Group Composition and Cooperation∗
Alexander Smith†
May 15, 2009
Abstract
This paper presents an experiment designed to measure how heterogeneous
identity affects contributions in a voluntary contribution mechanism (VCM) linear
public good game. Identity was induced using a team-building activity and then
subjects were assigned to groups consisting of a varying number of subjects from
each team. Majority members generally made higher contributions than minority
members. In addition, beliefs about the contributions of group members from
the same team were a stronger determinant of behaviour than beliefs about the
contributions of group members from the other team.
Keywords: Public Good Game; Group Identity; Altruism; Reciprocity
Classification Codes: C9
∗
The author thanks Subhasish Dugar, Robert Oxoby and Jennifer Winter.
PhD Candidate, Department of Economics, University of Calgary, 2500 University Drive NW,
Calgary AB Canada T2N 1N4; smithad@ucalgary.ca; tel. +1 403 220 4602, fax. +1 403 282 5262.
†
1
1
Introduction
From neighbours helping each other with outdoor projects to the nations that are
members of the world’s trade organizations, cooperation has the potential to make
everyone better off. However, cooperation varies across individuals and environments.
For example, evidence suggests that being a member of a minority group or having
low income reduces participation in community activities such as groups and clubs
(Alesina and La Ferrara, 2000). The same study finds that income inequality and ethnic
diversity (at the community level) decrease participation. Related research suggests
that spending on public goods including education, roads, sewers and waste removal
is decreasing in ethnic fragmentation in US metropolitan areas (Alesina et al., 1999).
Unfortunately for policy-makers aiming to correct the inefficiencies, it is not clear how
heterogeneity reduces people’s willingness to cooperate.
To address the issue, this paper studies cooperation using an experiment based on
the public good game of Isaac et al. (1984). Cooperation is measured by the amount
of money subjects contribute to a public account. While contributions to the public
account earn a return and increase the total surplus of the group, they decrease the
payoff of the contributor. The aim is to determine how heterogeneity affects cooperation
and ultimately, the efficiency of public good provision. The results suggest that in
heterogeneous groups, majority members contribute more than minority members, and
beliefs about the contributions of similar group members strongly affect behaviour.
The provision of public goods is an important part of daily life throughout modern
society. People benefit from public goods ranging from environmental quality such as
clean air and water to protection in the form of national defense. In many developed
countries, services including education and health care are non-excludable and thus
exhibit characteristics of public goods as well. The social capital literature suggests
that social cohesion supporting the provision of public goods promotes economic activity
2
and development (Glaeser et al., 2002; Putnam, 2000). For example, Knack and Keefer
(1997) find that increased trust at a national level is associated with higher annual
growth rates. However, Zak and Knack (2001) provide evidence that trust is adversely
affected by population heterogeneity such as income inequality and ethnic diversity.
This paper uses an experiment to determine how heterogeneous identity affects
cooperation. Identity was induced using a team-building activity, as in Eckel and
Grossman (2005) and McLeish and Oxoby (2007), and then subjects were assigned
to groups consisting of a varying number of subjects from each team. Groups of six
consisted of either five subjects from one team and one from the other, four subjects
from one team and two from the other, or three subjects from each team. Subjects
played a repeated voluntary contribution mechanism (VCM) linear public good game
as in Isaac et al. (1984). In addition to making contribution decisions in each round,
subjects were asked how much they believed the other subjects from their team and
from the other team would contribute. Repetition of the public good game with rematching in each round meant that subjects served as majority and minority members,
and allowed for the updating of beliefs.
Aggregate contributions vary as a function of group composition and are highest
when groups consist of four subjects from one team and two from the other. Individual
contributions are increasing in the number of group members sharing the subject’s team
affiliation and beliefs about the contributions of other group members. However, beliefs
about the contributions of group members from the same team have a larger effect on
behaviour than beliefs about the contributions of group members from the other team.
In addition, subjects base their beliefs on the expectation that other subjects make
contributions increasing in the number of group members with whom they share the
same team affiliation and that subjects make contributions similar to the amounts
previously contributed by other subjects of the same type.
