Playing with the Good Guys A Public Good Game with Endogenous Group Formation∗ Kjell Arne Brekke, Karen Evelyn Hauge, Jo Thori Lind, Karine Nyborg

†

Department of Economics, University of Oslo January 12, 2010

Abstract Individuals who are generally more cooperative than others may self-select into groups committed to charity. This yields higher local public good provision in such groups, an effect which is reinforced by conditional contribution behavior. We present a model describing this process, and test its predictions using a public good game experiment. Subjects choose between two group types: one where subjects receive a fixed extra payoff; one where this extra payoff is donated, instead, to the Red Cross. Contributions in the latter groups are initially higher and stay high, while contributions in the former groups display the well-known declining pattern.

JEL codes: D11, D12, D64, H41 Keywords: Altruism; conditional cooperation; self-selection

∗

We are grateful to the Research Council of Norway (RCS) for funding through the RAMBU/Miljø2015 programmes, to Geir Asheim and numerous conference and seminar participants for comments and suggestions, and to Kenneth Birkeli, Sunniva P. Eidsvoll, and Kristine Korneliussen for excellent research assistance. Part of this project was undertaken while Brekke and Nyborg were employed by the Ragnar Frisch Centre for Economic Research. The authors are part of the ESOP - Centre of Equality, Social Organization, and Performance, which is supported by the Research Council of Norway. † PB 1095 Blindern, 0317 Oslo, Norway. Emails: [email protected], [email protected], [email protected], [email protected].

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1

Introduction

Voluntary contributions to public goods are much more common than one would expect assuming purely selfish behavior (see e.g. Andreoni, 1988a, 1990; Nyborg and Rege, 2003), a finding which is confirmed by substantial evidence from public good game experiments.1 A striking finding from such experiments, however, is that average contributions, although starting off at high levels, usually decline rather dramatically as games are repeated.2 Several studies indicate that this decline can largely be attributed to conditional cooperators who withdraw their contributions if others free-ride too much.3 If high contributors are exogenously matched with each other, average contribution levels tend, indeed, to stay high.4 However, in many real life situations group formation is endogenous; and if some groups succeed in sustaining cooperation, free-riders will have an incentive to invade those groups (Ehrhart and Keser, 1999).5 Groups’ ability to sustain voluntary contributions is important in a wide range of real life situations. When individual efforts are unobservable in a teamwork context, workers’ efforts can be regarded as voluntary contributions to a local public good;6 maintaining a high level of cooperativeness in such teams can be vital to firms’ survival. Similarly, groups such as clubs and organizations, schools, neighborhoods and friends may all depend on individuals’ voluntary local public good provision, for example by creating a good social atmosphere and a pleasant environment, by attending meetings, being active in classroom discussions, volunteering for local community work, or hosting parties.7 A better understanding of how and why voluntary contributions can (or cannot) be sustained is thus of general interest. The idea we want to explore in this paper is that if some individuals are generally more cooperative than others, groups may use socially beneficial and costly commitments as a screening device to attract such individuals. Our analysis draws on Brekke and Nyborg (2008), who demonstrate that if cooperative behavior originates from an underlying ethical principle, while the weight attached to this principle varies between individuals, a positive correlation between a given individual’s cooperativeness in different contexts will arise. Based 1

See e.g. Ledyard (1995); Fehr and G¨ achter (2000, 2002); Zelmer (2003). In addition to the references above, see Andreoni (1988b); Croson (1996); Fehr and G¨achter (2000); Keser and van Winden (2000). 3 Fischbacher, G¨ achter, and Fehr (2001); Fischbacher and G¨achter (2006, forthcoming); Croson, Fatas, and Neugebauer (2006); Croson (2007); Hauge (2009). 4 G¨ achter and Th¨ oni (2005); Gunnthorsdottir, Houser, and McCabe (2007); Ones and Putterman (2007). 5 See also Page, Putterman, and Unel (2005), G¨ urerk, Irlenbusch, and Rockenbach (2006), and Ahn, Isaac, and Salmon (2008). 6 See Holmstr¨ om (1982) for an early treatment of this issue. 7 Brekke, Nyborg, and Rege (2007). For overviews of club theory, see Cornes and Sandler (1986) and Scotchmer (2002). 2

