 1 only
Cooperationrate

All rounds#1

Treatment difference
Reputation Reputation-H

Cooperation
rate

Treatment difference#1
Reputation Reputation-H

Baseline

68.6%

0.996

0.537

52.1%

0.703

0.301

Reputation

72.9%

----

0.547

50.7%

----

0.514

Reputation-H

63.6%

----

----

58.5%

----

----

Note: #1 Two-sided p-values (see Appendix Table B.2).

5

Figure 2: Cooperation Rates, Supergame by Supergame
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
Baseline

0.1

Reputation

Reputation-H

0
1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Supergame number(A) Round 1 only
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
Baseline

0.1

Reputation

Reputation-H

0
1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Supergame number(B) Average over All Rounds

3.2. Strategy Choices
Why didn’t the reputational information improve cooperation? A structural estimation
finds that a certain fraction of subjects acted according to the AD (Always Defect) strategy(Figure 3).2 More than 15% of subjects used the AD strategy in all treatments. This resonateswith Sugaya and Wolitzky (2020) who argues theoretically that cooperation does not evolve if
there is a certain fraction of AD types in the population. While the remaining subjects acted
The same holds for the data of Camera and Casari (2009), Camera et al. (2012), Kamei (2017), and Kamei and
Nesterov (2020) under private monitoring.

2

6

according to cooperative strategies, the popularity of cooperative strategies differs markedly bytreatment. In the Baseline treatment, 61.3% of the subjects acted according to the tit-for-tat(TFT) strategy. This percentage is much larger compared with the private monitoring treatments
in Camera and Casari (2009), Camera et al. (2012), Kamei (2017), and Kamei and Nesterov(2020) – see Appendix Tables B.6 and B.7. This difference may be due to the number ofsupergames: considerably more than five for this study versus five or six for these earlier
studies.3
In both the Reputation and Reputation-H treatments, the TFT strategy was much lesscommon. Instead, 35.7% (58.2%) of the subjects in the Reputation (Reputation-H) treatment
selected cooperation conditional upon their partner’s reputational information. Such strategies
under reputational information were also observed in the data of Camera and Casari (2009),
Kamei (2017), and Kamei and Nesterov (2020) – see again the Appendix.
In summary, Result 1 is largely driven by the presence of AD types in each treatment. It
is worth noting that in every treatment of Fudenberg et al. (2012), while strategy choices werequite heterogeneous, a substantial fraction of subjects used the AD strategy, and cooperative
types found it difficult to learn optimal responses.
Figure 3: Distributions of Strategy Choices
100%
11.9%

90%
35.7%

80%
70%

61.3%

46.3%

60%
50%

29.5%

40%
30%

16.8%

20%
10%

21.9%

15.6%

16.9%

Reputation

Reputation-H

0%
Baseline
AD

WSLS

AC

Grim

TFT

TK

Rep

PMC

Notes: Estimated using the method by Dal Bó and Fréchette (2011). The Rep strategy is a strategy where subject i
selects cooperation conditional upon her partner j’s cooperation rate in his reputational record. The PMC strategy is
3This could also be due to the difference in the matching condition and/or experimentation (online versus lab).

7

one in which i selects cooperation conditional upon j’s past experiences on mutual cooperation. The TK strategy is
the trigger strategy with K rounds of punishment. Appendix Table B.5 includes the detailed results.

Result 2: (i) More than 15% of subjects used the AD strategy in all treatments. (ii) More thanthe majority of subjects acted according to the TFT strategy in the Baseline treatment. Subjects
in the Reputation and Reputation-H treatments relied on their partner’s reputation to choose anaction, rather than adopt the TFT strategy.
4. Conclusions
This paper provided evidence that reputational information by itself does not improvecooperation in an IRPD. A certain fraction of players always selected defection irrespective of
the presence of the information.
REFERENCES
Breitmoser, Y., 2015. “Cooperation, but No Reciprocity: Individual Strategies in the RepeatedPrisoner’s Dilemma.” American Economic Review, 105(9):2882-2910.
Camera, G., Casari, M. 2009. “Cooperation among Strangers under the Shadow of the
Future.” American Economic Review, 99(3):979-1005.
Camera, G., Casari, M. 2018. “Monitoring Institutions in Indefinitely Repeated Games.”
Experimental Economics, 21: 673-691.
Camera, G., Casari, M., Bigoni, M., 2012. “Cooperative Strategies in Anonymous Economies:
An Experiment.” Games and Economic Behavior, 75:570-586.
Dal Bó, P., Fréchette, G. 2011. “The Evolution of Cooperation in Infinitely Repeated Games:
Experimental Evidence.” American Economic Review, 101(1):411-429.
Fudenberg, D., Rand, D., Dreber, A., 2012. “Slow to Anger and Fast to Forgive.” American
Economic Review, 102(2): 720-749.
Kamei, K., 2017. “Endogenous Reputation Formation under the Shadow of the Future.” Journalof Economic Behavior & Organization, 142:189-204.
Kamei, K., Nesterov, A., 2020. “Endogenous Monitoring through Gossiping in an Infinitely
Repeated Prisoner’s Dilemma Game: Experimental Evidence.” Durham University Business
School Working Paper.
Kandori, M., 1992. “Social Norms and Community Enforcement.” Review of Economic Studies,
59(1):63-80.
8Nowak, M., Sigmund, K., 1998, “Evolution of Indirect Reciprocity by Image Scoring.” Nature,
393:573-577.
Stahl, O., 2013. “An Experimental Test of the Efficacy of a Simple Reputation Mechanism to
Solve Social Dilemmas.” Journal of Economic Behavior & Organization, 94:116-124.
Sugaya, T, Wolitzky, A, 2020. “A Few Bad Apples Spoil the Barrel.” American Economic
Review, 110(12):3817-3835.
Takahashi, S., 2010. “Community Enforcement when Players Observe Partners’ Past Play.”
Journal of Economic Theory, 145(10):42-62.