3
The findings build on previous research examining how identity affects cooperation
in public good games. Eckel and Grossman (2005), for example, find that promoting a
common identity within a homogeneous group increases contributions. Castro (2006)
studies heterogeneous groups by matching two subjects of one nationality with two
subjects of another and finds a decrease in contributions compared to when groups
are homogeneous. A primary contribution of this paper is to explore the interaction
of majority and minority group members. In this regard, the paper extends the work
of Oxoby and Spraggon (2006), who consider heterogeneity with respect to the source
of endowments and find that aggregate contributions decrease in the presence of a
minority.
The results also provide evidence about the role of altruism and reciprocity in determining cooperation. Some experiments (Andreoni, 1988; 2005) suggest that altruism
is the main determinant of contributions in public good games while others (Croson,
2007; Fischbacher et al., 2001) find that positive contributions are primarily because of
reciprocity. This experiment suggests that altruism and reciprocity are both important.
Altruism has a direct effect on contributions and influences subject’s beliefs about the
contributions of others, which affect cooperation due to reciprocity effects.
The remainder of the paper is organized as follows. Section 2 discusses the literature
on public good experiments, focusing on papers examining the effects of heterogeneity.
Section 3 describes the experiment and develops hypotheses motivated by altruism and
reciprocity. Section 4 presents results and section 5 concludes.
2
Related Literature
Isaac et al. (1984) are among the first to use a public good game to study cooperation.
Subjects are assigned to groups of four or ten members and provided with endowments
4
of tokens in each of ten rounds of play. In each round, subjects decide how many tokens
to keep for themselves and how many to contribute to a community account. The
contributions, which serve as the measure of cooperation, are added up and multiplied
by 0.3 or 0.75 to determine the amount returned to each group member.1 The Nash
equilibrium (under the assumption of individual wealth maximization) is to contribute
nothing, but the total surplus is maximized when everyone contributes their whole
endowment.
Subjects contribute an average of 42%, and while MPCR positively affects contributions, the effect of group size is small. The results of Isaac et al. (1984) are very
robust.2 However, there are multiple explanations for subjects’ willingness to cooperate. Andreoni examines the roles of strategy (1988) and confusion (1995) and concludes
that altruism is an important factor determining contributions. Related research studies altruism in Prisoner’s Dilemma games (Andreoni and Miller, 1993; Cooper et al.,
1996).
Many experiments consider heterogeneity between subjects. Fisher (1995) finds that
in groups consisting of subjects with different MPCRs, subjects make contributions
increasing in their MPCR. Other authors investigate heterogeneity in income (Buckley
and Croson, 2006; Chan et al., 1996), where income is the amount subjects receive
at the start of each round. They find that low income subjects contribute similar
absolute amounts to high income subjects, who contribute relatively smaller shares of
their endowment. Chan et al. (1999) report a positive interaction effect between income
heterogeneity and heterogeneity in preferences for a non-linear public good. Buckley
and Croson (2006) find that subjects are unaffected by wealth, captured by accumulated
earnings.
Cherry et al. (2005) report a decrease in aggregate contributions when endowments
1
2
The multiplier is often referred to as the Marginal Per Capita Return (MPCR).
See Ledyard (1995) for a survey of the literature on public good experiments.
5
are heterogeneous. They show that the finding is robust to the origin of endowments,
which are either randomly assigned or earned by performing well on a quiz. However,
all subjects in each group have the same source of endowments. In contrast, Oxoby
and Spraggon (2006) consider heterogeneity with respect to the origin of endowments
and find that when two of four subjects in a group earn their endowment (as opposed
to having it randomly assigned), contributions are similar to when groups are homogeneous. When one subject has an endowment of a different origin from the other three
subjects, contributions decline.
Other research studies heterogeneity between subjects not affecting the pecuniary
costs and benefits of making contributions to the public account. For example, Anderson et al. (2008) give subjects unequal show-up payments, but provide them with
homogeneous endowments to use in the public good game. Contributions are lower than
when subjects receive the same show-up fee. Ruffle and Sosis (2006) find that members
of the Israeli kibbutz are more cooperative when they are grouped with each other than
with city residents. A related experiment by Castro (2006) finds that contributions
decrease when British and Italian subjects are grouped together.