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on this premise, Brekke and Nyborg (2008) show that socially responsible firms can attract workers who exert more non-observable effort and are thus more productive. However, the empirical evidence for correlated contribution behaviors is sparse and somewhat mixed. Several studies do find positive correlations, but correlations are often relatively low.8 We are not familiar with any previous studies within experimental economics explicitly designed to test this, although a few recent studies focusing on other issues could be interpreted as supporting it (Blanco, Engelmann, and Normann, 2007; Johnson et al., 2009). Thus, in the present paper we provide results from a public good game experiment designed specifically to test for the presence and possible impact of correlated contribution behaviors. While Brekke and Nyborg (2008) focus on a certain type of unconditional altruism, their model disregards conditional cooperation. Since conditional cooperation appears to be an important driving force of behavior in public good games, this phenomenon cannot be disregarded when interpreting our experimental results. Thus, before presenting the experiment and its result in detail, we outline a theoretical model with conditional and unconditional altruism. We first present a base-case version yielding predictions conforming well to the standard findings in public good games such as high initial and declining contributions. Then, we extend this model to allow multiple and correlated contribution behaviors, and derive the model predictions relevant for our experiment. The model predicts that cooperative individuals will self-select into groups committed to charity contributions; this will lead to an initial effect of higher local public good provision in such groups. Moreover, due to conditional cooperation, these groups may be able to sustain or even increase their high public good provision over time. Our experiment consists of three parts. The first part, labelled the one-shot game, is a standard one-shot public good game with exogenous group formation and no informational feedback. In the second part, labelled the partner game, the game is repeated 10 times, and the group composition remains fixed for all 10 periods. However, before groups are formed in the partner game, subjects can choose between two group types. The difference between the two is that for each member in what we label a blue group, an extra, fixed amount of money is donated to each group member. In the other groups, called red groups, the same extra amount is, instead, given to the Red Cross. In the third part, the stranger game, the number of periods is increased to 20, new groups are formed in every period, and subjects decide on their preferred group type between each period. We find that throughout the second and third part, a substantial share of subjects, about 35-40 percent, choose red groups. Contributions in red groups are, on average, substantially ¨ E.g., Thøgersen and Olander (2006). A classical study is Hartshorne and May (1929). For overviews, see Piliavin and Charng (1990) and Aronson, Wilson, and Akert (2005). 8

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higher than in blue groups. While the blue groups display the usual deterioration of contributions over time, no clear downwards trend is observed in the red groups.

2

Theory and predictions

Consider a public good game with n members in each group, where each player is given an exogenous initial endowment Y . The game is repeated T times and group composition is fixed throughout T . Let t denote period number (1 ≤ t ≤ T ). Each player decides simultaneously and anonymously how much of Y to contribute to her group in period t, git , keeping the remaining part of Y for herself. Contributions to the group are multiplied by a factor M (1 < M < n), and then shared equally between group members. Consequently, git is a voluntary contribution to a local public good. We will start by modelling the case of a standard public good game, extending the framework later on to allow for both local and public good contributions.

2.1

Choice of contribution

Let each individual i have preferences of the following kind: uti = xti + β i git −


2 α t gi − gˆit 2

(1)

where α > 0. Here, uti is individual i’s utility in period t, xti denotes i’s monetary payoff in period t, while the other terms reflect social preferences. β i is the unconditional warm glow of giving experienced by i per unit contributed to the local public good (Andreoni, 1990). The last term can be considered a conditional warm glow, which depends not only on i’s own contribution git , but also on the level of some yardstick gˆit (Konow, 2009). This is similar to the self-image model of Brekke, Nyborg, and Kverndokk (2003), who interpreted gˆit as i’s idea about the morally ideal contribution, which they assumed, in turn, to be determined through a Kantian-style ethical argument. Although our assumptions about the determination of gˆit will be different, the interpretation is similar: we consider gˆit to be i’s idea of the morally ideal contribution, implying that conditional warm glow is higher the closer i’s actual contribution is to her perception of what she should, ideally, have contributed. Note that conditional warm glow is always negative, but less so when git is closer to gˆit ; thus one may alternatively think of conditional warm glow as cognitive dissonance.9 9

Festinger (1957). Cognitive dissonance is the discomfort experienced by ’performing an action that is discrepant from one’s customary, typically positive self-conception’ (Aronson, Wilson, and Akert, 2005, p. 166).

