DP2015-31

Reciprocity and Exclusion inInformal Financial Institutions:
An Experimental Study of Rotating
Savings and Credit Associations
Shimpei KOIKE
Mayuko NAKAMARU
Tokinao O TAKA
Hajime SHIMAO
Ken-Ichi SHIMOMURA
Takehiko YAMATO
July 23, 2015

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Reciprocity and exclusion in informal financial institutions:an experimental study of rotating savings and credit associations

Shimpei Koike 1, Mayuko Nakamaru 1, Tokinao Otaka 2, Hajime Shimao 1,
Ken-Ichi Shimomura 3, Takehiko Yamato 2
July 2015(1) Department of Value and Decision Science, Tokyo Institute of Technology, Tokyo, 152-8552,
Japan(2) Department of Social Engineering, Tokyo Institute of Technology, Tokyo, 152-8552, Japan(3) Research Institute for Economics and Business Administration, Kobe University, Kobe, 657-8501,
Japan
Corresponding author: M. Nakamaru
e-mail: nakamaru.m.aa@m.titech.ac.jp

2
Abstract
Rotating savings and credit associations (Roscas) are worldwide informal financial
institutions, in which all participants contribute to a fund and one of them receives it in rotation. A
crucial problem is that participants have incentives to default on contributing after receiving the fund.
We conducted an experiment and found that Roscas were sustained using a rule of excluding
defaulters from the group by voting. We observed that group members behave reciprocally andrevengefully: a member contributed (or did not contribute) to the fund of other members who had (orhad not) contributed to theirs. This voluntary behavior sustained Roscas.

Keywords: Rosca, Exclusion, Reputation, Reciprocity, Punishment
Classification codes: C92, D71, G21

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1. Introduction
Rotating savings and credit associations (Roscas) are informal financial institutions thatexist all over the world. They are common in developing countries and among migration groups indeveloped countries (Geertz 1962; Ardener 1964; Light 1972; F. Bouman 1977, 1995; Bonnett 1981;
Ardener and Burman 1995; Schreiner 2000; Chamlee-Wright 2002). Some microfinanceorganizations, such as Grameen Bank, and credit cooperatives have their origins in Roscas(Armendáriz and Morduch 2010). Ardener (1964) simply defined Roscas as “association(s) formed
upon a core of participants who agree to make regular contributions to a fund which is given, in
whole or in part, to each contributor in rotation.” If n participants join a Rosca, the meeting is held ntimes regularly. At every meeting, each participant contributes a fixed amount of money to a fund,and the fund is given to one of the participants. Therefore, after the end of the n-th meeting, all theparticipants have contributed n times and received the fund once. The Rosca participants use the fundto buy durable goods (Timothy Besley and Levenson 1996), invest in the business (Light 1972), or
make precautionary savings for unplanned expenses (Handa and Kirton, 1999). The merit of joining
a Rosca is that except for the last receiver, participants obtain the money earlier than if they had
saved the same amount on their own. In general, there are three types of Roscas according to themanner of determining the order of receiving the fund: a random Rosca; a fixed Rosca; and a bidding
Rosca. With the random Rosca, the receiver is selected randomly by lottery at every meeting fromamong the participants who have not hitherto been chosen. On average, participants can receive thefund at the (n+1)/ 2-th meeting. With the fixed Rosca, the order is determined before the first meeting.
With the bidding Rosca, the participants bid for the fund at each meeting, and the bidder whose
contribution or one-time dividend is the highest receives the fund.
One important characteristic of Roscas is that contributions to the fund are voluntary. If allparticipants contribute to the fund after they have received the payment, the Rosca is managed
successfully. If some participants default on their contribution after receiving the fund, the defaulterssave the money that they should have contributed at the meeting. If this occurs, the other participants
obtain a lower amount than they should have received. So without any external enforcement, how
can Roscas prevent defaulters?
Social connectedness among Rosca participants is key to preventing this default problem(Coleman 1990; Putnam 1993; Besley, Coate, and Loury 1993). Participants can obtain information
about defaulters based on their social connections, and potential participants’ reputation for honesty
and reliability is important in the formation of Rosca groups. Excluding unreliable participants
avoids the risk of the default problem, and group members are deterred from defaulting by threat of
exclusion. Koike et al. (2010) conducted evolutionary game simulations to investigate the effect of

4excluding unreliable Rosca members based on their reputation—termed peer selection—on
sustaining Roscas. In addition to peer selection, the forfeiture rule is applied: this prevents a member
from receiving the fund if that member has not previously made a contribution. The forfeiture rulecan be interpreted as a costless punishment in a mutual-aid game (Sugden, 1986). Koike et al. (2010)
showed that the combination of peer selection and the forfeiture rule can prevent defaulters andmaintain Roscas.
In the present study, we conducted a laboratory experiment to examine whether these two
factors prevented subjects from becoming defaulters and sustained Roscas in the case of the fixed
Rosca, where the participants are shuffled randomly for each cycle. Our experiment showed that peer
selection based on voting increases the contribution rate before and after receiving the fund by
excluding low contributors from the groups and allowing medium and high contributors toparticipate. Accordingly, the mean payoff for subjects who participated in the Rosca with peer
selection was significantly higher than that of those who participated in the Rosca without it.
However, the difference between our result and that of Koike et al. (2010) is that the forfeiture rule
did not increase the contribution rates. That is because almost all subjects retaliated against a
defector who had not contributed to their own funds by refusing to contribute to the fund that thedefector would have received without the forfeiture rule. Therefore, our results suggest that theexclusion of defaulters based on their reputation can solve the default problem of Roscas even
without external enforcement.
This paper proceeds as follows. In the next section, we review the related literature.
Section 3 describes the design of our experiment and theoretical prediction based on evolutionary
game simulations. Sections 4 and 5 present our results and our conclusions, respectively.