Ruffle and Sosis (2006) and Castro (2006) address the issue of how heterogeneous
identity affects cooperation. Germane to this topic is the work of Eckel and Grossman
(2005) who find that creating and promoting a common identity among subjects increases cooperation in public good games. Their paper is part of a growing literature
about identity including theoretical and experimental research. Akerlof and Kranton
(2000) propose that identity influences behaviour because utility is a function of the
affiliations people share with those affected by their actions. Chen and Li (forthcoming) test the predictions of Akerlof and Kranton’s (2000) model using a series of simple
two-person sequential games to estimate a model of social preference incorporating
identity. The games measuring reciprocity (Dufwenberg and Kirchsteiger, 2004; Rabin,
6
1993) suggest that subjects are more likely to reward in-group members (as opposed to
out-group members) for positive treatment and less likely to punish them for negative
treatment, leading Chen and Li to conclude that positive reciprocity is stronger among
those sharing the same affiliations.
In the context of a public good game, reciprocity is captured by the relationship
between contributions and beliefs about the contributions of other group members
(Dufwenberg, 2008). A number of experiments suggest that reciprocity is an important
motive for cooperation. Fischbacher et al. (2001) find that while many subjects are
“free-riders,” most are what they term “conditional cooperators.” That is, they are
willing to contribute more when the average contribution of the other group members
is higher. Subsequent experiments suggest that beliefs about the contributions of other
group members positively affect individual contributions (Croson, 2007; Fischbacher
and Gachter, 2006).
3
The Experiment
The experiment used a repeated VCM linear public good game similar to the game
of Isaac et al. (1984). Group composition was manipulated across three treatments.
All treatments began by dividing subjects into two “teams” as they arrived at the
experiment. Each team was placed in a separate room and asked to answer a quiz
consisting of twenty questions. The quiz was casual in nature and involved unscrambling
jumbled letters to make words and determining the next number in a sequence of
numbers. The teams were allowed to submit only one answer sheet per team, so team
members had to interact while answering the quiz. The aim was for each team to
develop a common identity. The process was similar to the identity-building activity
used by McLeish and Oxoby (2007). While identity can be induced in a variety of
7
ways, it is often the case that only “strong” mechanisms such as group tasks influence
subsequent behaviour (Eckel and Grossman, 2005). If a team answered at least twelve
of the twenty questions on the quiz correctly, each member received a payment of $5,
otherwise each member received nothing.3
Following the quiz, subjects played twelve rounds of the public good game using
endowments of $10. In Treatment 1, groups consisted of a single minority subject
from one team and a five subject majority from the other team. At the start of each
round, groups were re-matched to eliminate the incentives for dynamic strategies such
as signaling the intention to make high contributions (Andreoni, 1988) and punishing
low contributions (Fehr and Gachter, 2000). The re-matching occurred in a manner
such that each subject was a minority member twice and a majority member ten times
over the course of the twelve rounds of the experiment. Subjects who were minorities in
a given round are labeled type 1 and subjects who were majority members are labeled
type 5. Subjects were informed of their minority or majority status before making any
decisions.
In each round, subjects decided how much of their endowment to keep and how
much to contribute to the “community account.” In addition, minority members were
asked to guess the average contribution of the majority members. This guess was
their out-group belief. Majority subjects were asked to guess the contribution of the
minority subject (their out-group belief) and the average contribution of their fellow
majority members (their in-group belief). Soliciting beliefs about the contributions of
other subjects has become a common feature of public good experiments aiming to
explain contribution decisions (Croson, 2007; Dufwenberg et al., 2008; Fischbacher and
Gachter, 2006). Once the subjects had made all their choices, the contributions of the
3
All teams were successful on the quiz so all subjects had the same accumulated earnings when
they played the public good game. However, it is not possible to determine how success on the quiz
affects choices in the public good game.
8
six group members were added up and multiplied by two. The total was divided by
six to determine each subject’s share of the community account, which was added to
the amount they kept initially to determine their payoff. The payoff of each subject is
given by:
πir = 10 − Cir + 0.33
6
X
Cjr
(1)
j=1
where Cir is the contribution of subject i in round r and the summation of contributions
is taken over the six group members indexed by j. Following the calculation of the
payoffs, the subjects were informed of their payoff and the average contributions of
their in-group and out-group members. Subjects received $1 for each belief within $1
of the actual amount, making their earnings in each round the sum of their payoff from
the public good game and up to $2 for correct beliefs. At the completion of the twelve
rounds, one round was randomly selected to determine each subject’s final earnings,
which were the sum of a $5 payment for success on the quiz and their earnings in the
randomly selected round. The payment mechanism meant that earnings could not be
accumulated across rounds; subjects played each round using their initial endowment
of $10. This ensured that decisions were not influenced by any possible wealth effects
due to accumulated earnings.4
In Treatment 2, groups consisted of two minority members labeled type 2 and four
majority members labeled type 4. Each subject was a minority member four times and
a majority member eight times during the twelve rounds. Both types of subject were
asked their in-group and out-group beliefs in each round, but in all other respects, the
decision-making proceeded in the same manner as in Treatment 1.