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In period t, monetary payoff to i is given by xti

=Y −

git

n MX t + g n j=1 j

(2)

where j = 1, ..., n are the members of i’s group. This implies (rearranging and inserting into (1)) that utility can be written as uti

  MX t α n−M =Y + git − (git − gˆit )2 gj + β i − n j6=i n 2

(3)

Assume, first, that gˆit and gjt (j 6= i) are exogenous. Since the finite time horizon rules out Folk Theorem-type equilibria, the utility maximizing contribution can be solved separately for each period. The first order condition for an interior solution requires that marginal warm glow equals the net monetary cost of a marginal contribution so
n−M β i − α git − gˆit = . n

(4)

If the solution is not interior, we must take into account that git can neither be negative nor exceed the initial endowment Y . The utility-maximizing contribution can thus be written as follows: 
1 n−M t  0 if g ˆ + β − 1, the ideal gˆit and thus also the marginal warm glow from contributions to the local public good will now be increasing in others’ contributions, and i will tend to be what Fischbacher, G¨achter, and Fehr (2001) classify as a conditional cooperator. If individuals are forward-looking, eq. (8) will give rise to strategic considerations: person j may want to contribute high amounts in early periods in order to increase others’ ideals, and thus their contributions, in later periods. While such strategic interaction complicates the analysis considerably, experimental evidence indicates that this is not the most important force at play in public good games. Testing this explicitly, Neugebauer et al. (2009) rejected the hypothesis that strategic play is the driving force of the decay in contributions over time, concluding that “[t]he only viable hypothesis according to our data is the one of conditional cooperation and adaptive belief learning” (op.cit, p.57). Thus, we will simplify our analysis by making the following assumption: Individuals are myopic in the sense that they do not take into account that ideals will change over time. More specifically, they act as if gˆjt = gˆjs for all s > t and for j = 1, ..., n. From (8), we note that the ideal will be stable, increasing or decreasing in t depending on whether g¯i t = gˆit , g¯it > gˆit , or g¯it < gˆit respectively. The latter is equivalent to (due to eq. (4)) n−M E git |τ i = B provided that 0 < git < Y for some β i in the support. 13

Expectations here and in the following are to be interpreted as the expectations of an outside observer, that is, the average value if the game is played many times with different individuals drawn from the same population.

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n o Proof. From the discussion above we know that the event {τ i = R} ⇔ θi > θˆi with θˆi = D. Thus the Proposition applies, and β i |τ i = R stochastically strictly dominates β i |τ i = B. In particular this dominance applies in the part of the support where git is interior. Since interior contributions are linearly increasing in β i , the claim follows. Hence individuals with high θi self-select into red groups; due to the correlation, these individuals have high β i and thus contribute more to their groups. However, we must also consider dynamic effects. Assume now that eq. (8) holds, and that individuals are myopic and do not, at the outset, expect different behavior from members of blue and red groups.14 From Proposition 1 above, we know that β i , or rather its group average, is the crucial parameter determining whether contributions will in fact decline over time. Individuals with high θi and, by correlation, high β i , will be more prone to choose red. Thus, individuals’ contributions must be expected to decline faster in blue groups than in red.15 Assume that every i has the same exogenous initial ideal gˆi1 . Moreover, assume that after each period, individuals observe the average contribution in their own group. Although there will be random differences in β i between members in each red, respectively blue, group, the expected level of β i will be equal within each group type. Since individuals hold identical initial ideals, the expected development of the ideal will also be identical within each group type. Let gˆτt denote the expected ideal in group type τ = {R, B} in period t, while g¯τt denotes the expected average contribution in group type τ in period t. At the beginning of period 2, when one observation has been made, the expected difference in ideals is given by gˆR2 − gˆB2 = (1 − λ)(¯ gR1 − g¯B1 ) =

1−λ ¯ (β R − β¯ B ). α

where β¯ R = E [β i |τ i = R] and β¯ B = E [β i |τ i = B] are expected average β i in the two group types. Hence, after the second period, g¯τt+1 will differ between red and blue groups both due 14 If individuals are myopic but expect members of red groups to contribute more, this would reinforce the sorting of individuals with high β i into red groups. 15 Whether contributions will increase, be constant or decrease in either group types, depends on the level of β i in the group.