2. Related Literature
Several theoretical studies have investigated the conditions for solving the default problem
and sustaining Roscas. Besley et al. (1993) showed in the case of the random Rosca that the Rosca ismaintained if the benefit to the first receiver after defaulting is not greater than the default cost. The
default cost represents social sanctions: a bad reputation being spread about defaulters, their being
excluded from other Roscas in the future, or damage to their personal property. Anderson et al.
(2009) investigated random and fixed Roscas, in which the same participants joined the Roscas
repeatedly. The authors showed that the first receiver is always inclined to leave and chooses todefect—even if the player is excluded from all future meetings. Their field survey in Kenya reported
that Rosca members enforced social punishment, such as confiscating the defaulter’s property.
However, the argument of Anderson et al. (2009) depends on the assumption that the same members

5join the same Rosca repeatedly: they did not investigate whether exclusion can prevent defaulters if
there are changes in the Rosca membership.
To the best of our knowledge, no experimental study has been undertaken about Roscas.
Using public goods experiments, several studies have found that exclusion based on reputation canpromote the contribution level by expelling low contributors from the game (Cinyabuguma, Page,
and Putterman 2005; Maier-Rigaud, Martinsson, and Staffiero 2010; Feinberg, Willer, and Schultz2014). This exclusion can be interpreted as costless punishment. By contrast, a number ofexperimental studies have investigated costly punishment. Costly punishment to free riders has beenfound to increase the contribution level in public goods experiments (Yamagishi and Cook 1993;
Ostrom, Walker, and Gardner 1992; Fehr and Gächter 2002; Fehr and Gächter 2000; Bochet, Page,
and Putterman 2006; Page, Putterman, and Unel 2005; Carpenter 2007). However, Herrmann et al.
(2008) suggested that antisocial punishment, which they defined as a free rider punishing
contributors with paying a punishment cost, is observed in societies with weak norms of civic
cooperation and a weak rule of law. Under some social conditions, costly punishment is ineffective
in increasing the contribution level (Nikiforakis 2008; Gächter and Herrmann 2009; Gächter andHerrmann 2011).
We would expect that the exclusion of defaulters from Rosca groups would make Roscas
sustainable. There is a critical difference between Roscas and the public goods game: with a Rosca,
one player can receive the fund at each meeting, whereas all players receive the same fund in the
public goods game. The incentive to default with Roscas depends on the order of receiving the fund;by contrast, all players have the incentive to choose defection in the public goods game. Thus, we
conducted a laboratory experiment to examine whether the exclusion of defaulters makes Roscas
sustainable.

3. Experiment
3.1 Design
The experiment consisted of four types of sessions: Treatment B; Treatment P; Treatment V; andTreatment VP. Figure 1 is a summary of the experimental procedure for each treatment. The
experimental procedure with Treatment B is as follows. With each treatment, each session consistedof 10 rounds, each of which consisted of four periods. At the beginning of a session, each of 20
subjects was assigned to one computer in a laboratory and received instructions (the instruction sheet
for Treatment B appears in Appendix A). After the experimenter read the instructions aloud to thesubjects, they were randomly divided into five groups, each consisting of four members. At the6
beginning of each round, the order for receiving the fund was randomly determined; that order foreach group appeared on the computer screens, and each member knew the order for all members.
The member who received the fund in the n-th period was termed the n-th receiver.

Round 1Treatment B

Treatment P

Divide members into five groups

Divide members into five groups

Determine the order of receiving fund

Determine the order of receiving fundGet 100 points

Get 100 points

Period 1

Receiver 2-4
Contribute to the fund or not

Receiver 2-4
Contribute to the fund or not

Receiver 1

Receiver 1
Recive the fund

Treatment VP

Same as Treatment B

Same as Treatment P

Divide members into five groups

Divide members into five groups

Do more than tw o subjects
decide to exclude

Do more than tw o subjects
decide to exclude

Round 1Round2

Yes

No

Receive the fund

Yes

No

Determine the order
Period 1

Period 2Treatment V

Get 100 points

Determine the orderGet 100 points

Get 100 points

Get 100 points
Receiver 1,3,4
Contribute to fund or not
Receiver 2

If Receiver 2 has not contributed
NOT
Receiver 1,3,4Receive the fundReceive the fundSame asTreatment B
Period 2