All subjects in Treatment 3 were type 3 subjects and there were no minority or
majority members. However, subjects were once again re-matched in each round and
asked their in-group and out-group beliefs, as in Treatments 1 and 2.
4
Note that Buckley and Croson (2006) find no significant effect of accumulated earnings (wealth).
9
To summarize the definition of type, a subject’s type is given by t {1, 2, 3, 4, 5}
where t refers to the number of subjects in their group with their team affiliation.
Hypotheses
Theories of altruism and reciprocity incorporating identity motivate hypotheses for
the experiment. The experiments of Andreoni (1988, 1995) provide evidence altruism
plays a role in determining public good contributions. In addition, the literature on
identity argues individuals are more altruistic toward those with whom they share
affiliations (Chen and Li, forthcoming; Simpson, 2006). According to this reasoning,
subjects sharing the same team affiliation with a larger number of group members have
a stronger incentive to be altruistic and should make higher contributions. This suggests
the following:
Hypothesis 1: Contributions are increasing in a subject’s type. That is,
∂Cir (t)
∂t
> 0.
In general, majority members are expected to contribute more than minority members. Specifically, Hypothesis 1 predicts that Cir (1) < Cir (2) < Cir (3) < Cir (4) <
Cir (5). However, Hypothesis 1 does not predict the differences in contributions between subject types. As a result, it is not clear which Treatment will have the highest
aggregate contributions (given that Treatment 1 consists of type 1 and 5 subjects,
Treatment 2 of type 2 and 4 subjects and Treatment 3 of only type 3 subjects).
While altruism provides a simple hypothesis regarding individual contributions,
more recent evidence suggests reciprocity as an alternative explanation for public good
game results (Croson, 2007). Experiments show that subjects make contributions conditional on the contributions of others (Fischbacher et al., 2001) and contribute more
when they believe others are contributing high amounts (Croson, 2007; Fischbacher and
Gachter). Also, identity experiments find that reciprocity effects are stronger among
10
in-group members than out-group members (Chen and Li, forthcoming; McLeish and
Oxoby, 2007). This suggests that subjects should contribute more when they believe
their in-group members are contributing high amounts. The same effect may exist for
out-group members, but would be less pronounced. Therefore, we have:
Hypothesis 2: Contributions are increasing in a subject’s in-group belief, and to a
lesser degree, in their out-group belief.
Hypothesis 2 predicts relationships between contributions and in-group and outgroup beliefs. However, it is not clear what determines a subject’s beliefs. A possibility is that subjects initially believe others are altruistic in the manner captured by
Hypothesis 1. This suggests that majority (minority) members will believe in-group
(out-group) members will make high contributions and out-group (in-group) members
will make low contributions. Of course, given the repeated nature of the public good
game, it is expected that as the rounds progress, beliefs will be determined primarily
by experience in previous rounds.
4
Results
The experiment was conducted at our University’s experimental economics laboratory
using subjects recruited from the undergraduate student body. The decision-making
rounds were programmed in z-Tree (Fischbacher, 2007) and occurred over a closedcircuit computer network. Three sessions were conducted using a total of 36 subjects.
Each session lasted about 75 minutes and average earnings were $19.45 with a standard
deviation of $3.56. The minimum earnings were $12.70 and the maximum was $26.70.
The 36 subjects each made twelve contribution decisions generating a total of 432
observations. Average contributions in each round are plotted by subject type in Figures
11
1-3.