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to different ideals in period t and to different β i ’s. In general,16

gˆRt+1 − gˆBt+1 = (1 − λ) g¯Rt − g¯Bt + λ gˆRt − gˆBt 1−λ ¯ = t(β R − β¯ B ) > 0 α where the inequality is due to Proposition 2, securing that β¯ R > β¯ B . Thus, in the first period, individuals in red groups must be expected to have higher β i values than members of blue groups; after the first period, they must, in addition, be expected to have higher ideals than members of blue groups. Thus, contributions in red groups will typically be higher even in the first period; for each subsequent period, the difference in contributions will increase. We summarize this as a Proposition. Proposition 3. Assume that the ideal changes according to (8). Expected contributions to the local public good are then higher in red groups than in blue groups in every period, and the difference is increasing over time.

2.5

Group choice with group specific ideals

Until now, we have assumed that the group composition is kept fixed over time. Consider now the case with T periods where each individual can choose group type for each new period, such that group composition changes over time. In the previous section, we saw that the ideal developed differently in red and blue groups. Since any given individual was then only member of one group throughout the repeated game, the ideal in the other group type would be largely irrelevant for her; as the game evolved, she might not even be aware that contributions were developing differently. Let us now assume that after each period, every individual receives information about average contributions in at least one blue and at least one red group. If the average contributions differ between group types, individual i’s idea of the morally ideal contribution may not be the same for both group types: if she expects others in her group to contribute a lot, it seems more reasonable that she will demand more of herself, and vice versa. Let us thus modify (8), the equation determining i’s ideal, such that in any period t > 1, t t i has two ideals, gˆiR and gˆiB , one for each group type, where the ideal for group type τ is 16

Allowing for corner solution, the equation can be written t

t+1 t+1 gˆR − gˆB =


1−λX ¯ s s ¯ (ˆ β R (ˆ gR )−β B gB ) . α s=1

For a proof, see Appendix A.2.

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updated using the information i has received about average contributions in group type τ : t+1 t t gˆiτ + λˆ giτ = (1 − λ)¯ giτ

(12)

t where g¯iτ is the information received by i in period t about average contributions in group type τ . Since individuals within the same group type have different β i ’s and are distributed t t for i 6= j if i and j have received information 6= gˆjτ randomly into groups, we may have gˆiτ from different groups. Still, an outside observer has of course no reasons initially to have different expectations for i and j. We can thus define a group type specific expected ideal: t t ). ) = E(ˆ gjτ giτ gˆτt = E(ˆ A main difference between constant and changing group compositions over time, is that constant group composition gives a stronger strategic motive for early contributions. We showed above, however, that due to the myopia assumption, group choice did not depend on such dynamics even for constant group compositions, only on whether D ≷ θi . Moreover, the choice of red versus blue and the choice of git were independent. With myopic individuals, the results will be very similar when group composition is allowed to change over time. In the first period, individuals with high β i will self-select into red groups, just as before; thus expected average contributions in the first period will be higher in red than in blue groups, t the result being that gˆR2 > gˆB2 . For later periods, i’s group-specific ideals gˆiτ are updated according to (12); and both values of β i and ideals are in expectation higher in red than blue groups. The result is that gˆRt > gˆBt , for every period. Moreover, as more periods pass, the difference must be expected to increase. Now, let gτt i denote the contribution of individual i in period t given that i has chosen to be in a group of type τ in this period. (As i can actually be in only one type of group t t will be hypothetical.) The first order conditions for a utilityor gBi at a time, either gRi t maximizing contribution gτ i is now

gτt i

=

gˆτt i

1 + α

  n−M βi − n

(13)

