Living in two neighborhoods--social interaction effects in the laboratory.

Falk, Armin ; Fischbacher, Urs ; Gachter, Simon 等

I. INTRODUCTION

It is a long-standing and fundamental problem of the social sciences to understand whether and in what way humans are influenced by the behavior exhibited by the members of the social group to which they belong. We speak of a "social interaction effect" if an individual changes his or her behavior as a function of his or her respective group members' behavior. Social interaction effects are economically important because they may be present in many decision domains. (1)

From a theoretical viewpoint there are at least two potentially important sources for social interaction effects even in otherwise identical environments; both are studied in this paper. A social interaction effect can occur if the game that people play in their group has multiple equilibria which are because of the material payoff structure of the game. Behavior across groups can be different simply because different groups coordinate on different equilibria of the same game. A second and less straightforward source of social interaction effects concerns those interactions that operate via non-material psychological payoffs, such as conformism, social approval, fairness, reciprocity, or guilt aversion. These motives can induce players to adapt their behavior to that of others, even if the material payoff structure does not provide any incentive to do so.

The identification of social interaction effects requires several problems to be overcome (Akerlof 1997; Manski 1993, 2000): (1) identifying the reference group for which social interaction effects are sought to be established, (2) circumventing the problem of self-selection of group members by investigating randomly composed groups, (3) controlling correlated effects that affect all group members in a similar way, and (4)controlling contextual effects such as exogenous social background characteristics of group members. In this paper we present the design of an experiment that circumvents these problems and therefore allows us to study the behavioral logic of social interactions.

We argue that the experimental laboratory provides the researcher with a valuable tool to study social interactions because it guarantees more control than any other available data source (Falk and Heckman 2009). The ideal data set would observe the same individual at the same time in different groups or neighborhoods, which are identical--apart from different neighbors. Obviously, this is impossible in the field. In contrast, it is possible to come very close to this "counterfactual state" in the laboratory. In our experiment, we are able to observe decisions of the same subject at the same time in two economically identical environments. The only reason to behave differently in these two environments is the presence of social interactions, that is, the fact that a person is systematically and differentially affected by the behavior of his neighbors in the two environments. Our within-subjects two-group design circumvents the above-mentioned identification problems. Using the terminology of Manski (2000), in our study reference groups are well-defined; the setup avoids self-selection; subjects make simultaneous decisions in two economically identical environments, which controls for correlated effects, including experience; the decision problem is abstractly framed and decisions are taken anonymously, which avoids contextual effects. Moreover, our laboratory approach has the added advantage of eliminating measurement errors.

We investigate social interaction effects in two experimental games, which represent the two broad classes of strategic situations mentioned above--a coordination game that possesses multiple equilibria in material payoffs and a cooperation game which has only one equilibrium in material payoffs. The coordination game we study is a version of the "minimum-effort game" (Van Huyck, Battalio, and Beil 1990; see Camerer 2003, chapter 7; Devetag and Ortmann 2007 for overviews). In this game the lowest effort of a group member determines the payoff everyone will achieve. The incentives are such that all effort constellations where every player chooses the same effort are strict Nash equilibria and the Nash equilibria are Pareto ranked. Thus, because there are many Nash equilibria, different groups may play different equilibria or, in the case of mis-coordination, may exhibit different out-of-equilibrium behaviors. Evidence for a social interaction effect in this setup occurs if the same individual adapts his or her behavior to that of his or her respective group members. This may entail the same individual coordinating on different equilibria across his or her two groups.

Our choice of a cooperation game is a linear public goods game with full free riding as the unique equilibrium in material payoffs. If none of the mentioned psychological payoffs plays a role, there cannot be a social interaction effect because this game has only one equilibrium in material payoffs. If some people care about psychological payoffs, however, social interaction effects might occur because these people want to reciprocate others' contributions, or avoid letting others down, or simply conform to what others do. If the game is repeated, the presence of these motives might even induce the cooperation of individuals who are only interested in maximizing their material payoffs. Thus, to the extent that groups differ in their composition with respect to how important material and psychological payoffs are to its members, social interaction effects can be observed if individuals differentiate their contributions depending on their neighbors' contributions in their respective groups.

Our data lend strong support for the importance of social interactions. In both the coordination game and the public goods game, the same individual adapts his or her behavior to that of his or her respective group members. In many cases this entails coordinating on different equilibria across the two groups in the coordination game or displaying different cooperation levels across the two groups playing a cooperation game. The behavioral patterns of social interaction are surprisingly similar in the coordination and the cooperation games.

Our dual-membership design relates our paper to a recent literature on the behavioral effects of playing multiple (cooperation) games with different players at the same time (Bednar et al. 2009; Cason, Savikhin, and Sheremeta 2009). We will discuss these papers and their relation to our research in more detail in Section III(B).

II. DESIGN, PROCEDURES, AND HYPOTHESES

A. Design

The philosophy and novel feature of our experimental design is to put the same person at the same time into two different, yet economically identical environments. Thus, it is only the behavior of other neighbors in these environments that can explain possible behavioral differences in the two environments. Finding such a different behavior is therefore evidence for social interaction effects. We will apply this idea in two different games, a coordination game and a public goods game. Moreover, to test whether being a member of two different groups simultaneously leads to different behavior than being a member of only one group, we complement our two-group design by a one-group design, conducted in a public goods environment.