Get 100 points

Same asTreatment P
Get 100 points

Receiver 2
Receive the fund

Period 3, 4Same as Period 2

Round 2-10

Same as Period 2

Period 3, 4Same as Period 2

Same as Period 2

Round 3-10

Fig. 1. Experimental procedures with the four treatments
In each period, the experimenter gave 100 points to all the members, and all members
except the receiver had to choose whether or not to contribute those 100 points to the fund. If somemembers decided to contribute to the fund, they lost 100 points; if they decided not to contribute to
the fund, they saved 100 points. We assumed that members who received the fund earlier would
profit more than those who received the fund later. This was because the earlier a member received
the fund, the earlier they could purchase durable goods and invest in their business and then make aprofit. If mC is the number of contributing members and n is the number of periods, the payoff ofreceiving the fund is,where δ is the discount factor.
We used δ = 0.3, and the payoffs for receiving the fund in each period are presented inTable 1. After receiving the fund, all members were informed which members had contributed to thefund as well as the payoffs to all members in that period (Fig. 2). After the fourth period, the total
payoffs to all members in that round were shown to all members. At the beginning of the next round,7
new groups were randomly formed. If some members belonged to the same group as in previous
rounds, they were unaware of that fact. After the end of the 10th round, the subjects answered aquestionnaire and were paid a reward in proportion to their total payoff in that session.
Table 1.
Payoffs for receiving the fund in each period in δ = 0.3
PeriodFourthNumber of members who contribute to the fund
0

1

2

3

First

100

320

539

759

Second

100

269

438

607

Third

100

230

360

490

100

200

300

400

With Treatment P, we introduced a forfeiture rule: no member who had not contributed in
the preceding periods could receive the fund. For example, if the third receiver did not contribute in
the first or second period, they could not receive the fund in the third period but saved 100 points.
The other members also saved 100 points because they did not need to contribute 100 points.
Following Sugden (1986), we term the forfeiture rule the punishment rule in this experiment.

Fig. 2. Example of a confirmation screen
With Treatment V, we introduced a voting system. In this system, 20 subjects were8
randomly divided into five groups at the beginning of each round. All members in each group were
aware of how many times each member had actually contributed in the previous rounds and how
many times each member could decide to contribute in the previous rounds. Based on thisinformation, each member decided who should be excluded from the group. This voting system was
not applied in the first round. If more than two members chose to exclude a particular member, thatmember was expelled from the group. The excluded members could not participate in that round andreceived 400 points. At the end of each round, the 20 subjects were randomly divided into fivegroups for the next round. Therefore, subjects excluded from the group in a previous round had thechance to join the group in the next round. Treatment VP was the same as Treatment P with theaddition of the voting system (Fig. 1).
We conducted two sessions for each treatment at Tokyo Institute of Technology from
December 2011 to June 2013 using the program z-Tree (Fischbacher 2007). We recruited 160 (20 × 4
× 2) subjects from a Tokyo Institute of Technology subject pool. They consisted mainly ofundergraduate students who had never participated in similar experiments. The average payment
made to the subjects was 3,506 yen (approximately 35.06 US dollars at a rate of 1 US dollar = 100
yen).
3.2 Theoretical Predictions
We analyzed the game with Treatment B, in which four players played four periods andobtained the subgame-perfect equilibrium, whereby every player paid no contribution at each period(the proof appears in Appendix B). We were unable to evaluate games corresponding to Treatments V,
P, and VP within the framework of game theory. Koike et al. (2010) studied random Roscas bymeans of an evolutionary game simulation: they investigated the sustainability of Roscas through theeffect of peer selection based on reputation and the forfeiture rule. The authors showed that the
combination of the forfeiture rule and peer selection resulted in the greatest contribution rate before
receiving the fund; the forfeiture rule produced the second-highest rate; peer selection thethird-highest rate; and the baseline model lacking both the forfeiture rule and peer selection resulted
in the worst rate. Therefore, we predicted that the order of the contribution rate before receiving thefund in our experiment would be VP = P > V > B. Accordingly, the order of the contribution rate
after receiving the fund in our experiment was predicted as VP > P = V > B.
In the following sections, we will compare the theoretical prediction by Koike et al. (2010)
with the results of our experiment.

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4. Results
4.1 Average contribution rates and total profit
We consider first the contribution rate in each treatment. We categorized the contribution
rates into two types: the contribution rate before receiving the fund (β0) and the contribution rate
after receiving the fund (α0). Figure 3a shows the average value of β0 in each round. In Treatments B
and P, the average values of β0 in the first round were 0.42 and 0.59, respectively; however, the rate
was not always higher in Treatment P (thin line) than in Treatment B (thick line). The average valueof β0 in Treatment V (dot-dashed line) was the highest among the four treatments except in the 10thround. In the first half of the rounds, the average value of β0 in Treatment VP (dashed line) was
between that of Treatments V and B, but it showed a declining trend in the second half of the rounds.
In the final round, the end-game effect caused the average values of β0 in Treatments VP and V todecrease. This tendency is the same as in results observed in public goods experiments(Cinyabuguma, Page, and Putterman 2005; Maier-Rigaud, Martinsson, and Staffiero 2010)a
Average Contribution Rate