9

NOT FOR PUBLICATION

Online Supplementary Appendix to: Kamei, Kobayashi and Tse:#“Observability of Partners’ Past Play andCooperation: Experimental Evidence”

Tables of Contents

Appendix A: Sample Instructions Used in the Experiment . . . . . . . . . . . . . . . . . . . . . . . . p. 2
Appendix B: Additional Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p. 16#

Kamei: Durham University (kenju.kamei@gmail.com), Kobayashi: Kansai University(kobayashihajime72@gmail.com), Tse: Osaka University (tszkwantse@iser.osaka-u.ac.jp). The authors
thank Guillaume Fréchette for kindly providing the original code for strategy estimation and Maria Bigoni
for providing the modified code for strategy estimation.

1

Appendix A: Experiment Procedure and Sample Instructions Used in the Experiment
Four sessions per treatment were conducted online using oTree and Zoom from February
through April 2021, following the same procedure as the standard laboratory experiment.1 Eachsession consisted of 16 subjects. A total of 192 Osaka University students participated in theexperiment. No attrition occurred during the experimental game. The instructions were neutrally
framed (Appendix A). The average supergame lengths were 15.22, 15.36 and 14.74 rounds in the
Baseline, Reputation and Reputation-H treatments, respectively.
This part of the Appendix includes the instructions for the Reputation-H treatment as an
example. All the experiment sessions were conducted in Japanese. The session time wascontrolled as it may affect subjects’ behaviors: each treatment has two sessions conducted in themorning and the other two conducted in the afternoon.
The following includes both the original instructions in Japanese and its translated English
version.
[At the onset of the experiment, the following instructions (PowerPoint file) were shown on
Zoom, and were read aloud to subjects by the researchers. Subjects remained anonymous during
the entire session without seeing other participants’ faces, names, etc.]
Original Japanese Version:Slide 1:

1

Subjects’ IDs were check using Zoom before the sessions commenced.

2

Slide 2:

Slide 3:3

Slide 4:

Slide 5:

4

Slide 6:

Slide 7:

5

Slide 8:

Slide 9:6

Slide 10:

Slide 11:7

Slide 12:

Slide 13:8

English Translated Version:Slide 1:

Welcome!
x

You are now taking part in a decision-making experiment. Depending on yourdecisions and the decisions of other participants, you will be able to earn moneyin addition to the ¥500 guaranteed for your participation.

x

During the experiment, you are not allowed to communicate with otherparticipants. Please switch off all of your electronic devices (e.g., mobile phone,iPad). If you have a question during the experiment, please write it in the chat box
of Zoom. We will answer your question individually.

x

In the experiment, your earnings will be calculated in points. During theexperiment, you can accumulate earnings through your decisions as will be
explained now. At the end of the experiment, points will be converted to Japanese
yen at the following rate:
3 points = 1 Japanese yen.

xYour total earnings (including the participation fee of ¥500) will be paid out toyou using an Amazon gift card after the experiment is over.

Slide 2:

Welcome!
xx

There are multiple phases in the experiment.

x

Once a phase is over, your group composition will randomly change, i.e., youwill be randomly re-assigned to a group of size four in this session and the next
phase will begin.

x

We will explain both the ending rule and the duration of each phase later.

At the beginning of each phase, all participants will be randomly divided into
groups of four individuals, and you will interact with these individuals only(you will not interact with participants outside your group in any period).

9

Slide 3:Your Decisions in Each Phase:xWhile each phase consists of multiple periods, all periods have the samestructure.

x

At the onset of a given period, each participant is randomly paired with a memberof his or her group.

x

The pairing is completely random. Neither your decisions in previous periods inthis phase nor your decisions/outcomes in previous phases affect the pairing
process.

x

Since there are four individuals in your group, the probability that you will bematched with the same individual in two consecutive periods of a given phase is
1/3.

Slide 4:Your Decisions in Each Phase:x

In each period, you and your partner simultaneously choose X or Y. Since both
you and your partner make binary choices, there are 4 (= 2u2) possible
interaction outcomes. The earnings resulting from each scenario will besummarized as below:(a) If you choose X and your counterpart also chooses X, you earn 30 points.
(b) If you choose Y and your counterpart also chooses Y, you earn 15 points.
(c) If you choose X and your counterpart chooses Y, you earn 5 points.
(d) If you choose Y and your counterpart chooses X, you earn 35 points.

xYour partner has the same earnings formulas as you.

10

Slide 5:Your Decisions in Each Phase:
x

x
x
x

x

You will be informed of your matched partner’s choices (either X or Y) in themost recent five periods and choices of your partner’s matched partners in these
five periods (i.e., you will learn the interaction outcomes). This information will
be shown in the table on the lower right side of the computer screen (please see
an image on the next slide).
For example, in period 7, you will be informed of your partner’s choice, either X
or Y, in each of periods 2 to 6.
In the screen image on the next slide, you can see that this partner selected Y inperiod 4 and that this partner’s period 4 partner selected X in period 4.
Until five periods have passed, you will be informed of your current partner’s
choices and interaction outcomes in all periods of the phase so far (you will not
be informed of your partner’s choices in the previous phases).
For example, suppose now that it is period 3 of phase 4. You will then be
informed of your current partner’s action choices (X or Y) in periods 1 and 2 andhis/her interaction outcomes in these periods.

Slide 6: (note: There is no “current (e.g., period 7) partner’s past partner’s choice” column for
the Reputation treatment. The two reputation treatments are identical except for this difference.)