The implementation of the "two neighborhood" design in the coordination game and the public goods game was straightforward (Figure 1): nine participants formed a so-called matching group. Within such a matching group, all participants were simultaneously members of two neighborhoods called "groups." Participants were told that they were members of a "group 1" and a "group 2" (see the instructions in Appendix S l, supporting information). The two groups were formed such that each subject had two different neighbors in each group. For example, subject 4 formed a group with subjects 1 and 7, and another group with subjects 5 and 6. (2) Likewise, subject 9 formed a group with subjects 3 and 6 and another group with subjects 7 and 8. Let [G.sup.1.sub.i] be the set of the members of player i's group 1 and let [G.sup.2.sub.i] be the set of the members of player i's group 2. For example, individual 4 from Figure 1 belongs to the two groups [G.sup.1.sub.4] = {1,4,7} and [G.sup.2.sub.4] = {4, 5, 6}.

The matching structure shown in Figure 1 was used to study behavior in two different economic environments, a coordination game and a voluntary contribution game.

[FIGURE 1 OMITTED]

Coordination Game. As a workhorse for studying coordination and social interaction in our two-group design, we developed a variant of the so-called minimum-effort coordination game (Van Huyck, Battalio, and Beil 1990; see also Cason, Savikhin, and Sheremeta 2009) for a design with multiple memberships). In our version of the minimum-effort coordination game, each player can choose an integer number c between 20 and 100. All group members receive the minimum of the three chosen numbers (min) as payoffs. Those group members whose numbers exceed the minimum receive the minimum minus the difference between their chosen number and the minimum. Thus, for each subject i the payoff function was as follows:

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where the upper indices 1 and 2 denote group 1 and group 2, respectively. The coordination games of the two groups were technologically completely independent of each other. Subjects took two decisions, between 20 and 100, one for each group.

Cooperation Game. In the cooperation game, subjects made a contribution to a standard linear public good, one for each group. The public goods of the two groups were technologically independent of each other. Each subject was endowed with 20 tokens in each group and could invest up to 20 tokens into the public good of the respective group. Let [G.sup.1.sub.i] be the set of the members of player i's group 1 and let G2 be the set of the members of player i's group 2. Let [c.sup.1.sub.i] ([c.sup.2.sub.i]) denote i's voluntary contribution to group 1 (group 2). For both groups, the following budget constraints had to hold: 0 [less than or equal to] [c.sup.1.sub.i] [less than or equal to] 20 and 0 [less than or equal to] [c.sup.2.sub.i] [less than or equal to] 20. If a subject decided, for example, to invest 10 tokens in group 1, she could nevertheless only invest at most 20 tokens in group 2. Any token not invested in the public good of the respective group was automatically invested into a private good. Thus, for each subject i the payoff function was as follows:

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where j and k are indices for neighbors of group 1 and group 2, respectively. In our experiment, [alpha], the marginal per capita return of the public good, was set equal to 0.6; the social marginal return was therefore 1.8. Thus, because [alpha] < 1 < 3[alpha], a selfish individual has a dominant strategy to free ride completely, while total payoffs are maximized if everybody fully invests into the group account.

In both treatments, the minimum game and the public goods game, it was commonly known that subjects were randomly allocated to the groups and remained paired for 20 periods. The experiment was computerized using the experimental software z-Tree (Fischbacher 2007). At the beginning of each period, subjects had to make their choices for both groups on the same screen. The decision screen was separated into two vertical parts (called "group 1" and "group 2") and contained an input box for each group. On the same screen where subjects had to simultaneously make their decisions, subjects were also informed for both group 1 and group 2 about the average outcome of all respective group members and their respective incomes in the previous period. Full anonymity between subjects was maintained throughout the whole experiment.

B. Discussion of the Two-Group Design

The purpose of our study is to identify social interaction effects, which require extensive control. First, we control for any self-selection effect. This is achieved by the fact that subjects were randomly allocated to their groups and that we observe the same subject's behavior in two different groups. (3) Even without random allocation, this latter feature alone circumvents self-selection problems. Second, we control for correlated effects, that is, for the possibility that neighborhood characteristics influence behavior (Manski 1993). In our experiment, the two environments in which subjects make their decisions are economically exactly identical. In each group all subjects have the same action space, the same endowment and budget constraint, the same information conditions, and the same material incentives. Both groups are completely independent of each other--a decision in group 1 does not change the endowment, the action space, or the incentives in group 2. Moreover, groups are equal in size and each neighbor faces the same economic incentives. The two-group design also controls for correlated effects that might be caused by the fact that different sessions are conducted at different dates and times. Even more importantly, it controls for experience and learning. When a subject makes a decision in both groups she has exactly the same experience for both decisions. This cannot be achieved in a one-group design.

Third, we control for contextual effects, that is, for the fact that a person may show a different behavior in the two groups because of the socioeconomic composition of the two groups (Manski 1993). Control in this respect is ensured by the fact that experimental subjects were very homogeneous with respect to their socioeconomic background and, more importantly, interaction was anonymous. Fourth, while in the field one can only hypothesize about the relevant comparison group and try to find some good proxy (language group, neighbors of the same block, zip code, etc.), the laboratory environment controls the available information. Subjects receive information only about the behavior of those groups to which they actually belong. This implies, for instance, that subjects cannot compare to any other group. (4) Fifth, our computerized laboratory environment excludes measurement errors.

C. Procedures

In total, 198 people participated in our experiments. All experiments comprised 20 periods with the same group memberships in all periods. In the two-group coordination game, 72 subjects participated in eight independent matching groups of 9 members each (Figure 1). They took 2,880 decisions in total. In the two-group public goods game, 126 subjects made a total of 5,040 contribution decisions. They formed 14 independent matching groups of nine members each. No subject participated in more than one treatment. We conducted the experiments in the computer laboratories at the Universities of St. Gallen and Zurich. All participants were students from various fields. After reading the instructions, subjects had to solve a set of computerized control questions that tested their understanding of payoff calculations. The experiment started only after all participants had answered all questions correctly.