Before Receiving (β0)
1.00.8Treatment B

0.6

Treatment P

0.4

Treatment V

0.2

Treatment VP

0.0

1

2

3

b

4

5
6
Round

7

8

9

10

Average Contribution Rate

After Receiving (α1)
1.00.8Treatment B

0.6

Treatment P

0.4

Treatment V

0.2

Treatment VP

0.0

1

2

3

4

5
6
Round

7

8

9

10

Fig. 3. Average contribution rates in each round10

Table 2 presents the average contribution rates over 10 rounds. To compare the averagevalues of β0 in the four treatments, we conducted Pearson’s chi-squared test. The average values of β0
in Treatments B and P were both 0.42 and were not significantly different (p = 0.93). With the voting
system in Treatment V, the average value of β0 was 0.82, which was significantly higher than that inTreatment B (p < 0.001). However, in Treatment VP, which had the punishment rule and voting
system, the average value of β0 was 0.56; that was significantly smaller than in Treatment V but
higher than in Treatments B and P (p < 0.001).
We categorized the contribution rate after receiving the fund (α0) into three types: thecontribution rate that a focal player contributed to the receiver who has contributed to both the focal
player and other members (α1); the contribution rate that a focal player contributed to the receiver
who has contributed to the focal player but not contributed to other members (α2); and thecontribution rate that a focal player contributed to the receiver who has not contributed to the focal
player (α3). The punishment rule prohibited subjects from contributing to the receiver who had notpreviously contributed, and so α0 in Treatments P and VP was represented by α1. α0 in Treatments B
and V was represented by the contribution rate that a focal player contributed to the receiver
regardless of the receiver’s past behavior. Hereafter, we do use not α0 but α1 in comparing thecontribution rate after receiving the fund in the four treatments under the same criteria.
Figure 3b shows the average value of α1 in each round. In Treatment V, the average valueof α1 was the highest among the four treatments except for the 10th round; however, no marked
differences were observed in the average values of α1 among Treatments B, P, and VP. The averagevalues of α1 over the 10 rounds in Treatments B, P, and VP were 0.40, 0.38, and 0.42, respectively;
they were not significantly different (p > 0.10) (Table 2). In Treatment V, the average value of α1 overthe 10 rounds was 0.76, which was significantly higher than in Treatments B, P, and VP (p < 0.001)(Table 2).

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Table 2.
Average contribution rates in the four treatments over 10 rounds
Treatment

Before receiving

After receiving

β0

α0

α1

α2

α3

Treatment B

0.42

0.18

0.40

0.31

0.04

Treatment P

0.42

0.38

0.38

-

-

Treatment V

0.82

0.64

0.76

0.60

0.15

Treatment VP

0.56

0.42

0.42

-

-

1–3

1–3

Pearson’s chi-squared testp < 0.01

1–3, 1–4, 2–3, 2–4, 3–4-

1–3, 2–3, 3–4

Not significant

1–2-

1–2, 1–4, 2–4

Observation 1a) The contribution rates before and after receiving the fund in Treatment V were significantly higher
than those in Treatments B, P, and VP.
b) The contribution rates before and after receiving the fund in Treatments B and P were notsignificantly different.
We now consider the distribution of the total payoff at the end of the treatments (Fig. 4).
Figure 4b shows that the payoffs for all subjects in Treatment V were greater than 4,000 points,
which was the same as the amount that all subjects received during one treatment (100 points × 4
times × 10 rounds). The payoffs for seven, eight, and five subjects were lower than 4,000 points in
Treatments B, P, and VP, respectively. The mean payoff in Treatment V was 4,980 points, and it wassignificantly higher than the mean payoffs in Treatment B, P, and VP, which were 4,681, 4,566, and
4,494, respectively (p < 0.05 in Student’s t test). They were not significantly different (p > 0.10).

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c

a
Mean : 4,681
Max : 6,120
Min : 3,484
Std : 677

Mean : 4,556
Max : 6,442
Min : 3,538
Std : 662

db
Mean : 4,980
Max : 6,142
Min : 4,159
Std : 548

Mean : 4,494
Max : 5,504
Min : 3,639
Std : 471

Fig. 4. Total profits after the treatments
Observation 2a) The mean payoff in Treatment V was significantly higher than that in Treatments B, P, and VP.
b) The mean payoffs in Treatments B, P, and VP were not significantly different.
4.2 Why did the punishment rule not work well?
To determine why the contribution rates in Treatments B and P were not significantly
different, we focus on the differences among the average values of α1, α2, and α3. Table 2 shows thatthe average values of α1, α2, and α3 in Treatment B were 0.40, 0.31, and 0.04, respectively. The
average values of α1 and α2 were not significantly different (p = 0.21 by Pearson’s chi-squared test),
and the average value of α3 was significantly smaller than the others (p < 0.001). This suggests thatthe subjects in Treatment B discriminated between receivers who had and had not contributed tothem and also that they rejected non-contributors. This behavior can be interpreted as a kind of
costless punishment to non-contributors. Hence, the subjects had a tendency to punish receivers who