An Example of Computer Screen 1: (when making decisions)11

Screen image with translation
in English

Slide 7:

Slide 8:Your Decisions in Each Phase:xYour partner will also be informed of your choices made in the most recent five
periods and the interaction outcomes in these periods.

x

Once all participants in a session have made their decisions and click the button,
you will be informed of the outcome of the interactions in a given period.

xSpecifically, you will be informed of:(1) your partner’s choice in the current period (X or Y);(2) your earnings (in points) for that period.

12

Slide 9:

An Example of Computer Screen 2: (the outcome screen)
Screen image with translation
in English

Slide 10:The Number of Periods in Each Phase:x

The number of periods in each phase is not predetermined. It is instead
determined by a randomization. The probability that a given phase willcontinue and you will have another period in a given phase is 14/15.

x

Specifically, at the end of each period, the computer randomly draws aninteger between 1 and 100 for this session.

x

The integer drawn will be shown on the computer screen along with yourinteraction outcome (please see the “An Example of Computer Screen 2”
image shown on the previous slide).

x

If the integer drawn is less than or equal to 14, your interaction in thecurrent phase continues. You will be randomly paired with anotherindividual in your group and will interact with that individual.

x

If the integer drawn is 15, then the current phase is over. You will move onto the next phase, and you will be randomly re-assigned to a group of fourindividuals in the session.
13

Slide 11:

The Number of Periods in Each Phase:xxx

The next phase has the same structure (e.g., what kinds of decisions tomake, how to calculate earnings) as the current one.
Since the probability that the current phase will continue to the next period
is 14/15, the expected number of periods in any given phase is 15
mathematically.
However, since the decision to discontinue your interactions in each phaseis randomly determined by the computer, you may have a phase with moreor less than 15 periods.

Slide 12:The Experiment Durationx

This experiment consists of multiple phases.

xx

The experiment interactions will continue for at least 60 minutes.
Your interactions will end once the number 15 is randomly drawn for the
first time by the computer, after 60 minutes of interactions have passed.

14

Slide 13:

Paymentxx

After the experiment, you will be paid privately based on youraccumulated earnings across all the phases in addition to the participation
fee of ¥500.
Please write any question that you may have in the chat box of Zoom. We
will start the experiment once all questions are answered.

15Appendix B: Additional Tables
Table B.1: Descriptive Statistics and Cooperation Rates by Session
Sessiondate

A. Baseline treatment
Session 1 2021/02/22

Average
Average Number of Avg SG Number % of
% ofround 1 cooperation supergames lengthoffemale economics
cooperation rate acrossplayed[rounds] subjects subjects
major
rate [%]
all rounds
per[%]session56.25%(3.21)
82.92%(2.43)
52.68%(4.74)
75.00%(3.01)

26.96%(0.87)
57.27%(0.81)
51.39%(0.95)
67.93%(0.84)

15

10.87

16

6.25%

6.25%

15

15.47

16

18.75%

0.00%

7

25.00

16

20.00%#1

18.75%

13

14.69

16

50.00%

18.75%

B. Reputation treatment
Session 2 2021/03/01
78.33%(2.67)
Session 5 2021/03/02
77.78%(3.48)
56.25%
Session 8 2021/03/04(5.58)
66.96%
Session 11 2021/04/13(4.46)

57.83%(0.93)
72.51%(1.03)
34.17%(1.15)
36.79%(0.99)

15

11.87

16

25.00%

12.50%

9

13.11

16

33.33%#1

12.50%

5

21.40

16

31.25%

12.50%

7

21.43

16

43.75%

12.50%

C. Reputation-H treatment
Session 3 2021/03/01
61.93%(3.67)
60.80%
Session 6 2021/03/03(3.69)
52.50%
Session 10 2021/03/05(5.62)
76.56%
Session 12 2021/04/20(3.76)

59.38%(1.04)
54.37%(1.04)
32.75%(1.17)
81.34%(0.85)

11

12.73

16

50.00%

6.25%

11

13.00

16

56.25%

0.00%

5

20.00

16

50.00%

12.50%

8

16.63

16

31.25%

18.75%

Session 4 2021/03/02
Session 7 2021/03/03
Session 9 2021/03/05

Notes: The numbers in parentheses are standard errors. #1 One subject did not answer gender each in Session 5 andSession 7. The % of female subjects was 33.33% (5/15) in Session 5 and 20.00% (3/15) in Session 7.

Remark: The collected demographic information was used as control variables in regression analyses
reported in Table B.2 to Table B.4.

16

Table B.2: Treatment Effects of Reputational Information (supplementing Table 2 of the paper)
Two models were used to test the impact of reputational information. The first one is a probit
regression considering that each subject’s decision is binary (either cooperate or defect). In the estimation,subject random effects are included to control for the panel structure; and session random effects areincluded to control for within-session dependencies in subjects’ behaviors. Notice that within-session
dependencies can be controlled by including session-level clustering. However, there is no theoreticallyvalid way to include subject random effects and session-level clustering simultaneously for the probit
model (Wooldridge, 2010). The second model is a standard linear probability model with subject random
effects and session-level clustering. A linear probability model, rather than non-linear estimators such as
probit, may be appropriate for experiment data, since the sample size of experiment data is usually small
unlike empirical research. The following table, which reports estimation results when control variables
are included, indicates no significant treatment differences in the cooperation rate, regardless of whichmodel is used. Results are qualitatively similar even if control variables are not included.
Dependent variable: a dummy which equals 1(0) if a subject i cooperated (defected) in round t
Estimation method:

Independent
variables:

Mixed effects probit regressions(i.e., both session random effects andsubject random effects are included)

Subject random effects linear
regressions
with session-level clustering
Round 1 only
All rounds(3)(4)

Round 1 only(1)

All rounds(2)(a) Reputation treatment
dummy

0.002
(0.453)0.149(0.392)-0.008(0.078)0.047(0.087)(b) Reputation-H treatment
dummy-0.275(0.447)0.408(0.394)-0.039(0.076)0.124(0.095)Constant