During the experiments income was counted in "Guilders," which were translated to Swiss Francs at the end of the experiment (at an exchange rate of 100 Guilder = 0.70 Swiss Francs in the minimum game and 1 Guilder = 0.03 Swiss Francs in the public goods games). On average, subjects earned 29.90 Swiss Francs in the minimum games and 33 Swiss Francs in the public goods games (1 Swiss Franc US$ 1.21-1.70 [approximately equal to] 1.50 [euro] at the time of the experiments). The experiments lasted between 60 and 80 min.

D. Hypotheses

In the minimum-effort coordination game there are multiple equilibria, which are characterized by all players choosing the same number. Deviating in any direction lowers a player's payoff. In contrast, the material game structure of the public goods games is such that there is a unique equilibrium: under the assumption of common knowledge of rationality and selfishness, players are predicted to contribute zero to both public goods, that is, we should see full free riding. In the stage games this is obvious because it is a dominant strategy to contribute nothing. In our finitely repeated games it holds with backward induction. In contrast to this prediction it is known from many public goods experiments that some people cooperate, at least in the early periods of an experiment. An important motive that explains cooperation is reciprocity in the form of conditional cooperation as discussed, for example, in Sugden (1984), Guttman (1986), Andreoni (1995), Keser and van Winden (2000), and Fischbacher, Gachter, and Fehr (2001). (5) Guilt aversion (Dufwenberg, Gachter, and Hennig-Schmidt 2006) and conformism (Alpizar, Carlsson, and Johansson-Stenman 2008; Bardsley and Sausgruber 2005; Carpenter 2004) are further motivations leading to conditional cooperation. In the presence of conditional cooperation, the prediction of a unique equilibrium with complete free riding no longer holds. Instead, some players now prefer cooperating over defecting as long as others also contribute. In other words, there are multiple equilibria in the public goods game as long as there are a sufficient number of reciprocally motivated players.

In both the minimum-effort game and the public goods game, social interaction implies that subjects' choices of numbers or contributions, respectively, are affected by the choices of their neighbors. Let us state this hypothesis more formally for the minimum-effort game. Let [c.sup.1.sub.i] denote subject i's chosen number in period t to group 1 and let [g.sup.1.sub.i] denote the minimum in group 1 in period t - 1. Analogously, [c.sup.2.sub.i] denotes subject i's number in period t to group 2 and [g.sup.2.sub.i] denotes the minimum in group 2 in period t - 1. Social interactions require that corr[([c.sup.1.sub.i] - [c.sup.2.sub.i]), ([g.sup.1.sub.i] - [g.sup.2.sub.i])] > 0, that is, the larger the difference of the minima in both groups in the previous period, the larger is the difference in current chosen numbers of a group member to the two groups. In contrast, if there are no social interactions, we should see no such correlation. In the public goods game, social interactions can be defined analogously, where [c.sup.1.sub.i] then denotes subject i's contribution in period t to group 1 and [g.sup.1.sub.i] denotes the average contribution of i's neighbors in group 1 in period t - 1. Moreover, [c.sup.2.sub.i] denotes subject i's contribution in period t to group 2 and [g.sup.2.sub.i] denotes the average contribution of i's neighbors in group 2 in period t - 1.

III. RESULTS

In our discussion of the results, we first look at the aggregate-level findings from the coordination game (Section III(A)) and the public goods game (Section III(B)). In Section III(C) we investigate individual heterogeneity in both games.

A. Coordination Game

In our version of the coordination game the average minimum number in the first five periods was 60.9, rising to 79.7 in the last five periods. The coordination rate (i.e., the fraction of cases where group members in a group of three coordinated on the same number) rose steadily from 27.1% in the first five periods to 68.8% in the last five periods.

Our main result in the minimum game concerns the presence of social interaction effects, however. We find strong and systematic social interaction effects: on average, subjects systematically chose a higher number in the group that had the higher minimum in the previous period. Support for this result comes from Figures 2-4 and Table 1. Figure 2 plots the average difference in current numbers ([c.sup.1.sub.i] - [c.sup.2.sub.i]) as a function of the difference of the neighbors' minima in the respective groups in the previous period ([g.sup.1.sub.i] - [g.sup.2.sub.i]). In the absence of social interaction this graph should fluctuate around 0; instead we observe a very strong positive relationship between ([c.sup.1.sub.i] - [c.sup.2.sub.i]) and ([g.sup.1.sub.i] - [g.sup.2.sub.i]) with observations lying almost exactly on the 45[degrees] line.

Figure 3 looks at social interaction from a different angle. As a function of ([g.sup.1.sub.i] - [g.sup.2.sub.i]) it shows three graphs, indicating the probability of choosing a higher or lower number in group 1 than in group 2, or the same in both groups, respectively. Figure 3 is based on all data from all matching groups and uses intervals for ([g.sup.1.sub.i] - [g.sup.2.sub.i]). The intervals were determined such that each interval contains roughly the same number of observations. For each interval the three graphs add up to a probability of 1.