Figure 1: Average Contributions in Treatment 1
7
6
Contribution
5
4
Type 5
Type 1
3
2
1
0
1
2
3
4
5
6
7
8
9
10
11
12
Round
Figure 2: Average Contributions in Treatment 2
8
7
Contribution
6
5
4
Type 4
Type 2
3
2
1
0
1
2
3
4
5
6
7
Round
12
8
9
10
11
12
Figure 3: Average Contributions in Treatment 3
4.5
4
3.5
Contribution
3
2.5
2
Type 3
1.5
1
0.5
0
1
2
3
4
5
6
7
8
9
10
11
12
Round
The average contribution of type 5 subjects is decreasing with repetition. The
average contribution of type 1 subjects is more volatile because there are only two
observations from each round. For the most part, the trend for type 5 subjects lies above
the trend for type 1 subjects. Average contributions in Treatment 2 are decreasing, but
not as sharply as for type 5 subjects. Type 2 and type 4 subjects contributed more
than in previous rounds on multiple occasions. The trend for type 4 subjects lies almost
entirely above the trend for type 2 subjects. The trend in Treatment 3 is negative and
fairly smooth.
Average in-group and out-group beliefs in each round are plotted by subject type in
Figures 4-6.
13
Figure 4: Average Beliefs in Treatment 1
9
8
7
Belief
6
5
Type 5 (In-group)
Type 5 (Out-group)
Type 1 (Out-group)
4
3
2
1
0
1
2
3
4
5
6
7
8
9
10
11
12
Round
Figure 5: Average Beliefs in Treatment 2
9
8
7
Belief
6
5
Type 4 (In-group)
Type 4 (Out-group)
Type 2 (In-group)
Type 2 (Out-group)
4
3
2
1
0
1
2
3
4
5
6
7
8
Round
14
9
10
11
12
Figure 6: Average Beliefs in Treatment 3
4.5
4
3.5
Belief
3
2.5
2
Type 3 (In-group)
Type 3 (Out-group)
1.5
1
0.5
0
1
2
3
4
5
6
7
8
9
10
11
12
Round
Beliefs are decreasing with repetition in Treatment 1. The average in-group belief
of type 5 subjects is higher than the average out-group belief in every round, indicating that type 5 subjects consistently thought their fellow majority members would
contribute more than the minority member in their group. This suggests that type 5
subjects had beliefs consistent with the prediction of Hypothesis 1, that contributions
are increasing in a subject’s type. The average out-group belief of type 1 subjects is
similar to the average in-group belief of type 5 subjects, suggesting that minority and
majority members had similar expectations regarding the contributions of majority
members.
Beliefs are decreasing less with repetition in Treatment 2 than in Treatment 1. Type
4 subjects had in-group beliefs higher than their out-group beliefs while type 2 subjects
were mostly the opposite, often thinking that in-group members would contribute less
than out-group members. These observations provide evidence that type 2 and 4 subjects also had beliefs consistent with Hypothesis 1. The average in-group and out-group
15
beliefs of type 3 subjects are approximately equal in each round. However, in the first
four rounds, type 3 subjects had a small bias toward thinking that in-group members
would be more altruistic than out-group members.
The amounts contributed are pooled across rounds and summary statistics are given
in Table 1. Average contributions are plotted by subject type in Figure 7.
Table 1: Summary Statistics for the Amounts Contributed
Mean Median Mode Std. Dev.
Treatment 1
2.80
2
0
2.63
type 1
2.04
1
0
2.26
type 5
2.95
2
0
2.68
Treatment 2
5.03
5
0
3.87
type 2
3.42
3.5
0
3.41
type 4
5.84
6
10
3.85
Treatment 3 (type 3)
2.10
2
0
2.30
Aggregate
3.31
2
0
3.26
N
144
24
120
144
48
96
144
432
Figure 7: Average Contributions by Type
7
6
Contribution
5
4
3
2
1
0
1
2
3
4
5
Type
The mean contribution in Treatment 1 is 2.80 and the median is 2. Type 1 subjects
contributed an average of 2.04 compared to 2.95 for type 5 subjects. A Wilcoxon
16
ranksum test is suggestive that type 1 subjects contributed less than type 5 subjects
(p = 0.12, see Table 3). This finding is consistent with Hypothesis 1, that contributions
are increasing in a subject’s type.
The mean and median in Treatment 2 (5.03 and 5) are considerably higher than in
Treatment 1. A Wilcoxon test provides strong evidence of a difference in contributions
between the two treatments (p < 0.01, see Table 2). An explanation is that since
there were two minority members in each group in Treatment 2, there was a potential
for in-group reciprocity between minority members that did not exist in Treatment 1,
where there was only one minority member in each group. Higher contributions by the
minority group members may have positively affected the contributions of the majority
group members. Type 2 subjects contributed an average of 3.42 compared to 5.84 for
type 4 subjects. The contributions of type 2 subjects are not statistically different from
those of type 1 (p = 0.16) or type 5 subjects (p = 0.74). In contrast, type 4 subjects
contributed more than all other subject types (p < 0.01 for all pair-wise comparisons).