1.518(1.650)21,6150.936(0.618)1,4370.802*(0.417)# of Observations

2.199(3.056)
1,430

R-squared
Wald χ2
Prob > Wald χ2--96.57
0.000--958.24
0.000

0.147
-----

0.104
-----

Wald χ2 test for H0: (a) = (b)Wald χ2
Two-sided p-value

0.360
0.547

0.430
0.514

0.280
0.597

0.650
0.422

21,615

Notes: The number of rounds in the previous supergame, a female dummy which equals 1 for female, an economics
major dummy, the national center test score for university admissions (self-report), age dummies, supergame
number dummies are also included as control variables. The coefficient estimates of these controls are omitted toconserve space. The number in parentheses are standard errors.
*, **, and *** indicate significance at the .10 level, at the .05 level and, at the .01 level, respectively.

17

Table B.3: Cooperation Trends by Treatment (supplementing Figure 2 of the paper)
Dependent variable: a dummy which equals 1(0) if a subject i cooperated (defected) in round t
Data:

Round 1 only
Reputation Reputation-H(2)(3)

Baseline(4)

All rounds
Reputation Reputation-H(5)(6)

0.030***(0.005)0.097***(0.008)0.085***(0.008)-3.051(4.218)-0.010***(0.001)5.794**(2.731)-0.027***(0.002)
1.318*(3.977)-0.019***(0.002)-5.179*(2.774)403
45.45
0.0000

9,511
325.010.00006,143446.620.00005,961
308.040.0000Independent
variables:

Baseline(1)

Supergame number {=1, 2, 3, 4, …}

0.073***(0.026)0.139**(0.057)0.187***(0.044)

---

---

---

5.785
(4.452)8.671**(8.742)617
34.24
0.0006402
19.47
0.1092Rounds withinsupergame
Constant# of Observations
Wald χ2
Prob > Wald χ2

Notes: Mixed effects probit regressions (both session random effects and subject random effects are included). The
number of rounds in the previous supergames, the 1st supergame dummy which equals 1 for the first supergame (0otherwise) as the previous supergame length cannot be defined, a female dummy which equals 1 for female, an
economics major dummy, the national center test score for university admissions (self-report), and age dummies arealso included as control variables. The coefficient estimates of these controls are omitted to conserve space. The
number in parentheses are standard errors.
*, **, and *** indicate significance at the .10 level, at the .05 level and, at the .01 level, respectively.

Remark: Key messages, namely, stable or gradually increasing across-supergame trends, are similar evenif subject random effects linear regressions with standard errors clustered by session ID are used instead.
The results are summarized below:
1. Results on the increasing trend in cooperation in the Baseline treatment are somewhat weaker due tolarger standard errors when the subject random effects linear regressions are used. However, thesupergame variable obtains a positive and significant coefficient at the 5% level (two-sided p = 0.15) for
subjects’ decisions to cooperate in the first round when data before the 10th supergame are used.
2. Results in the Reputation treatment are qualitatively the same as the ones summarized in columns (2)and (5) above. The supergame variable is significantly positive regardless of whether data from round 1
or all data are used.
3. Results in the Reputation-H treatment are somewhat weaker due to larger standard errors when thesubject random effects linear regressions are used. However, the supergame variable obtains a positiveand significant coefficient at the 10% level (two-sided p = 0.87) for subjects’ decisions to cooperate in thefirst round. The trends are stable if all data are used.

18

Table B.4: Reputational Information and Decisions to Cooperate
Dependent variable: a dummy which equals 1(0) if a subject i cooperated (defected) in round t
Treatment:

I. Reputation

II. Reputation-H

(i)

(ii)

(i)

(ii)

(iii)

(iv)

(a) i’s round t partner’s pastcooperation rate according to
his recorded information

2.449***(0.067)---2.315***(0.069)

---

---

---

(b) i’s round t partner’s
cooperation decision in roundt – 1 {=1(0) if hecooperated(defected)}---

1.149***(0.074)---0.959***(0.064)------(c) i’s round t partner’s
cooperation rate between
rounds t – 2 and t – 5 in his
recorded information ([0,1])---

1.453***(0.086)---1.562***(0.082)------(d) % in which mutual
cooperation was realized forrecent five rounds in the i’sround t partner’s reputational
record ([0,1])

---

---

---

---

2.286***(0.071)---(e) i’s round t partner’s round t– 1 mutual cooperation
dummy {= 1 if his round t – 1
outcome was mutual
cooperation}

---

---

---

---

---

0.934***(0.068)(f) % in which mutual
cooperation was realized
between round t – 2 and t – 5
in the i’s round t partner’s
reputational record ([0,1])

---

---

---

---

---

1.600***(0.085)0.403(4.365)5,741
1567.360.00000.336(4.338)5,383
1503.970.0000-6.055*(3.143)5,5501484.690.0000-6.556**(3.300)5,1741428.130.0000-5.299*(2.875)

Independent variables:

Constant# of Observations
Wald χ2
Prob > Wald χ25,5501401.84
0.0000-5.706*(3.057)5,174
1357.460.0000Notes: Mixed effects probit regressions (both session random effects and subject random effects are included). The
number of rounds in the previous supergames, a female dummy which equals 1 for female, an economics major
dummy, the national center test score for university admissions (self-report), age dummies, and supergame number
dummies are also included as control variables. The coefficient estimates of these controls are omitted to conserve
space. The number in parentheses are standard errors. Only observations where variable (a) (variables (b) and (c))
can be defined were used in columns I.i and II.i (I.ii and II.ii). Only observations where variable (d) (variables (e)and (f)) can be defined were used in column II.iii (II.iv). Results for coefficient estimates (a) to (f) are qualitatively
the same when subject random effects linear regressions with standard errors clustered by session ID are instead
used (the results are omitted to conserve space). *, **, and *** indicate significance at the .10 level, at the .05 level
and, at the .01 level, respectively.