Figure 3 conveys several observations. First, the probability of contributing more to group 1 than to group 2 is very low if [g.sup.1.sub.i] < [g.sup.2.sub.i] and is slightly increasing in ([g.sup.1.sub.i] - [g.sup.2.sub.i]). For [g.sup.1.sub.i] - [g.sup.2.sub.i] = 0, the probability is well below 10%. For ([g.sup.1.sub.i] - [g.sup.2.sub.i])> 0 the probability is strongly and monotonously increasing in ([g.sup.1.sub.i] - [g.sup.2.sub.i]), reaching 100% for high values of ([g.sup.1.sub.i] - [g.sup.2.sub.i])). Second, the probability of choosing higher numbers in group 2 than in group 1 as a function of ([g.sup.1.sub.i] - [g.sup.2.sub.i])) is almost exactly the mirror image of the probability to invest more in group 1. Third, the probability of contributing the same amount in both groups is higher the smaller the absolute value of ([g.sup.1.sub.i] - [g.sup.2.sub.i])). It reaches its maximum of almost 95% for [g.sup.1.sub.i] - [g.sup.2.sub.i]) = 0. Note that even for very small deviations from [g.sup.1.sub.i] - [g.sup.2.sub.i]) = 0, the probability drops sharply. Taken together, Figure 3 strongly supports the existence of social interaction effects.

[FIGURE 2 OMITTED]

Remember that our design involves matching groups of nine subjects each. These matching groups form the strictly independent observations of our data set. Figure 4 investigates social interactions at the level of matching groups by providing scatter plots of ([c.sup.1.sub.i] - [c.sup.2.sub.i]) as a function of ([g.sup.1.sub.i] - [g.sup.2.sub.i])) for each of our eight matching groups.

The first observation from Figure 4 is that the relationship we find at the aggregate-level holds for all eight matching groups. In all our matching groups the bulk of observations lies on the 45[degrees] line. Thus, the observation in Figure 2 is not an artifact of aggregation. Further analysis also reveals that social interaction effects are stable over time. In all periods, the difference in numbers in period t is positively correlated with the difference of minimum numbers in period t - 1. (6)

[FIGURE 3 OMITTED]

In the following, we test the statistical significance of social interactions. As a first test, note that we observe a strictly positive correlation between ([c.sup.1.sub.i] - [c.sup.2.sub.i]) and ([g.sup.1.sub.i] - [g.sup.2.sub.i]) in all eight matching groups. The probability of finding a strictly positive correlation in one matching group is (slightly) smaller than one-half in the absence of social interactions. The probability of finding a positive correlation in all eight matching groups without social interaction is therefore smaller than [1/2.sup.8] [approximately equal to] 0.004. As a second test, Table 1 (first column) records the results of ordinary least squares (OLS) regressions. Because within a matching group contributions are not independent, we calculated robust standard errors that allow for correlated errors within matching groups. The dependent variable is ([c.sup.1.sub.i] - [c.sup.2.sub.i]). We regress this variable on ([g.sup.1.sub.i] - [g.sup.2.sub.i]), that is, the difference in neighbors' chosen numbers in the previous period. To study possible time effects, we also include the period index and interact "period" with ([g.sup.1.sub.i] - [g.sup.2.sub.i]). The regression strongly supports our previous arguments. The coefficient on ([g.sup.1.sub.i] - [g.sup.2.sub.i]) is positive and the robust standard errors are extremely low, with a very high t value (t = 11.25). (7)

So far we have shown that subjects differentiated their contributions according to the contributions of their respective neighbors such that corr [[c.sup.1.sub.i] - [c.sup.2.sub.i]), ([g.sup.1.sub.i] - [g.sup.2.sub.i]] > 0 holds. However, we have not yet looked at how this positive correlation comes about. In particular, it is interesting to know whether the behavior of the neighbors in group 2 had an impact on contribution behavior in group 1 and vice versa. For example, it could be that the more the neighbors contributed to group 2 the less a person was inclined to contribute to group 1. To study the impact of the neighbors' contributions in group 1 (group 2) on own contributions in group 2 (group 1) we report two further regressions in Table 1.

[FIGURE 4 OMITTED]

The regression in column 2 shows that while the contribution decision in group 1 ([c.sup.1.sub.i]) is strongly and positively influenced by the behavior of neighbors in group 1 ([g.sup.1.sub.i]), the behavior of neighbors in group 2 ([g.sup.2.sub.i]) has only a slightly positive and insignificant effect. Likewise, the third regression model shows that only [g.sup.2.sub.i] but not [g.sup.1.sub.i] strongly influences [c.sup.2.sub.i]. (8) Even though the coefficient on [g.sup.1.sub.i] is significant, it is more than 20 times smaller than the coefficient on [g.sup.2.sub.i].

When we only consider [g.sup.1.sub.i] and the constant in the second regression, we observe that in the possible range (i.e., between 20 and 100), the model predicts that the number is chosen above the previous minimum (16.112 + 20 x 0.881 > 20 and 16.112 + 100 x 0.881 > 100). Actually, this is also what we observe at the beginning of the experiment. However, because the coefficient on "period" is negative and highly significant, this effect decreases over time, that is, the increase slows down and in the experiment, numbers converge. Taken together, the regressions in columns 2 and 3 reveal that there are hardly any spillover effects from one neighborhood to the other. A subject's decision in group 1 is not strongly influenced by the behavior of group 2 neighbors and vice versa.

B. Public Goods Game

The pattern of contributions over time is in line with previous findings: on average people contributed 11.3 tokens in the first five periods and contributions steadily declined to 7.0 tokens in the last five periods. There was also a strong endgame effect: in the last period contributions dropped to 3.4 tokens on average.

However, our main interest is not in the temporal contribution patterns but in social interaction effects. In our public goods game we find strikingly similar results as in the minimum game. This finding also supports the importance of social interactions for voluntary contribution games with a unique equilibrium. On average, subjects contributed more to the group that had contributed more in the previous period. Support for this result comes from Figures 5-7 and Table 2, which are constructed analogously to Figures 2-4 and Table 1.