Note that the last term is independent of group type. Since gˆRt > gˆBt , this Proposition follows: Proposition 4. For t > 1, any given individual will in expectation contribute more as a member of a red group than as member of a blue group. Finally, consider the choice between red and blue. As above, those who choose red have high values of θi and, by correlation, of β i . When considering ideals that depend on group type, there is an additional argument for choosing red, which is strongest for those with the 12

highest values of β i : Entering a red group will induce i to make larger contributions than she would in a blue group. Thus, red group membership yields more warm glow both in terms of the unconditional warm glow of global public good provision, θi , but also more warm glow of local public good provision, β i gi , which is increasing in β i . Thus, this argument reinforces the expected self-selection of cooperative individuals into the red groups. For details, se Appendix A.3.

3

Experimental design

Let us now turn to our experimental design. As mentioned in the introduction, the experiment consists of 3 parts, a one-shot public good game, a repeated game with fixed groups (the partner game), and a sequence of games with varying group composition (the stranger game). All subjects participate in all three parts in the same order. We denote by t = 0 the one-shot game, by t = 1, . . . , 10 the 10 periods of the partner game, and by t = 11, . . . , 30 the 20 periods of the stranger game. Part 1 of the experiment, the one-shot game, is a standard one-shot public good game experiment with exogenous group formation. Groups of 3 are formed randomly, and each subject is given an initial endowment of NOK 60.17 The subject’s task is to decide how much to allocate to her group and how much to keep for herself. Every contribution to the group is doubled by the experimenters, and then divided equally between the three group members. Each subject is thus paid according to the following monetary payoff function: 3

x0i

= 60 −

gi0

2X 0 g + 3 j=1 j

(14)

where x0i is subject i’s monetary payoff and gi0 is i’s contribution to her group in the one-shot game. Before this part starts, subjects are tested in their understanding of the instructions. They are informed that two additional experiments will take place after this one, but that their choice in part 1 neither will affect neither their payoffs nor available choices in parts 2 and 3. No further information is provided about the contents of parts 2 and 3. Before proceeding to part 2, subjects receive no feedback about behavior in part 1. Part 2 of the experiment, the partner game, is a repeated public good game where the group composition remains fixed for all 10 periods. The stage game is very similar to the 17 Given the exchange rate at the time of the experiment (February 2008), this was equivalent to about 11 USD.

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one-shot game described above. Before the repeated public good game is played, however, each subject can choose whether she prefers to be in a red or blue group18 . Each member of a blue group receives an extra payoff of NOK 50. For each member of a red group, an extra NOK 50 is donated, instead, to the Norwegian Red Cross. To the largest extent possible, subjects are allocated to groups of their preferred type; if the number of subjects preferring a given group type is not divisible by 3, there will be one mixed group, and the type of this group is determined by the majority preference within the group. The payoff function for a member of a red group in any period of the partner game (part 2) can then be written as 3 2X t t xiR = 60 − gi + gj (15) 3 j=1 for t = 1, ..., 10, and for a member of a blue group, 3

xtiB

2X gj = 110 − gi + 3 j=1

(16)

for t = 1, ..., 10. Actual payment to i for her choices in the partner game is determined by her average P10 t P10 t 1 1 calculated payoff through all periods 1 to 10 (that is, 10 t=1 xiR or 10 t=1 xiB , respectively). For given contribution levels, the monetary payoff to members of blue groups must obviously be higher than in red groups. However, we can have xtiR > xtiB (t ∈ {1, ..., 10}) if the contributions of the other two group members are sufficiently higher in the red group. With our design, we will have xtiR > xtiB if the average other in the red group contributes at least NOK 37,5 more than the average other in the blue group (that is, if the sum of others’ contributions is at least NOK 75 higher in the red than in the blue group). Subjects are tested in their understanding of the instructions before the partner game starts. After each period, every subject receives feedback on how many units she contributed, how many units were contributed on average in her group, and her calculated monetary payoff from that period. Due to the feedback given, individual choices in the partner game can be considered independent observations only in period 1. Part 3 of the experiment, the stranger game, is quite similar to part 2, but now new groups are formed in every period. Moreover, subjects now decide on their preferred group type again in each new period, and the number of periods is increased to 20. Period payoffs xtiR and xtiB for t = 11, ..., 30 are calculated exactly as in the partner game, 18

In the experiment, group types were called Z groups and X groups instead of red and blue, in order to avoid framing effects. To avoid confusion, there is a reminder of the difference on every screen where subjects make choices concerning X and Z.