13
had not contributed to them in Treatment B. As a result, even though Treatment P is the combinationof Treatment B and the punishment rule that prohibited subjects from contributing to the receiver
who had not previously contributed, the contribution rates in Treatments B and P did not differ
significantly.
Similarly, in Treatment V, the average values of α1, α2, and α3 were 0.76, 0.60, and 0.15,
respectively (Table 2). The average value of α3 was significantly smaller than the others (p < 0.001).
This suggests that the subjects in Treatment V also retaliated against their non-contributors.
4.3 Why did the voting system work well?
To show why the voting system itself promoted the contribution rates, we investigated thenumber of participants in each group and the number of subjects excluded from each group. In Fig. 5,
the subjects are categorized into three types based on the cumulative contribution rate: low
contributors, whose cumulative contribution rate was less than 0.40; medium contributors, whose
cumulative contribution rate was 0.40–0.80; and high contributors, whose cumulative contribution
rate was equal to or greater than 0.80. The upper section in each part of Fig. 5 shows the number ofparticipants who were never excluded from the groups (non-excluded participants; white bars) andthe number of participants who were excluded in previous rounds (excluded participants; gray bars).
The lower section in each part of Fig. 5 indicates the number of subjects who were excluded from thegroups (excluded subjects; black bars). The horizontal axis represents the number of rounds; theupper and lower vertical axes represent the number of participants and number of subjects,
respectively. In Treatment V, low contributors were frequently excluded from the groups (Fig. 5a);medium and high contributors were not excluded from the groups so often (Fig. 5b, c). Over the 10
rounds in Treatment V, the voting system excluded 72% of low contributors and 6% of medium andhigh contributors. The difference was significant (p < 0.001). Therefore, because low contributors
were excluded from the groups and the voting system made medium and high contributors
participate in the groups, the contribution rates in Treatment V were higher than those in Treatments
B and P, which lacked the voting system.

14aNumber ofParticipants

Low Contributors in Treatment Vd

Low Contributors in Treatment VP

E xclu d e d P a rticip a n ts
N o n e xclu d e d P a rticip a n ts

Number of
Subjects

Roundb

Excluded SubjectseMedium Contributors in Treatment VP

Number ofParticipants

Medium Contributors in Treatment V

Number of
Subjects

Round

c

f

High Contributors in Treatment VP

Number ofParticipantsHigh Contributors in Treatment V

Number of
Subjects

Round

Fig. 5. Total number of participants and excluded subjects in each round over two sessions
Although low contributors were excluded from the groups, the average number ofparticipants in each round in Treatment V was at least three out of four subjects (Fig. 6). The reason
is as follows: in the upper part of Fig. 5a, all the low contributors who were allowed to participate in
the groups were excluded participants. This suggests that the voting system gave the excluded low
contributors a chance of participating in a group again, and as a result the number of group members
was around three to four.
In Treatment VP, the number of excluded subjects was not always higher than that of

15participants among low contributors (Fig. 5d); however, among medium and high contributors, thenumber of excluded subjects was lower than that of participants in each round (Fig. 5e, f). Because
the average contribution rates (β0, α1) continued declining in the second half of rounds (Fig. 3), thenumber of high contributors also decreased and that of medium contributors increased. Over the 10
rounds in Treatment VP, the voting system excluded 51% of low contributors and only 8% of both
medium and high contributors from the groups, respectively. These exclusion rates were significantly
different (p < 0.001).
In a comparison of Treatments V and VP, the exclusion rates of high contributors were 6%
and 8%, respectively; they were not significantly different (p = 0.34). The average exclusion rate of
low contributors in Treatment V (72%) was significantly higher than that in Treatment VP (51%, p <0.038). This is why the contribution rates in Treatment V were higher than those in Treatment VP.

Participants

Average Number of

4.0

3.5

Treatment V

3.0

2.5

Treatment VP

1

2

3

4

5

6

7

8

9

10

Round

Fig. 6. Average number of participants in each round
Observation 3a) The voting system excluded low contributors from the groups and let medium and highcontributors participate in the groups.
b) The average exclusion rate of low contributors in Treatment V was significantly higher than that inTreatment VP.
4.4 Order effect of receiving the fundIn our experiment, each subject was informed of the order in which they received the fundin each round. Here, we examine how the order influenced the contribution rates.
In Table 3, the average value of β0 of the second receivers was significantly higher thanthat of the third receivers in all the treatments. The average value of β0 of the third receivers was
significantly higher than that of the fourth receivers for all the treatments. Focusing on the discount16
factor (δ = 0.3), we explain this as follows: if the second receiver contributed to the fund for the firstreceiver, the first receiver may have been willing to contribute to the fund for the second
receiver—at least if direct reciprocity worked and the first receiver was willing to contribute for thesecond receiver who had contributed for that first receiver. The fund of the second receiver is thetotal contribution multiplied by (1+δ)2 . If direct reciprocity worked, the fourth receiver would
contribute to the fund for the first, second, and third receivers, who would contribute to the fund forthe fourth receiver. The fund of the fourth receiver is the total contribution multiplied by (1+δ)0 . As
a result, the second and the third receivers contributed more before receiving the fund than the fourthreceivers.
The average values of α1 among the first, second, and third receivers were not significantly
different in all four treatments (Table 3). We expected that the average value of α1 of the earlier
receivers would be lower than that of the later receivers in Treatments B and P because the earlier
receivers would not contribute to the fund after they had received it. However, because the subjects
had the tendency to behave reciprocally, the order of receiving the fund did not change the averagevalues of α1 among the first, second, and third receivers.
Observation 4a) The contribution rates before receiving the fund gradually decreased in the order of the second,
third, and fourth receivers in all four treatments.
b) The contribution rates after receiving the fund among the first, second, and third receivers did not
differ significantly in all four treatments.