Figure 5 plots the average difference in current contributions ([c.sup.1.sub.i] - [c.sup.2.sub.i]) as a function of the difference of the neighbors' contributions in the respective groups in the previous period ([g.sup.1.sub.i] - [g.sup.2.sub.i]. As before, we find a very strong positive relationship between ([c.sup.1.sub.i] - [c.sup.2.sub.i]) and ([g.sup.1.sub.i] - [g.sup.2.sub.i]), that is, people tended to contribute more to group 1 than to group 2 (i.e., [c.sup.1.sub.i] > [c.sup.2.sub.i]) if [g.sup.1.sub.i] > [g..sup.2.sub.i] and vice versa. Note, however, that the correlation is somewhat weaker than in the minimum game. An explanation for this is that material incentives favor social interaction effects in the coordination game but do not in the context of the public goods game.

[FIGURE 5 OMITTED]

Figure 6 shows that the likelihood in the current period to contribute more to group 1 than to group 2 depends positively on ([g.sup.1.sub.i] - [g.sup.2.sub.i]) (and vice versa for group 2). The figure is based on data from all matching groups and uses intervals for ([g.sup.1.sub.i] - [g.sup.2.sub.i]). As in Figure 2, the intervals were determined such that each interval includes roughly the same number of observations. For each interval the three graphs add up to a probability of 1. The figure is remarkably similar to Figure 2: the probability of contributing more to group 1 than to group 2 is very low if [g.sup.1.sub.i] < [g.sup.2.sub.i] and is slightly increasing in ([g.sup.1.sub.i] - [g.sup.2.sub.i]). For [g.sup.1.sub.i] - [g.sup.2.sub.i] = 0, the probability is about 10%. For ([g.sup.1.sub.i] - [g.sup.2.sub.i]) > 0 the probability is strongly and monotonously increasing in ([g.sup.1.sub.i] - [g.sup.2.sub.i]), reaching roughly 85% for high values of ([g.sup.1.sub.i] - [g.sup.2.sub.i]). The probability to invest more in group 2 than in group 1 as a function of ([g.sup.1.sub.i] - [g.sup.2.sub.i]) is the mirror image of the probability to invest more in group 1. Finally, the probability to contribute the same amount in both groups is higher the smaller the absolute value of ([g.sup.1.sub.i] - [g.sup.2.sub.i]), reaching its maximum of roughly 85% for [g.sup.1.sub.i] - [g.sup.2.sub.i] = 0. Note that, as is the case for the coordination game, even for very small deviations from [g.sup.1.sub.i] - [g.sup.2.sub.i] = 0 (intervals [-2,0) and (0,2]), the probability sharply drops from 85 to about 50%.

Similar to Figure 4, Figure 7 reveals the existence of social interactions at the level of matching groups by providing scatter plots of ([c.sup.1.sub.i] [c.sup.2.sub.i]) as a function of ([g.sup.1.sub.i] - [g.sup.2.sub.i]) for each of our 14 matching groups. In all 14 matching groups we observe strong social interactions, indicated by the fact that the bulk of observations is in the upper right and the lower left quadrants (defined by [c.sup.1.sub.i] - [c.sup.2.sub.i] = 0 and [g.sup.1.sub.i] - [g.sup.2.sub.i] = 0). The likelihood of finding a positive correlation in all 14 matching groups without social interaction is extremely small--[1/2.sup.14] [approximately equal to] 6 x [.10.sup.-5]. In all matching groups, however, there are also a certain number of contribution decisions with [c.sup.1.sub.i] - [c.sup.2.sub.i] = 0 for [g.sup.1.sub.i] - [g.sup.2.sub.i] [not equal to] 0. These are contribution decisions that are unaffected by social interactions. We will return to this observation in our analysis of individual behavior.

Further analysis also reveals that social interaction effects are stable over time. In all periods, the difference in contribution in period t is significantly positively correlated with the difference in the contributions of the other players in the period t - 1. (9)

[FIGURE 6 OMITTED]

We study the statistical significance of the observed social interaction effects in the public goods game in Table 2, which is constructed analogously to Table 1. The dependent variable is ([c.sup.1.sub.i] - [c.sup.2.sub.i]), which is regressed on ([g.sup.1.sub.i] - [g.sup.2.sub.i]), that is, the difference in neighbor's contributions in the previous period. We study time effects by including the period index and an interaction term "period x ([g.sup.1.sub.i] - [g.sup.2.sub.i])." It turns out that the coefficient on ([g.sup.1.sub.i] - [g.sup.2.sub.i]) is positive and highly significant (t = 11.25). Moreover, the social interaction effect is not affected by experience, as can be inferred from the insignificant interaction term period x ([g.sup.1.sub.i] - [g.sup.2.sub.i]). (10)

It is interesting to compare coefficients and explanatory power across our coordination and cooperation games. It turns out that social interaction effects are stronger in the coordination game context. Both coefficients as well as the [R.sup.2] are considerably higher in the latter than in the former. A potential explanation could be the fact that material incentives favor social interaction in coordination games with multiple equilibria but favor unconditional behavior in voluntary contribution games.

As in Table 1, we also check whether the behavior of the neighbors in group 2 has an impact on contribution behavior in group 1 and vice versa. The regression in column 2 shows that contribution decisions in group 1 ([c.sup.1.sub.i]) are strongly and positively influenced by the behavior of neighbors in group 1 ([g.sup.1.sub.i]); the behavior of neighbors in group 2 ([g.sup.2.sub.i]) has virtually no effect. A similar picture arises from the third regression model showing that [c.sup.2.sub.i] is strongly influenced by [g.sup.2.sub.i] but not by [g.sup.1.sub.i]. (11)

As in the minimum-effort game, there are little if any spillover effects from one neighborhood to the other. This suggests that when deciding on an action that affects people in a particular group, behavior of this group's members is very important but behavior of people in the other group is largely irrelevant. As long as groups are separated and external effects are confined to a particular group, we expect social interactions to be confined to that very group as well. Put differently, dual memberships should not lead to a different cooperation behavior than a single membership. (12)

In order to investigate whether dual membership matters, we compare the contribution patterns of our two-group design with that of additional experiments run under a standard one-group design. Parameters in the one-group experiments are exactly identical (Section II). The only difference is that while subjects make two decisions in two different groups in the two-group design, they make just a single contribution decision in the one-group design. (13) Forty-eight subjects who formed 16 independent groups participated in the one-group experiments. Figure 8 shows the evolution of average contributions in both treatments by pooling data from all matching groups.