The difference between type 2 and type 4 subjects is consistent with Hypothesis 1.
Pair-wise comparisons between the contributions in Treatment 3 (mean = 2.10 and
median = 2) and the contributions in Treatments 1 (p = 0.02) and 2 (p < 0.01)
provide strong evidence that the contributions in Treatment 3 are the lowest of the
three treatments. The type 3 subjects made contributions comparable to those of type
1 subjects (p = 0.83) and lower than those of type 2 (p = 0.05), type 4 (p < 0.01)
and type 5 (p = 0.01) subjects. While the low contributions of type 3 subjects are
unexpected given the potential for in-group reciprocity in Treatment 3, the lack of
majority members may have caused a coordination failure where all subjects hoped the
subjects from the other team would make high contributions.
17
Table 2: Pair-wise Comparisons of Contributions by Treatment
Treatment
Treatment
1
2
3
1
0.00
0.02
2
0.00
Cells report the p-value of a Wilcoxon ranksum test.
Table 3: Pair-wise Comparisons of Contributions by Type
Type
3
Type
1
2
4
5
1
0.16
0.83
0.00
0.12
2
0.05
0.00
0.74
3
0.00
0.01
4
0.00
Cells report the p-value of a Wilcoxon ranksum test.
Only one session of each treatment was conducted. As a result, comparisons between
treatments and types may be confounded by session effects. In an effort to control for
this, the average contribution of each subject type is divided by the average contribution
in their session. The normalized average contributions are plotted in Figure 8.
Figure 8: Normalized Average Contributions by Type
1.4
Normalized Contribution
1.2
1
0.8
0.6
0.4
0.2
0
1
2
3
Type
18
4
5
Minority members (type 1 and 2 subjects) contributed less than the average in their
sessions and majority members (type 4 and 5 subjects) contributed more, consistent
with the prediction of Hypothesis 1.
Regressions determine how contributions are affected by subject type, repetition
and beliefs. A random effects Tobit model preserves degrees of freedom and corrects
for censoring. Contributions are regressed on the subject’s type, the round number and
beliefs about the contributions of in-group and out-group members as follows:
contributionir = βo + βt type + βr round + βin beliefin + βout beliefout + εir
(2)
where contributionir is the contribution of subject i in round r, type is their type, round
is the round number, beliefin is the subject’s belief about the average contribution
of their in-group members in that round, beliefout is their belief about the average
contribution of their out-group members and εir is the error term. The 24 observations
from type 1 subjects are omitted because type 1 subjects had no in-group beliefs. The
regression results are reported in Table 4.
19
Table 4: Regressions of Contributions
Coefficients
Variables
(1)
(2)
type
0.98***
(0.18)
type3
0.85
(0.59)
type4
2.26***
(0.62)
type5
2.71***
(0.67)
round
-0.08*
-0.09*
(0.05)
(0.05)
beliefin
0.99***
0.95***
(0.07)
(0.10)
beliefout
0.26***
0.30***
(0.10)
(0.11)
constant
-6.45***
-4.19***
(0.98)
(0.98)
N
408
408
***: Significant at 1%
**: Significant at 5%
*: Significant at 10%
Specification (1) uses the variable type to capture the subject’s type. Specification
(2) replaces the variable type with a set of dummy variables (type3, type4 and type5)
and uses type 2 subjects as the reference group. The coefficient for the variable type
(0.98) in specification (1) is highly significant and suggests that each unit increase
in type is associated with an increase in contributions of 0.98. This finding strongly
supports Hypothesis 1. In specification (2), the coefficient for the variable type3 (0.85)
indicates that type 3 subjects contributed 0.85 more than type 2 subjects. However, this
finding is not statistically significant. In contrast, the coefficients for the variables type4
(2.26) and type5 (2.71) are highly significant and suggest that type 4 and 5 subjects
contributed 2.26 and 2.71 more than type 2 subjects. The coefficients for the dummy
variables are all consistent with Hypothesis 1.