17
Table 3.
Order effect of contribution rates
Order of receiving fund
Treatment B

Treatment P

Treatment V

Treatment VP

Contribution rate before receiving (β0)
First receiver

-

-

-

-

Second receiver

0.77

0.69

0.95

0.78

Third receiver

0.52

0.43

0.85

0.59

Fourth receiver

0.25

0.28

0.73

0.35

2–3, 3–4, 2–4

2–3, 3–4, 2–4

3–4, 2–4

2–3, 3–4, 2–4

Pearson’s chi-squared testp < 0.01

2–3

p < 0.05
Contribution rate after receiving (α1)
First receiver

0.39

0.34

0.77

0.42

Second receiver

0.42

0.42

0.76

0.43

Third receiver

0.38

0.45

0.74

0.36

Fourth receiver

-

-

-

-

1–2, 2–3, 3–4

1–2, 2–3, 3–4

1–2, 2–3, 3–4

1–2, 2–3, 3–4

Pearson’s chi-squared test
Not significant

5. Concluding Remarks
We conducted a laboratory experiment to show a mechanism for solving the default
problem in the fixed Rosca whose participants are shuffled randomly for each Rosca cycle. We
observed that the exclusion of defaulters based on voting increased the contribution rates before andafter receiving the fund. We also found that the punishment rule, corresponding to the punishment
rule of Sugden (1986) and the forfeiture rule of Koike et al. (2010), did not improve the contribution
to the fund. In consequence, contrary to our theoretical prediction, the contribution rates and mean
payoff of the subjects in Treatment V were significantly higher than those in the other treatments.
These results support those of field studies of Roscas, in which social sanctions through exclusion
suppressed the default problem even without external enforcement (Ardener 1964; Handa and Kirton
1999).
Previous studies using the public goods game have shown that exclusion promoted thecontribution rate (Cinyabuguma et al. 2005; Maier-Rigaud et al. 2010; Feinberg et al. 2014). The

18
present investigation also supported those results even though our game structure was different fromthe public goods game. However, an interesting finding in our Rosca game was the observed
voluntary direct reciprocity and voluntary retaliation (Treatment B and V). These two phenomena are
not observed in the public goods game, where all the players contribute to the fund, which is
distributed equally to all players. Another interesting finding with the present study was that eventhough we introduced an explicit costless punishment rule (the forfeiture rule), it did not improve thecontribution rate (Treatments P and VP). In our experiment, we were unable to determine how
voluntary direct reciprocity and voluntary retaliation influenced explicit punishment and vice versa.
Voluntary direct reciprocity and voluntary retaliation are reminiscent of the repeated gamebetween two players, in which a player can behave reciprocally and revengefully toward theiropponent. However, the Rosca game is not the same as the repeated game: the order of receiving thefund influences reciprocity and retaliation in the Rosca game. Further investigation of the Rosca
game should give us new viewpoints on this game.
Hechter (1988) examined Roscas and argued that members can suppress non-contribution
before receiving the fund without difficulty. This is because if a member fails to contribute to thefund before receiving, the other members can prevent that member from obtaining the fund.
However, in our treatments, the subjects often failed to make a contribution before receiving the funddespite the forfeiture rule prohibiting such non-contributors from receiving the fund. This result
reinforces the importance of exclusion based on reputation.
Exclusion based on majority voting has two characteristics: (1) low contributors are mainly
excluded from groups; and (2) low contributors who have been excluded sometimes have a chance toparticipate in a group again. Item (1) is in accordance with the results of public good experiments(Cinyabuguma, Page, and Putterman 2005; Maier-Rigaud, Martinsson, and Staffiero 2010), but noexperimental studies about exclusion have examined item (2). Sugden (1986) proposed a mutual-aid
game based on informal health insurance in England: insurance members pay a subscription and one
member chosen randomly from the group members receives the insurance money each period;
because the choice is random, that member may receive the fund again even after having previously
received it. The mutual-aid game differs from Roscas in that every member has an equal chance ofreceiving the fund in each period. Sugden’s theoretical analysis showed that a kind of tit-for-tat
strategy, which has the three features of “brave reciprocity,” “punishment,” and “reparation,” is astable equilibrium. Our results correspond to Sugden’s tit-for-tat strategy: in our experiment, thesubjects behaved reciprocally and punished defectors by excluding them from the group. Thus, weconsider that allowing excluded members to join a group again gives those members a chance tomake reparation for their past defaults.
In this study, we investigated how social exclusion based on peer selection can prevent the19default problem in the fixed Rosca; however, future research is needed to examine the effectivenessof such social exclusion in the random and bidding Roscas so as to verify the robustness of ourresults. In the random Rosca, the subjects cannot use a retaliation strategy because the receiver ischosen randomly after they have decided to contribute. Therefore the forfeiture rule, which did notwork in the fixed Rosca in our experiment, may be needed to sustain the Rosca. Because our study
did not assume costly punishment, it would be interesting to investigate how such costly punishment
as confiscating the defaulter’s property influences the sustainability of Roscas—even in thelaboratory situation.