The result is striking: the contribution patterns between the two treatments are almost indistinguishable. In both treatments, average contributions started at about 12 tokens (60% of the endowment), showed a slow downward trend until period 17 and a sharp drop in the final three periods. Final average contribution levels were about three tokens (15%). A Mann-Whitney test on matching groups reveals that contributions in both treatments are not significantly different (p = 1.000). Thus, the fact that subjects interacted in two groups did not lead to behavioral spillovers, that is, a contribution pattern different from that which we usually see in single-group public goods experiments.

This result confirms our hypothesis derived from the findings reported in columns 2 and 3 of Table 2. Methodologically, the absence of behavioral spillovers is good news because it shows that the abstraction to study public goods behavior in games where people are only acting in one group is, ceteris paribus, a good approximation for behavior under multiple group memberships, which often is a realistic feature outside the laboratory.

Our finding is consistent with the results of Cason, Savikhin, and Sheremeta (2009) who, among other treatments, studied coordination behavior in a dual-membership design. They found strong spillovers when treatments were played sequentially. But in the treatment most comparable to ours, subjects simultaneously played a minimum-effort game in one group and a median effort game in the other group and found no difference in the outcome. However, our finding is somewhat in contrast to Bednar et al. (2009) who did find behavioral spillovers between games. Bednar et al. (2009) are interested in how play of a prisoner's dilemma is affected by simultaneously playing with another player a "self-interest game" or games that require alternation to secure maximal payoffs. The authors find substantial behavioral spillovers compared to playing the games in isolation. There might be several reasons for the difference in findings, because the respective designs differ in several dimensions.

C. Individual Heterogeneity

In our aggregate analysis we have provided unambiguous evidence for the importance of social interaction effects both in the minimum and the public goods games. On average, subjects are very strongly influenced by the decisions of their respective neighbors. In this section we study social interactions at the individual level. We investigate to what extent subjects are affected by social interactions. We expect social interaction effects to be more widely present in the coordination game because in this game social interaction effects are predicted for any type of player while in the public goods game, selfish players are not expected to exhibit social interaction effects. Figure 9 documents this individual heterogeneity. It shows the relative frequency of subjects who exhibit a particular intensity level of social interactions in our coordination game (left panel) and the public goods game (right panel). This intensity level is measured with simple OLS regressions for each individual, where [c.sup.1.sub.i] - [c.sup.2.sub.i] is regressed on [g.sup.1.sub.i] - [g.sup.2.sub.i] for periods 2-20, setting the constant to 0.14 Figure 9 shows the distribution of these coefficients, where each individual coefficient is rounded to a multiple of 0.2. A coefficient equal to 1 means that a subject perfectly matches the difference [g.sup.1.sub.i] - [g.sup.2.sub.i], while a coefficient of 0 implies no social interactions.

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

Figure 9 offers several interesting insights. In the coordination game only 1 of 70 subjects had a negative coefficient, 5 had a coefficient of exactly 0 and all other subjects had a positive coefficient. (15) This is not surprising because coordination is in the interest of all players. Interestingly, also in the public goods game, where selfish players are not interested in coordination, 89% of the subjects show a positive coefficient. Thus, in line with our previous arguments, the majority of individuals show social interaction effects. Nevertheless, in particular in the public goods game, there is pronounced individual heterogeneity--subjects are very differently affected by social interactions. There are 14 subjects (11%) with a (rounded) coefficient of 0. Five of these 14 subjects have a coefficient of exactly 0 (see the light gray part of the column at 0). (16) Thus, roughly 11% of subjects show no social interactions at all.

[FIGURE 9 OMITTED]

IV. SUMMARY AND CONCLUDING REMARKS

Identifying social interaction effects is a notoriously difficult task (Manski 1993, 2000). After reviewing the problems, Manski (1993, 541) writes: "The only ways to improve the prospects for identification are to develop tighter theory or to collect richer data. (...) Empirical evidence may also be obtained from controlled experiments (...). Given that identification based on observed behavior alone is so tenuous, experimental and subjective data will have to play an important role in future efforts to learn about social effects."

In recent years, the availability of rich microeconomic field data sets has led to considerable progress. In the typical field research paper, identifying a social interaction effect usually amounts to finding a significant coefficient of the group dummy variables (that capture the social groups one is interested in)--after circumventing self-selection problems and after controlling a multiple regression model for variables that arguably capture the most important correlated and contextual effects. Yet, the approach is only indirect: any variance that cannot be attributed to the correlated and contextual effects is attributed to social interaction effects. The problem of omitted variables can never be completely circumvented.