20
The coefficients for the variable round (-0.08 and -0.09) are significant at 10% and
suggest that contributions decrease by almost 0.10 in each round. Decreasing contributions are consistent with previous results in the literature.5 The coefficients for the
variable beliefin (0.99 and 0.95) are significant at 1% and reflect an approximately oneto-one relationship between contributions and beliefs about the average contributions
of in-group members. The coefficients for the variable beliefout (0.26 and 0.30) are also
significant at 1%, but are smaller in magnitude than the coefficients for the variable
beliefin (p < 0.01 in both specifications). The belief coefficients support Hypothesis 2,
that contributions are increasing in a subject’s in-group belief, and to a lesser degree,
in their out-group belief. The negative regression constants (-6.45 and -4.19) indicate
that there may be non-linear relationships between the variables of interest that are
not captured by the linear specifications.
Separate regressions for each subject type examine whether the effects of repetition
and beliefs differ across subject types. The results are reported in Table 5.
Table 5: Regressions of Contributions by Type
Coefficients
Variables
(1)
(2)
(3)
(4)
round
-0.51*
0.27**
-0.18*
-0.20*
(0.30)
(0.11)
(0.09)
(0.10)
beliefin
1.06***
0.52***
1.26***
(0.17)
(0.18)
(0.15)
beliefout
-0.37
1.31***
0.34
0.29
(0.66)
(0.21)
(0.22)
(0.21)
constant
5.56
-10.01***
0.88
-3.07*
(4.08)
(2.07)
(1.33)
(1.59)
N
24
48
144
96
(5)
-0.04
(0.08)
1.06***
(0.16)
0.13
(0.14)
-1.45
(1.12)
120
***: Significant at 1%
**: Significant at 5%
*: Significant at 10%
Regression (1) uses the observations from type 1 subjects. The coefficient for the
5
See Ledyard (1995) for a survey.
21
variable round (-0.51) is significant at 10% and suggests that contributions decrease
by 0.51 in each round. Type 1 subjects had no in-group members in their group and
therefore had no beliefs about the contributions of such subjects. The coefficient for
the variable beliefout (-0.37) suggests that contributions decrease by 0.37 for every unit
increase in the belief about the average contribution of out-group members. However,
the effect is not statistically significant.
Regression (2) indicates that type 2 subjects behaved differently from type 1 subjects. The coefficient for the variable round (0.27) is significant at 5% and suggests that
contributions increase by 0.27 in each round. The coefficients for the variables beliefin
(1.06) and beliefout (1.31) are highly significant and suggest approximately one-to-one
relationships between contributions and beliefs about the average contributions of ingroup and out-group members. The finding that in-group beliefs have a smaller effect
on contributions than out-group beliefs is unexpected, but is unique to type 2 subjects.
The negative constant (-10.01) is indicative of non-linearities.
Regression (3) finds a small, negative effect of repetition for type 3 subjects, suggesting that contributions decrease with repetition. The coefficient for the variable beliefin
(0.52) is positive and highly significant while the coefficient for the variable beliefout
(0.34) is positive, but not statistically significant. Like regression (3), regressions (4)
and (5) find small, negative repetition effects, positive and highly significant effects of
in-group beliefs and insignificant effects of out-group beliefs. The results regarding the
effects of beliefs are generally consistent with Hypothesis 2.
We now consider the determination of beliefs. Beliefs about the average contribution
of in-group members are regressed on the subject’s type, the round and lagged variables
in a random effects Tobit model as follows:
22
beliefin = βo + βt type + βr round + βact act−1 + βacot acot−1
+βc contribution−1 + βp payof f−1 + εir
(3)
where act−1 is the average amount contributed by group members of the subject’s current type in the previous round, acot−1 is the average amount contributed by group
members of the type other than the subject’s current type in the previous round,
contribution−1 is the subject’s contribution in the previous round and payof f−1 was
their payoff.6 The results are given in Table 6.
Table 6: Regression of In-group Beliefs
Variable
Coefficient
type
1.02***
(0.13)
round
-0.22***
(0.03)
act−1
0.35***
(0.09)
acot−1
0.08
(0.05)
contribution−1
-0.03
(0.06)
payof f−1
-0.07
(0.08)
constant
1.16
(1.11)
N
374
***: Significant at 1%
**: Significant at 5%
*: Significant at 10%
The coefficient for the variable type (1.02) is highly significant and suggests that
each unit increase in type is associated with an increase in beliefin of 1.02. This result
6
Recall that subjects knew act−1 and acot−1 because they were informed of the average contributions of their in-group and out-group members at the end of each round.