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that is, according to eq. (15) and (16). Actual monetary payout to subjects is determined as the average calculated period payoff over all 20 periods (but note that now i may be a member of a red group in some periods and of a blue group in others). Among those who have chosen the same group type, groups are formed randomly in every period. As in part 2, if the number of subjects preferring a given group type is not divisible by 3, there will be one mixed group. Between each period, each subject receives information about how many units she contributed to the public good in that period, and how many units were contributed on average in her group. In addition, each subject is informed of the average contribution in one red group and one blue group.19 Due to the feedback given between periods, observations cannot be considered independent.

4

Experimental results

The experiment was programmed in z-tree (Fischbacher, 2007) and conducted at the Oeconlab at the University of Oslo. The main part of the experiment, conducted in February 2008, comprised 87 subjects recruited among students from several departments at the University of Oslo participated in the experiment. A modified version of the experiment was conducted in October 2009, comprising 39 subjects. Figures 1 and 2 summarize the data. Recall that period 0 corresponds to the one-shot game, period 1-10 to the partner game, and period 11-30 to the stranger game. In figure 1 subjects’ choice of group type is shown in the lower panel, while actual group types are shown in the upper panel. As illustrated in the upper panel, there were 41% homogeneously red and 52% homogeneously blue groups in the partner game, while 7% of groups were mixed (illustrated by the lighter shade). In the stranger game, the number of red groups was relatively stable during the 20 periods; averaged across all periods, the average percentage of subjects in red groups was 36%. The lower panel of Figure 1 shows players’ group choices. Again, the fractions remain fairly stable over the course of the game. The darker colors illustrate that about 25% of our subjects consistently chose blue, while 10% consistently chose red during the entire 20 19

To maximize the variation in the information received by different subjects, each subject is either shown the average contribution of the red group with the highest average contribution or that of the red group with the lowest average contribution, each with 50% probability. Likewise, each subject is shown the average contribution of the blue group with either the highest or the lowest average contribution, each with 50% probability. In the instructions, subjects are simply informed that they will be shown the average of one red and one blue group.

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Table 1: Relationship between contributions in the one-shot game and group choice in consecutive periods

Difference

(1) Partner game

(2) Stranger game

(3) Both games

6.947** (1.68)

11.94** (2.02)

11.32** (2.01)

Notes: The table shows the contribution difference in the initial one-shot game for agents who later choose red. Column (1) reports results from the partner game based on a t-test allowing for different standard deviations in the two groups (assuming identical standard errors gives a t-value of 1.62). Columns (2) and (3) report the contribution difference as a function of the fraction of subsequent periods spent in red groups based on OLS regressions. *, **, and *** denote significance at the 10%, 5%, and 1% level in the relevant one-sided test. periods of the stranger game. The remaining 65% switched between choosing red and blue at least once during the stranger game. We can summarize these results as Result 1. In each period of the experiment, both group types are being chosen by some subjects. The fraction choosing each type remains relatively stable. Figure 2 illustrates the average contribution levels in red and blue groups, respectively. The figure reveals a rather striking pattern. The first thing to note is that average contribution in red groups is higher than in blue groups in the one-shot game, in every period of the partner game, and in every period of the stranger game. We analyze this pattern in more detail below.