In our paper, we introduce an experimental design that provides us with direct evidence of social interaction effects in the context of two important types of games, a coordination and a public goods game. Our results are clear and unambiguous. First, subjects' average behavior is systematically influenced by social interactions both in the coordination and the public goods environment. Interestingly, social interaction is more pronounced in our coordination game, reflecting strong material incentives to coordinate, that is, to exhibit social interaction. This is not the case in the public goods game where material incentives suggest zero contributions irrespective of the behavior of other group members. Second, our individual data analysis in the public goods game reveals substantive heterogeneity. Subjects' inclination to display social interaction effects is very different and roughly 10% show no social interactions at all. The finding of two classes of subjects, those whose behavior is influenced by the behavior of their neighbors and those whose behavior is independent of others, is consistent with the assumption put forward by Glaeser, Sacerdote, and Scheinkman (1996). In their model, there is a group of agents whose decision to become criminal is influenced by the behavior of their neighbors while others, the so-called "fixed agents," are not affected by others.

Finally, some recent studies investigate behavioral spillover effects when people play different cooperation and coordination games at the same time with different players (Bednar et al. 2009; Cason, Savikhin, and Sheremeta 2009). We show for the public goods game context that the fact that subjects interact in more than one group does not lead to a contribution pattern that differs from the one exhibited in a single-group environment. The absence of behavioral spillover effects is an interesting finding from a methodological point of view. It suggests that studying contribution behavior in single-group designs is appropriate despite the fact that in reality people typically are members of many groups with some public good feature. It is an interesting question for future research to understand under which conditions behavioral spillovers actually matter.

ABBREVIATION

OLS: Ordinary Least Squares

doi: 10.1111/j.1465-7295.2010.00332.x

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SUPPORTING INFORMATION

Additional Supporting information may be found in the online version of this article:

APPENDIX S1. Experimental Instructions.

(1.) The literature is large and growing. Some examples comprise welfare participation (Bertrand, Luttmer, and Mullainathan 2000), work place behavior (Falk and Ichino 2006; Ichino and Maggi 2000) and unemployment (Topa 2001), the dynamics of urban poverty and crime (Glaeser, Sacerdote, and Scheinkman 1996; Katz, Kling, and Liebman 2001), academic success (Sacerdote 2001), savings behavior (Duflo and Saez 2002), and choice under uncertainty in general (Cooper and Rege 2008).

(2.) In the experiment subjects had no labels. We use the numbering of subjects in Figure 1 only for expositional reasons.

(3.) See Friedman and Cassar (2004) for a general discussion of related designs.

(4.) Relaxing this information condition could be an interesting treatment condition because it would allow insights with whom subjects choose to compare. This could be implemented, for example, by giving subjects the possibility to inform themselves about the behavior of groups to which they do not belong.

(5.) More recent evidence in different setups is presented in Croson (2007), Gachter (2007), Kocher et al. (2008), Muller et al. (2008), Herrmann and Thoni (2009), Duffy and Ochs (2009), Grimm and Mengel (2009), Neugebauer et al. (2009), Fischbacher and Gachter (2010), Ashley, Ball, and Eckel (2010), and Gachter et al. (forthcoming).

(6.) We also ran regressions of the difference in numbers in period t on the difference of minimum numbers in period t - 1 for every period. We used robust standard errors with matching groups as clusters to take the dependency of observations within matching groups into account. All regressions reveal a highly significant (<1%) positive relationship between the two variables.

(7.) Because the groups are identical we expect an intercept of zero (measured by the constant) and we do not expect that the intercept will be different from zero in later periods (measured by the variable "period"). This is also what we observe.

(8.) Note that the correlation between, for example, [c.sup.1.sub.i] and [g.sup.1.sub.i] is not a strict test for the existence of social interactions. Finding such a correlation could be because of, for example, correlated effects with respect to time. If all subjects for whatever reason were to reduce their contributions from one period to the next we would find such a correlation. In our two-group design we observe two contribution decisions at the same time, thereby ruling out correlated time effects. Ruling out these correlated effects is impossible in a standard one-group design.

(9.) We ran for this experiment the analogous regressions as those described in footnote 6. In this case, we also find for all periods a highly significant (<1%) positive relation between the difference in contributions of the other group members in the previous period and the difference in the own contributions in this period.

(10.) Because the groups are identical we expect an intercept of zero (measured by the constant) and we do not expect that the intercept will be different from zero in later periods (measured by the variable "period"). This is also what we observe.

(11.) Note that the correlation between, for example, [c.sup.1.sub.i] and [g.sup.1.sub.i]) is not a strict test for the existence of social interactions. Finding such a correlation could be because of, for example, correlated effects with respect to time. If all subjects for whatever reason were to reduce their contributions from one period to the next we would find such a correlation. In our two-group design we observe two contribution decisions at the same time, thereby ruling out correlated time effects. Ruling out these correlated effects is impossible in a standard one-group design.

(12.) of course, if there would be a joint budget constraint for the contributions to the two public goods, then spillovers would likely occur. However, such a budget constraint implies constraint interaction in the sense of Manski (2000) and our research question demands that we control for this. However, it might be interesting in future research to study the situation of one-joint budget constraint.

(13.) There are some public goods studies where subjects could observe what members of another group contributed (Bardsley and Sausgruber 2005; Carpenter and Matthews forthcoming; Sausgruber 2009). In Carpenter and Matthews, subjects could even punish members of another group. The goal of these studies is different from ours. Bardsley and Sausgruber (2005) and Sausgruber (2009) want to disentangle conformism and reciprocity; and Carpenter and Matthews investigate "social reciprocity." Furthermore, in some studies subjects contributed to more than one public good (a "local" and a "global" public good; see, e.g., Buchan et al. 2009; Fellner and Lunser 2008; Wachsman 2002) or a public good divided into two identical segments (Bernasconi et al. 2009).

(14.) In the coordination game, [g.sup.i] denotes the minimum number in group i in the previous period and in the public goods game; [g.sup.i] denotes the average contribution to group i in the previous period.