19

Table B.5. Structural Estimation of Subjects’ Strategy Choices (Supplementing Figure 3 of thepaper)The table on the next page summarizes the estimated percentages of strategies chosen by the subjects in eachtreatment based on the maximum likelihood method (Dal Bó and Frechétte, 2011). In addition to the strategies
used in Dal Bó and Frechétte 2011 (namely, AD, AC, Grim, TFT, WSLS, and T2), other possible strategies werealso included in the estimation. The definition of each strategy is as follows:
AD (“Always Defect”): a strategy in which a subject selects defection unconditionally.
AC (“Always Cooperate”): a strategy in which a subject selects cooperation unconditionally.
Grim (“Grim Trigger”): a strategy in which a subject selects defection as soon as s/he experiences defection (until
which s/he selects cooperation).
TFT (“Tit For Tat”): a strategy in which a subject selects cooperation (defection) if her last-round partnercooperated (defected).
WSLS (“Win Stay Lose Shift”): a strategy in which a subject selects cooperation if either mutual cooperation ormutual defection was realized in last round.
# Dal Bó and Frechétte (2011) only considered the T2 strategy below as a trigger strategy with some duration ofpunishment mode in their structural estimation. The present paper includes not only the T2 strategy, but also the
T1, T3 and T4 strategies, because, to the knowledge of the authors, there is no stylized evidence on the durationof the punishment mode under random matching.
T1 (“Trigger Strategy with 1 Round of Punishment”): a strategy in which a subject defects for one round, after
which she returns to cooperation, when she experiences defection.
T2 (“Trigger Strategy with 2 Rounds of Punishment”): a strategy in which a subject defects for two rounds, after
which she returns to cooperation, when she experiences defection.
T3 (“Trigger Strategy with 3 Rounds of Punishment”): a strategy in which a subject defects for three rounds, after
which she returns to cooperation, when she experiences defection.
T4 (“Trigger Strategy with 4 Rounds of Punishment”): a strategy in which a subject defects for four rounds, after
which she returns to cooperation, when she experiences defection.
# The LRep, Rep20, Rep40, Rep60, Rep80 and Rep100 strategies below are relevant for the Reputation and
Reputation-H treatments. Subjects who fall into these categories condition their action choices on their matched
partners’ past action choices.
LRep (“Cooperate based on the Last-round Reputation”): a strategy in which a subject selects cooperation in roundt if her round t partner selected cooperation in round t – 1.
Rep20: a strategy in which a subject selects cooperation in round t if her round t partner selected cooperation for
at least 20% of the occasions in the past according to the partner’s reputational information.
Rep40: a strategy in which a subject selects cooperation in round t if her round t partner selected cooperation for
at least 40% of the occasions in the past according to the partner’s reputational information.
Rep60: a strategy in which a subject selects cooperation in round t if her round t partner selected cooperation for
at least 60% of the occasions in the past according to the partner’s reputational information.
Rep80: a strategy in which a subject selects cooperation in round t if her round t partner selected cooperation for
at least 80% of the occasions in the past according to the partner’s reputational information.
Rep100: a strategy in which a subject selects cooperation in round t if her round t partner selected cooperation for
all the occasions in the past according to the partner’s reputational information.
# The LMC, MC20, MC40, MC60, MC80 and MC100 strategies below are relevant for the Reputation-H treatmentonly. Subjects who fall into these categories condition their action choices on their matched partners’ past action
profiles.

20

LMC (“Cooperate based on Last-round Mutual Cooperation”): a strategy in which a subject selects cooperation inround t if her round t partner achieved mutual cooperation in round t – 1.
MC20: a strategy in which a subject selects cooperation in round t if her round t partner experienced mutual
cooperation at least for 20% of the occasions in the past according to the partner’s reputational information.
MC40: a strategy in which a subject selects cooperation in round t if her round t partner experienced mutual
cooperation at least for 40% of the occasions in the past according to the partner’s reputational information.
MC60: a strategy in which a subject selects cooperation in round t if her round t partner experienced mutual
cooperation at least for 60% of the occasions in the past according to the partner’s reputational information.
MC80: a strategy in which a subject selects cooperation in round t if her round t partner experienced mutual
cooperation at least for 80% of the occasions in the past according to the partner’s reputational information.
MC100: a strategy in which a subject selects cooperation in round t if her round t partner experienced mutual
cooperation for all of the occasions in the past according to the partner’s reputational information.
These strategies (LRep, Rep20, Rep40, Rep60, Rep80, and Rep100, LMC, MC20, MC40, MC60, MC80, andMC100) were considered in the estimation because partial correlations between i’s cooperation rate and i’s partner’s
reputation were positive and significant (Appendix Table B.4).