Acknowledgement
We are grateful to Yoshifumi Ishiyama, Kensuke Kuze, Kanan Miura, Yuki Oide, Akira
Takata, and Akira Yokoyama for their assistance of our experiment, and Tokyo Institute ofTechnology for providing its support and facilities. Comments and suggestions on an earlier version
by Masahiro Tsujimoto were insightful, and discussions with Kazuo Ishizuka, Soichiro Ohishi,
Tomoki Takada and Shuta Terui were helpful. Nakamaru’s research was partially supported by JSPS
KAKENHI Grant Numbers 21770016 and 26440236. Shimomura’s research was partially supported
by JSPS KAKENHI Grant Numbers 24310110 and 25380228. Yamato’s research was partially
supported by Zengin Foundation for Studies on Economics and Finance and JSPS KAKENHI Grant
Number 26285045.

20

Appendix A: Instruction Sheet for Treatment B
Instructions
Overview of the Experiment
The experiment consists of 10 rounds, each of which consists of four periods. Each group has four subjects. In
the experiment, 100 tokens are given to you in each period. This does not mean that real token are given toyou, but please imagine that you have 100 tokens. Then please decide whether “to give" 100 tokens to thefund of your group or “not to give”. One of the members receives the fund, and the fund grows as periods
advance. The earlier you receive the fund or the more members give tokens to the fund, the more payoff you
can obtain.
Your earnings are determined according to your payoff in the experiment. As your payoff become
higher, you receive higher earnings. Your payoff depends on both your choice and the other members’.

Experiment Procedure
Step 1.
20 subjects are randomly made into five groups, each consisting of four subjects. You belong to one of thegroups. You cannot identify who are in your group. Similarly, none of your group members knows whether
you are in the group.

Step 2.
The computer determines “the order of receiving the fund" randomly. The order will be shown on yourcomputer screen. Please check your order.

21
Example 1:
If you are the second receiver, the following information is shown on your computer screen:Round
1 out of 10

You are B1 and the second receiver.

NEXT

Step 3.
Each round consists of four periods. Each period proceeds as follows.
First, you get 100 tokens at the beginning of each period. Your receiving order determines what to
do in each of the four periods.

(a) In the period when you do not receive the fund:You can choose either "to give" 100 tokens to the fund or "not to give".
If you choose "GIVE", then all 100 tokens will be added to the fund, and you will lose 100 tokens.
You cannot save anything and your payoff is 0 in this period.
If you choose "NOT GIVE", then you can save 100 tokens and your payoff in this period is 100.

(b) In the period when you receive the fund:You can receive the fund given by your group members. You do not need to choose "GIVE" or"NOT GIVE". The amount of the fund depends on the number of other members who give 100 tokens in thisperiod.

Your payoff in one round consisting of four periods is determined by both “the order of receiving
the fund" and “the number of the other members who give 100 tokens to the fund" as follows:22
The number of members choosing "GIVE"
0

1

2

3

The order

first period

100

320

539

759

of

second period

100

269

438

607

receiving

third period

100

230

360

490

the fundfourth period

100

200

300

400

More specifically, your payoff in one round is calculated as follows:Your payoff =(the number of members who have invested to the fund) * 100 * 1.3(4 - your receiving order) +100
This means that the fund is multiplied by 1.3 in each period after you receive the fund. Therefore,
the earlier you receive the fund or the more members give 100 tokens to your fund, the more payoff you canobtain. Meanwhile, "+ 100" in the second term of the right hand side means that you can automatically save
100 tokens which are given to you at the beginning of the period in which you receive the fund.

After all members finish making decisions in each period, two tables are displayed on your screen.

Example: Result and Payoff Tables after the second period.

Round
1 out of 10

Result in each period

Payoff in each period

A1

B1
(you)

C1

D1

Period 1

-

○

○

○

Period 2

○

-

○

×

Period 3

Period 4

-

A1

B1
(you)

C1

D1

Period 1

759

0

0

0

Period 2

0

438

0

100

Period 3-

Period 4NEXT

23
The table on the left indicates who gave 100 tokens and who did not. The mark “○” means
choosing "GIVE", the mark “x” means choosing " NOT GIVE", and "-" means you did not make any decisionbecause you were the receiver in that period. The table on the right indicates the payoffs of all members ineach period.
This process is repeated four times until every member has a chance to receive the fund. Then, one
round is over.

Example:Taking a specific example, we will show you how the experiment proceeds. Suppose that the orderof receiving the fund is
A1 → B1 (you) → C1 → D1.
The first period:
You have 100 tokens.
Player A1 receives the fund in this period.
You can choose either "GIVE" or "NOT GIVE".
Suppose that you choose "GIVE".
Your payoff in this period is 0.
Also, suppose that C1 and D1 choose "GIVE".
Then the choice and payoff of each member will be displayed on your screen as follows:Round
1 out of 10

Result in each period

Period 1

Period 2

Period 3

Period 4

Payoff in each period

A1

B1
(you)

C1

D1

-

○

○

○

-

Period 1

A1

B1
(you)

C1

D1

759

0

0

0

Period 2-

Period 3-

Period 4NEXT

A1 receives 300 tokens and A1's payoff will be 759 at the end of the fourth period:

24
300 * 1.3(4-1) + 100 ≒ 759.
The second period:
You have 100 tokens again.
In this period, you can receive the fund and you do not need to choose anything.
The payoff is determined by the choices of the other members.
Suppose that A1 and C1 choose "Give", and D1 chooses "Not Give".
Then the current and past choices and payoffs of each member will be displayed on your screen as follows:Round
1 out of 10

Result in each period

Payoff in each period

A1

B1
(you)

C1

D1

Period 1

-

○

○

○

Period 2

○

-

○

×

Period 3

Period 4

-

A1

B1
(you)

C1

D1

Period 1

759

0

0

0

Period 2

0

438

0

100

Period 3-

Period 4

NEXT

You receive 200 tokens and your payoff will be 438 at the end of the fourth period:

200 * 1.3(4-2) + 100 = 438.