(15.) Two subjects never observed a difference between the groups and have to be left out of the analysis.

(16.) of these five subjects, three are completely selfish, that is, they always defect while two always contribute independently of the other group members' decisions.

ARMIN FALK, URS FISCHBACHER and SIMON GACHTER *

* This paper was funded under the EU-TMR project ENDEAR (FMRX CT98-0238). Lukas Baumann, Michael Bolliger, Esther Kessler, and Christian Thoni provided very valuable research assistance. We received helpful comments from the referees and Gary Charness, Alan Durell, Stefano DellaVigna, Claudia Keser, Manfred Konigstein, Michael Kosfeld, Charles Manski, Shepley Orr, Ekkehart Schlicht, Jason Shachat, Frans van Winden, and participants at seminars and conferences in Amsterdam, Berlin, Boston, Essen, IBM T.J Watson (Yorktown Heights, USA), Jena, London, Munich, Norwich, St. Gallen, Venice, and Zurich. Simon Gachter gratefully acknowledges the hospitality of CES Munich, the University of Maastricht, and Bar-Ilan University (Israel) while working on this paper.

Falk: University of Bonn, Lennestr. 43, D-53113 Bonn, Germany; CESifo, Munich; IZA, Bonn; CEPR, London. Phone 228-73-9240, Fax 228-73-9239, E-mail [email protected]

Fischbacher: University of Konstanz, PO Box D 131, D-78457 Konstanz, Germany; Thurgau Institute of Economics, Hauptstrasse 90, CH-8280 Kreuzlingen, Switzerland. Phone 71677-0512, Fax 71677-0511, E-mail [email protected]; fischba [email protected]

Gachter: University of Nottingham, School of Economics, The Sir Clive Granger Building, University Park, Nottingham NG7 2RD, UK; CESifo, Munich; IZA, Bonn. Phone 115-846-6132, Fax 115-951-4159, E-mail [email protected]

TABLE 1
Social Interactions: Explaining Behavior in the Minimum-Effort Game
with the Behavior of Neighbors

 Dependent Variable

Independent Variable [c.sup.1.sub.i] - [c.sup.1.sub.i]
 [c.sup.2.sub.i]

[g.sup.1.sub.i] - 0.643 *** --
 [g.sup.2.sub.i] (0.061)
Period -0.043 -0.460 ***
 (0.052) (0.070)
Period x 0.0195 *** --
 ([g.sup.1.sub.i] - (0.003)
 [g.sup.2.sub.i])
[g.sup.1.sub.i] -- 0.881 ***
 (0.027)
[g.sup.2.sub.i] -- 0.023
 (0.013)
Constant 0.426 16.122 ***
 (0.687) (2.206)

 N = 1,368 N = 1,368
 F(3,7) = 2,536.73 *** F(3,7) = 372.97 ***
 [R.sup.2] = 0.89 [R.sup.2] = 0.88

 Dependent Variable

Independent Variable [c.sup.2.sub.i]

[g.sup.1.sub.i] - --
 [g.sup.2.sub.i]
Period -0.516
 (0.072)
Period x --
 ([g.sup.1.sub.i] -
 [g.sup.2.sub.i])
[g.sup.1.sub.i] 0.041 ***
 (0.009)
[g.sup.2.sub.i] 0.908
 (0.031)
Constant 13.379 ***
 (1.612)

 N = 1,368
 F(3,7) = 1,374.63 ***
 [R.sup.2] = 0.90

Notes: ([c.sup.1.sub.i] -[c.sup.2.sub.i]) measures own difference in
the number to group 1 and group 2 in period t; ([g.sup.1.sub.i] -
[g.sup.2.sub.i]) is the difference in minimum number in group 1 and
group 2 in t - 1; robust standard errors clustered on matching groups
in parentheses.

*** Significance at the 1% level.

TABLE 2
Social Interactions: Explaining Contributions in the Public Goods
Game with the Behavior of Neighbors

 Dependent Variable

 [c.sup.1.sub.i] - [c.sup.1.sub.i]
Independent Variable [c.sup.2.sub.i]

[g.sup.1.sub.i] - 0.605 *** --
 [g.sup.2.sub.i] (0.054)
Period 0.007 -0.103 ***
 (0.023) (0.018)
Period x 0.005 --
 ([g.sup.1.sub.i] - (0.005)
 [g.sup.2.sub.i])
[g.sup.1.sub.i] -- 0.750 ***
 (0.061)
[g.sup.2.sub.i] -- 0.021
 (0.037)
Constant -0.022 2.901-
 (0.416) (0.672)

 N = 2,394 N = 2,394
 F(3,13) = 144.9 *** F(3,13) = 101.4 ***
 [R.sup.2] = 0.44 [R.sup.2] = 0.46

 Dependent Variable

 [c.sup.2.sub.i]
Independent Variable

[g.sup.1.sub.i] - --
 [g.sup.2.sub.i]
Period -0.121 ***
 (0.024)
Period x --
 ([g.sup.1.sub.i] -
 [g.sup.2.sub.i])
[g.sup.1.sub.i] 0.069
 (0.045)
[g.sup.2.sub.i] 0.663
 (0.046)
Constant 3.418
 (0.776)

 N = 2,394
 F(3,6) = 185.0
 [R.sup.2] = 0.37

Notes: ([c.sup.1.sub.i] -[c.sup.2.sup.i]) measures own difference in
contribution to group 1 and group 2 in period t; ([g.sup.1.sub.i] -
[g.sup.2.sub.i]) is the difference in neighbors' contributions in
group 1 and group 2 in t - 1; robust standard errors clustered on
matching groups in parentheses.

*** Significance at the 1% level.