The following table summarizes the estimated distributions of strategy choices, the standard errors and two-sided
p-values for each treatment. The standard errors were calculated based on three-level bootstrapping: The computer
first selects sessions randomly 100 times for each treatment. The computer then chooses 16 subjects and alsosupergames randomly for each selected session.
The % of the TK strategy (Trigger Strategy with K Rounds of Punishment) in Figure 3 of the paper is the sum of
estimated percentages for T1, T2, T3 and T4. The % of the Rep strategy (Cooperate based on Partner’s Reputation)
in Figure 3 is the sum of estimated percentages for LRep, Rep20, Rep40, Rep60, Rep80, and Rep100. The % of
the PMC strategy (Cooperate based on partner’s past experiences of mutual cooperation) in Figure 3 is the sum of
estimated percentages for LMC, MC20, MC40, MC60, MC80, and MC100.
[I. Estimation Result:]
Treatment:

Baseline

Strategy

Fraction

Bootstrap
SE

AD

0.219

AC

Reputation

Reputation-H

p-value
Bootstrap p-value
Bootstrap
Fraction
Fraction(2-sided)SE(2-sided)SEp-value(2-sided)

0.069

0.001***

0.156

0.055

0.002***

0.169

0.089

0.028**

0.080

0.060

0.092*

0.047

0.036

0.093*

0.032

0.046

0.239

Grim

0.072

0.051

0.079*

0.145

0.061

0.009***

0.000

0.024

0.500

TFT

0.613

0.088

0.000***

0.295

0.050

0.000***

0.168

0.057

0.002***

WSLS

0.016

0.022

0.243

0.000

0.005

0.500

0.000

0.008

0.500

T1

0.000

0.000

0.500

0.000

0.010

0.500

0.000

0.008

0.500

T2

0.000

0.005

0.500

0.000

0.001

0.500

0.000

0.011

0.500

T3

0.000

0.002

0.500

0.000

0.009

0.500

0.000

0.023

0.500

T4

0.000

0.000

0.000***

0.000

0.010

0.500

0.049

0.014

0.000***

LRep

0.029

0.043

0.252

0.026

0.032

0.213

Rep20

0.120

0.047

0.005***

0.176

0.044

0.000***

Rep40

0.067

0.035

0.029**

0.211

0.055

0.000***

Rep60

0.090

0.051

0.037**

0.050

0.036

0.082*

21

Rep80

0.000

0.013

0.500

0.000

0.010

0.500

Rep100

0.051

0.000

0.000***

0.000

0.008

0.500

LMC

0.000

0.023

0.500

MC20

0.012

0.032

0.354

MC40

0.036

0.026

0.082*

MC60

0.038

0.033

0.126

MC80

0.033

0.029

0.128

MC100

0.000

0.000

0.000***

0.494

0.026

0.000***

γ

0.481

β

0.889

0.058

0.000

0.432

0.046

0.910

0.000

0.883

Notes: a The table reports the estimated percentage of each strategy in the population. b Ⱦ ൌଵ.

ଵାୣ୶୮ሺିଵൗఊሻ

[II. Comparison of Estimated Percentages across the Treatments:]
AD strategy:
Baseline
Reputation
Reputation-H

Reputation
5.755 (p < 0.01)-----

Reputation-H
5.558 (p < 0.01)
1.125 (p = 0.262)---

AC strategy:
Baseline
Reputation
Reputation-H

Reputation
9.500 (p < 0.01)-----

Reputation-H
7.457 (p < 0.01)-1.739 (p = 0.084)---

Grim strategy:
Baseline
Reputation
Reputation-H

Reputation-5.735 (p < 0.01)-----

Reputation-H
12.081 (p < 0.01)
17.315 (p < 0.01)---

TFT strategy:
Baseline
Reputation
Reputation-H

Reputation
28.950 (p < 0.01)-----

Reputation-H
38.882 (p < 0.01)
15.032 (p < 0.01)---

Notes: t tests using 300 estimated distributions of strategy choices (100 per treatment) based on three-levelbootstrapping (session, supergame, subject). Numbers in the tables are t values with (two-sided) p-values inparentheses.

22Remark: 1. Subjects may need some time to reach stable strategy choices, for which reason Dal Bó andFrechétte (2011) excluded subjects’ decision data in earlier supergames. In the context of the present paper,
subjects’ cooperation rates were on average low in the first supergame as seen in Figure 2 of the paper. Hence,as a robustness check, a strategy estimation was also performed for data excluding the observations from thefirst supergame, finding qualitatively similar results. The results are omitted to conserve space.
2. The number of supergames differs by session, which may render the treatment comparisons shown in I and
II above imprecise. To address this concern, an additional strategy estimation was performed by restricting thedata to the observations up to (and including) the 5th supergame because all 12 sessions went through the first
five supergames. The estimation results are qualitatively similar to the ones reported above. The results areomitted to conserve space.

23

Table B.6. Structural Estimation of Subjects’ Strategy Choices in Camera and Casari (2009)
We estimated distributions of strategies chosen by the subjects in the “Private Monitoring” treatment, the“Anonymous Public Monitoring” treatment and the “Non-Anonymous Public Monitoring” treatment of Camera
and Casari (2009) based on the maximum likelihood method (Dal Bó and Frechétte, 2011), using their replication
data files. All the strategies used in Dal Bó and Frechétte 2011 (namely, AD, AC, Grim, TFT, WSLS, and T2)
were considered in the estimations. In addition, the strategies considered in Table B.5 were also included as
possible strategies for the “Non-Anonymous Public Monitoring” treatment. As the subjects in their two public
monitoring treatments were also aware of the list of three members’ actions in every previous round, thefollowing strategies were also considered for these treatments:x

LRepXX_partners: A subject selects cooperation in round t if at least XX% of partners in community (i.e.,out of three other members) selected cooperation in round t-1.

x

RepXX_community: A subject selects cooperation in round t if the cooperation rate in the community
including the subject him/herself thus far was at least XX% according to the history table.

x

RepXX_partners: A subject selects cooperation in round t if the cooperation rate among partners in thecommunity thus far was at least XX% according to the history table.

x

RepXX_community_5rounds: A subject selects cooperation in round t if the cooperation rate in thecommunity including the subject him/herself for the last five rounds was at least XX% according to thehistory table.

x

RepXX_partners_5rounds: A subject selects cooperation in round t if the cooperation rate among thepartners in the community for the last five rounds was at least XX% according to the history table.