25
The third period:
You have 100 tokens again.
C1 receives the fund. You can choose either "GIVE" or "NOT GIVE".
Suppose that you choose "NOT GIVE".
Your payoff in this period is 100.
Suppose that A1 and D1 choose "NOT GIVE".
The current and past choices and payoffs of each member will be displayed on your screen as follows:Round
1 out of 10

Result in each period

Payoff in each period

A1

B1
(you)

C1

D1

Period 1

-

○

○

○

Period 2○-○

Period 3

××-

Period 4

A1

B1
(you)

C1

D1

Period 1

759

0

0

0

×

Period 2

0

438

0

100

×

Period 3

100

100

100

100

-

Period 4NEXT

C1 receives 0 token and his payoff will be 100 at the end of the fourth period:

0 * 1.3(4-3) + 100 = 100.

26
The fourth period:
You have 100 tokens again.
D1 receives the fund. You can choose either "GIVE" or "NOT GIVE".
Suppose that you choose "GIVE".
Your payoff in this period is 0.
Suppose that A1 and C1 decide to choose "GIVE".
The current and past choices and payoffs of each member will be

displayed on your screen as follows:Round
1 out of 10

Result in each period

Payoff in each period

A1

B1
(you)

C1

D1

A1

B1
(you)

C1

D1

Period 1

-

○

○

○

Period 1

759

0

0

0

Period 2

○

-

○

×

Period 2

0

438

0

100

Period 3

×

×

-

×

Period 3

100

100

100

100

Period 4

○

○

○

-

Period 4

0

0

0

400

Your payoff

538
NEXT

D1 receives 300 units and his payoff is 400 at the end of the fourth period:

300 * 1.3(4-4) +100 = 400.

27This is the end of one round. The payoff of each participant in this round is the sum of his/her
payoffs over four periods as the following table illustrates:

A1

B1(You)C1

D1

Period 1

759

0

0

0

Period 2

0

438

0

100

Period 3

100

100

100

100

Period 4

0

0

0

400

Sum

859

538

100

600

Step 4.
Go back to Step 1. In the next round, the 20 subjects are randomly made into five new groups. The sameprocedure will be repeated. As group members are randomly chosen, some members of your group in thesecond round may have belonged to your group in the first round or they may not.
This procedure will be repeated 10 times. The experiment consists of 10 rounds, each of which
consisting of four periods.

After choosing either "GIVE" or "NOT GIVE", please write down the reasons why you make thedecision in your record sheet.

Earnings
We will explain how to calculate your earnings that we will pay.
Your earnings = (the sum of your payoffs over 10 rounds) × 0.75 (JPY).
Any decimal places are rounded up.

This is the end of instruction. Please raise your hand if you have any questions.

Let us start the experiment. You will take 3 minutes to read the instruction to make you understandthe rules of the experiment completely.
Please raise your hand silently if you have any questions. Experimenters will come to you.
However, do not communicate with other subjects. Thank you.

28

Appendix B: Subgame Perfect Equilibrium of the Game with Treatment B
We demonstrate here that the subgame-perfect equilibrium for a four-person four-period
Rosca game is that at each period, every player takes the strategy “ to pay no contribution regardlessof the history before the period.”
Proof. Without loss of generality, assume that player i receives contributions from the other threeplayers in period i. That is,
Player 1 receives money from players 2, 3, and 4 in period 1;
Player 2 receives money from players 1, 3, and 4 in period 2;
Player 3 receives money from players 1, 2, and 4 in period 3; andPlayer 4 receives money from players 1, 2, and 3 in period 4.We solve the subgame-perfectequilibrium for this game by backward induction.
Period 4: Suppose that the players make their decisions in period 4. Period 4 is the final
stage, and so players 1, 2, and 3 have no incentive to pay money because they just lose payoffs ifthey contribute. Hence, player 4 receives nothing.
Period 3: Suppose that the players make their decisions in period 3. Players 1 and 2 haveno incentive to pay money because they lose payoffs by contributing in period 3, and they do notreceive any penalties in period 4 even if they do not contribute in period 3. Player 4 has no incentive
to pay money either because they obtain nothing in this game regardless of their contributions inperiod 3. Hence, player 3 receives nothing.
Period 2: Suppose that the players make their decisions in period 2. Player 1 has no
incentive to pay money because they lose the payoff by contributing in period 2, and they do notreceive any penalties in periods 3 or 4 even if they do not contribute in period 2. Players 3 and 4 haveno incentive to pay either because they obtain nothing in this game regardless of their contributions
in period 2. Hence, player 2 receives nothing.
Period 1: Suppose that the players make their decisions in period 1. Players 2, 3, and 4
have no incentive to pay because they obtain nothing in this game regardless of their contributions inperiod 1. Hence, player 1 receives nothing.
Thus, the subgame-perfect equilibrium is that every player takes the action of paying
nothing in each period when they are to contribute to another player.

Q.E.D.

29

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