23
indicates that subjects had in-group beliefs consistent with Hypothesis 1. The coefficient
for the variable round (-0.22) is significant at 1% and suggests that in-group beliefs
decrease by 0.22 in each round. The coefficients for the variables act−1 (0.35) and acot−1
(0.08) indicate that in-group beliefs are positively affected by the average contribution
of group members of the subject’s current type in the previous round, but not by the
average contribution of group members of the type other than the subject’s current
type. This finding suggests that subjects believed in-group members would conform to
social norms and contribute amounts similar to the amounts previously contributed by
other subjects of the same type. The variables contribution−1 and payof f−1 do not
have significant effects.
Beliefs about the average contributions of out-group members are regressed on the
same explanatory variables as the beliefs about the average contributions of in-group
members and the estimates are presented in Table 7.
Table 7: Regression of Out-group Beliefs
Variable
Coefficient
type
-0.50***
(0.07)
round
-0.14***
(0.03)
act−1
0.02
(0.08)
acot−1
0.17***
(0.05)
contribution−1
0.10*
(0.06)
payof f−1
0.03
(0.07)
constant
4.54***
(0.99)
N
396
***: Significant at 1%
**: Significant at 5%
*: Significant at 10%
24
The coefficient for the variable type (-0.50) is highly significant and suggests that
a one unit increase in type (and a one unit decrease in the type of the subject’s outgroup members) is associated with a decrease in beliefout of 0.50. This indicates that
subjects had out-group beliefs consistent with Hypothesis 1. The coefficient for the
variable round (-0.14) is significant at 1% and suggests that out-group beliefs decrease
by 0.14 in each round. The coefficient for the variable act−1 (0.02) is not significant, but
the coefficient for the variable acot−1 (0.17) suggests that subjects believed out-group
members would make contributions increasing in the amounts previously contributed
by other subjects of the same type.
5
Conclusions
In this paper, we examined how group composition affects cooperation in a repeated
VCM linear public good game. Identity was induced using a team-building activity
and subjects were assigned to groups consisting of a varying number of subjects from
each team. In addition to making contribution decisions, subjects revealed their beliefs
about the contributions of the other subjects in their group from their team and from
the other team.
A primary finding was that minority members contributed less than majority members. Even when controlling for beliefs, subjects made contributions increasing in the
number of subjects in their group from their team. This result supports the hypothesis
that altruistic preferences are a function of identity.
A second key finding was that contributions were increasing in beliefs about the
contributions of other group members. However, beliefs about the contributions of
group members from the same team had a larger effect on contributions than beliefs
about the contributions of group members from the other team. This suggests that
25
while both types of reciprocity have important effects, in-group reciprocity is a stronger
determinant of behaviour than out-group reciprocity, consistent with the hypothesis
motivated by identity and reciprocity.
A final issue is the formation of beliefs. The analysis of beliefs indicates that subjects
expected others to make contributions consistent with the hypothesis of identity-based
altruism. In addition, they also expected subjects to make contributions similar to the
amounts previously contributed by subjects of the same type. One interpretation is
that subjects thought others would conform to social norms and contribute the amount
typical for their type.
The results have important implications for social policy. To begin, for people to
cooperate in their community they must feel as though they are part of the “in-group.”
Disenfranchised individuals do not have the same incentives for cooperation and this
will reduce their participation in the provision of public goods. Also, insofar as beliefs
about the actions of others determine behaviour, it is the choices of similar individuals
influencing the decisions people make. Campaigns aimed at increasing community
involvement should promote the actions of citizens with whom most people identify.
For example, it is unsatisfactory to use advertising depicting white families to attempt
to reduce gang violence in predominantly black neighbourhoods.
Possibilities for future research include the use of larger groups allowing for more
variation in group composition. It seems this might produce additional interesting
results. For example, a group of ten subjects consisting of a nine member majority
might maintain high cooperation because they are undeterred by the free-riding of
the lone minority member. This would be different from the analogous treatment
in this experiment, where the five member majorities appeared dissuaded by the low
contributions of single member minorities.
26
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