Note that the LRep, RepXX, and RepXX_5rounds in the table below are defined as follows:x

LRep: A subject selects cooperation in round t if his/her partner matched in round t selected cooperation inround t-1.

x

RepXX: A subject selects cooperation in round t if the cooperation rate of his/her partner matched in roundt thus far was at least XX% according to the history table.

x

RepXX_5rounds: A subject selects cooperation in round t if the cooperation rate of his/her partner
matched in round t for the last 5 rounds was at least XX% according to the history table.

The estimation result for the Private Monitoring treatment (see column A below) finds that a non-negligible
fraction of subjects acted according to the AD strategy, whose finding is similar to the private monitoring
treatments of the present paper (Appendix Table B.5), Camera et al. (2012) and Kamei and Nesterov (2020).
Columns B and C below indicate that similar to the findings of the present paper (Appendix Table B.5) andKamei and Nesterov (2020), a large fraction of subjects selected cooperation conditional upon their partner’s
reputational information.
[Estimation Result:]
Treatment:
Strategy
AD(A) Private Monitoring
Fraction Bootstrap
SE(B) Anonymous Public(C) Non-Anonymous Public
Monitoring
Monitoring
p-value Fraction Bootstrap p-value Fraction Bootstrap p-value(2-sided)SE(2-sided)SE(2-sided)

0.202

0.021**

0.100

0.098

24

0.050

0.026**

0.050

0.066

0.224

AC

0.297

0.075

0.000***

0.038

0.016

0.002

0.454

Grim

0.156

0.064

0.007***

0.072

0.064

0.128

0.000

0.002

0.479

TFT

0.268

0.117

0.011**

0.110

0.052

0.017**

0.053

0.053

0.157

WSLS

0.025

0.028

0.187

0.000

0.014

0.500

0.000

0.000

0.000***

T1

0.051

0.051

0.157

0.000

0.002

0.500

0.000

0.000

0.000***

T2

0.000

0.025

0.500

0.000

0.012

0.500

0.000

0.009

0.495

T3

0.000

0.023

0.500

0.000

0.007

0.500

0.000

0.018

0.498

T4

0.000

0.000

0.000***

0.000

0.002

0.500

0.000

0.018

0.498

LRep33_partners

0.162

0.078

0.019**

0.084

0.055

0.063*

LRep67_partners

0.078

0.053

0.069*

0.000

0.019

0.497

LRep100_partners

0.000

0.001

0.500

0.000

0.000

0.000***

Rep20_community

0.037

0.021

0.037**

0.000

0.002

0.454

Rep40_ community

0.001

0.033

0.493

0.000

0.009

0.492

Rep60_ community

0.123

0.080

0.063*

0.078

0.061

0.102

Rep80_ community

0.093

0.047

0.023**

0.000

0.001

0.448

Rep100_ community

0.000

0.009

0.500

0.000

0.000

0.355

Rep20_partners

0.045

0.054

0.200

0.000

0.002

0.454

Rep40_partners

0.000

0.010

0.500

0.000

0.011

0.483

Rep60_partners

0.000

0.002

0.500

0.000

0.000

0.000***

Rep80_partners

0.000

0.010

0.500

0.000

0.000

0.000***

Rep100_partners
Rep20_ community_5rounds
Rep40_ community_5rounds
Rep60_ community_5rounds
Rep80_ community_5rounds
Rep100_ community_5rounds
Rep20_partners_5roun
ds
Rep40_partners_5roun
ds
Rep60_partners_5roun
ds
Rep80_partners_5roun
ds
Rep100_partners_5rou
nds
LRep

0.000

0.002

0.500

0.000

0.000

0.000***

0.000

0.002

0.500

0.000

0.002

0.455

0.094

0.069

0.087*

0.000

0.015

0.490

0.000

0.020

0.500

0.030

0.022

0.082*

0.000

0.010

0.500

0.010

0.006

0.044**

0.000

0.003

0.500

0.000

0.000

0.353

0.000

0.028

0.500

0.000

0.002

0.455

0.048

0.034

0.080*

0.000

0.000

0.068*

0.000

0.006

0.500

0.000

0.015

0.497

0.000

0.009

0.500

0.000

0.000

0.000***

0.000

0.000

0.000*** 0.000

0.000

0.000***

0.048

0.047

0.153

0.052

0.048

0.137

Rep20

25

0.008*** 0.000

Rep40

0.040

0.051

0.219

Rep60

0.191

0.059

0.001***

Rep80

0.054

0.064

0.201

Rep100

0.000

0.000

0.000***

Rep20_5rounds

0.000

0.041

0.498

Rep40_5rounds

0.169

0.071

0.009***

Rep60_5rounds

0.031

0.061

0.306

Rep80_5rounds

0.093

0.054

0.041**

Rep100_5rounds

0.011

0.000

0.000***

0.000*** 0.579

0.089

0.000***

γ

0.587

β

0.846

0.049

0.000***

0.554
0.859

0.043

0.849

Notes: a The table reports the estimated percentage of each strategy in the population. b Ⱦ ൌ

26

ଵ

.

ଵାୣ୶୮ሺିଵൗఊሻ

Table B.7. Structural Estimation of Subjects’ Strategy Choices in Kamei (2017)
We estimated distributions of strategies chosen by the subjects in the N treatment, the RG treatment and the
RP treatment of Kamei (2017), again based on the maximum likelihood method (Dal Bó and Frechétte, 2011).
The N and RG treatments of Kamei (2017) are the same as the “Private Monitoring” and “Non-anonymous
Public Monitoring” treatments, respectively, of Camera and Casari (2009). The same sets of strategies used inAppendix Table B.6 were considered here as well for these two treatments.
The RP treatment of Kamei (2017) is similar to the RG treatment, except that subjects in the former havesmaller sizes of reputational information compared with the latter. In the RP treatment, as in the RG treatment,
subject i is informed of his/her current-round partner’s ID before choosing an action. Subject i is also given therecord of the partner’s actions taken towards i in the past. However, i is not informed of any actions chosen by
the partner towards the other two players in the group. In estimating a distribution of subjects’ strategy choicesin the RP treatment, the LIRep and IRepXX strategies defined as follows, were considered:
LIRep (“Cooperate based on the Last-Interaction Reputation”): A subject i selects cooperation in round t if
his/her round t partner j selected cooperation toward i in their last interaction.
IRepXX: A subject i selects cooperation in round t if the cooperation rate of his/her round t partner j thus far
was at least XX% according to the past interaction record between i and j.
The estimation result for the N treatment (see column A below) finds that a non-negligible fraction ofsubjects acted according to the AD strategy, whose finding is similar to the private monitoring treatments ofthe present paper (Appendix Table B.5), the data of Camera and Casari (2009) – summarized in Table B.6,
Camera et al. (2012) and Kamei and Nesterov (2020).
Columns B and C below indicate that similar to the findings of the present paper (Appendix Table B.5), thedata of Camera and Casari (2009), and Kamei and Nesterov (2020), a large fraction of subjects selected
cooperation conditional upon their partner’s reputational information.
[Estimation Result:]
Treatment:

Fraction Bootstrap
SE(B) RG treatment (non(C) RP treatment
anonymous public
monitoring)
p-value Fraction Bootstrap p-value Fraction Bootstrap p-value(2-sided)SE(2-sided)SE(2-sided)

AD

0.439

0.165

0.004***

0.083

0.075

0.132

0.156

0.082

0.029**

AC

0.100

0.058

0.043**

0.002

0.031

0.472

0.127

0.063

0.021**

Grim

0.052

0.051

0.155

0.000

0.041

0.500

0.062

0.043

0.073*

TFT

0.370

0.102

0.000***

0.000

0.000

0.427

0.028

0.015

0.028**

WSLS

0.025

0.044

0.286

0.000

0.023

0.500

0.000

0.026

0.500

T1

0.000

0.000

0.333

0.000

0.000

0.399

0.000

0.018

0.500

T2

0.000

0.005

0.500

0.000

0.011

0.500

0.000

0.000

0.393

T3

0.000

0.000

0.334

0.000

0.027

0.500

0.000

0.004

0.500

T4

0.014

0.000

0.000***

0.000

0.003

0.500

0.000

0.005

0.500

LRep33_partners

0.025

0.025

0.157

LRep67_partners

0.030

0.046

0.256

Strategy(A) N treatment (private
monitoring)27

LRep100_partners

0.000

0.000

0.403

Rep20_community

0.109

0.039

0.002***

Rep40_ community

0.000

0.016

0.500

Rep60_ community

0.000

0.004

0.500

Rep80_ community

0.090

0.013

0.000***

Rep100_ community

0.000

0.010

0.500

Rep20_partners

0.000

0.003

0.500

Rep40_partners

0.000

0.006

0.500

Rep60_partners

0.000

0.000

0.407

Rep80_partners

0.000

0.003

0.500

Rep100_partners
Rep20_ community_5rounds
Rep40_ community_5rounds
Rep60_ community_5rounds
Rep80_ community_5rounds
Rep100_ community_5rounds
Rep20_partners_5roun
ds
Rep40_partners_5roun
ds
Rep60_partners_5roun
ds
Rep80_partners_5roun
ds
Rep100_partners_5rou
nds
LRep

0.000

0.000

0.407

0.002

0.031

0.472

0.000

0.019

0.500

0.000

0.001

0.500

0.000

0.003

0.500

0.000

0.000

0.482

0.000

0.003

0.500

0.038

0.066

0.280

0.000

0.000

0.403

0.000

0.000

0.392

0.000

0.000

0.470

0.062

0.042

0.069*

Rep20

0.258

0.109

0.009***

Rep40

0.098

0.077

0.102

Rep60

0.055

0.051

0.142

Rep80

0.000

0.001

0.500

Rep100

0.000

0.000

0.474

Rep20_5rounds

0.052

0.112

0.321

Rep40_5rounds

0.049

0.042

0.119

Rep60_5rounds

0.045

0.044

0.152

Rep80_5rounds

0.000

0.009

0.500

Rep100_5rounds

0.000

0.000

0.000***

LIRep

0.388

28

0.191

0.021**

IRep20

0.000

0.060

0.500

IRep40

0.081

0.088

0.180

IRep60

0.000

0.000

0.450

IRep80

0.158

0.104

0.065*

IRep100

0.000

0.000

0.000***

0.000*** 0.423

0.030

0.000***

γ

0.540

β

0.864

0.057

0.000***

0.402
0.923

0.049

0.914

Notes: a The table reports the estimated percentage of each strategy in the population. b Ⱦ ൌଵ.

ଵାୣ୶୮ሺିଵൗఊሻ

References:
Camera, G., Casari, M. 2009. “Cooperation among Strangers under the Shadow of the Future.” American
Economic Review, 99(3):979-1005.
Camera, G., Casari, M., Bigoni, M., 2012. “Cooperative Strategies in Anonymous Economies: An
Experiment.” Games and Economic Behavior, 75:570-586.
Dal Bó, P., Fréchette, G. 2011. “The Evolution of Cooperation in Infinitely Repeated Games: Experimental
Evidence.” American Economic Review, 101(1):411-429.
Kamei, K., 2017. “Endogenous Reputation Formation under the Shadow of the Future.” Journal of Economic
Behavior & Organization, 142:189-204.
Kamei, K., Nesterov, A., 2020. “Endogenous Monitoring through Gossiping in an Infinitely RepeatedPrisoner’s Dilemma Game: Experimental Evidence.” Durham University Business School Working Paper(https://papers.ssrn.com/abstract=3608749).

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