4.1

Selection into groups

Table 1 reports results on the relationship between contributions in the one-shot game and consecutive group choices. As it is not meaningful to say anything about causality, we may as well study average contributions in the one-shot game conditional on group choices in later periods.20 As Proposition 2 predicts higher contributions for members of red groups, the relevant test is a one-sided test. The first column studies the relationship between contributions in the one-shot game group choice at the beginning of the partner game. Members who later were to choose red groups in the partner game contributed on average 20

An regression of choosing a red group regressed on contribution yields qualitatively similar results – a logit coefficient of 0.0181 with a standard error of 0.00815 clustered at the individual level. Repeating this analysis perod by period yields similar results, but the estimates are not significant in all periods.

16

10

20

Blue groups

Red groups 0

Number of groups

29

Figure 1: Group choice by period

10

20

30

20

30

.75 .25

.5

Blue

Red

0

Fraction of agents

1

1

1

10 Period

Notes: The first panel shows the number of red (hatched) and blue (solid) groups by period. Mixed groups in light colors, homogeneous groups in dark colors. The second panel shows the fraction of agents who choose red (hatched) and blue (solid) groups by period. The fraction of agents who consistently choose red/blue groups in all the 20 periods in the stranger game are shown in dark colors agents who do not choose the same group throughout the stranger game are shown in light colors.

17

10

20

Contribution 30 40

50

60

Figure 2: Contribution in the different group types

10

1

10

20

30

20

30

t− and z−value 2 5 8

1

Period

Above: Average contribution by red and blue groups by period. Below: Test statistics of the difference between red and blue contributions. The solid line represents t-statistics from t-tests, the dashed-dotted line similar tests clustering at the group level, and the dashed line z-statistics from Mann-Whitney tests. The horizontal dotted lines are significance levels of 0.05 and 0.01. Data from mixed groups are excluded. 18

NOK 6.95 (out of 60) more than those who later chose blue groups. A t-test that allows for varying variances over time indicates that this difference is significant at the 5% level.21 To compare contribution in the one-shot game with group choices in the stranger game, where group choices are made every period, it is not possible to simply study the difference between two groups except for the agents who chose the same group type throughout this part of the game. Instead, we regress contributions in the one-shot game on the fraction of periods spent in red groups. This is done in Column (2). Now the difference between red and blue groups increases to NOK 11.94, which is clearly significant. The results when combining the group choices in the partner and stranger games are fairly similar (counting the partner game as the 10 periods it does constitute), although the difference is somewhat smaller at NOK 11.32. In fact, the correlation between contributions in the one-shot game and subsequent group choice is higher the further into the experiment we move: for example, contributions are NOK 8.49 higher for those choosing red in the first half of the stranger game (t=1.45) and NOK 13.60 higher for those choosing red in its second part (t=2.45). Thus, although many subjects appear to experiment with their group type choices throughout the experiment, high contributors in the one-shot game are more likely to choose red groups later on, and this tendency is stronger the later periods we look at. We can summarize these findings as Result 2. Individuals with high contributions in the initial one-shot game are more likely to choose red groups in subsequent stages of the experiment. This corresponds nicely to the predictions of Theorem 1 and Proposition 2. Not surprisingly, agents also seem to be motivated by profits in their group choices. In the partner game, players were given differentiated information about contributions in one red and one blue group. We used this information to study whether agents were more likely to choose a red group if they had been informed of high contributions in red groups. Specifically, we used a Bayesian updating approach to optimally process the information give to each player. This indicated that agents who had reasons to believe that contributions were high in red groups relative to blue groups were indeed more likely to opt for red groups. Full details are available in the working paper version of the paper (Brekke et al., 2009).

4.2

Contributions in different groups

While the previous section focused on the issue of self-selection, let us now compare, more explicitly, contributions in red and blue groups. The results reported in Figure 2 accord well 21

Although it is only significant at the 10% level when we do not account for varying variances.

19

with Proposition 2 and 3, stating that those who choose red groups should be expected to contribute more to the local public good than others, and that the contribution difference between group types will increase over time. The lower panel of Figure 2 shows the test statistics from an ordinary t-test, a t-test clustering at the group level, and a Mann-Whitney test, respectively. All these test whether mean contributions are equal for subjects in red and blue groups (for period 0: those who later chose red, respectively blue, in the partner game). The two t-tests assume draws from a normal distribution, while the Mann-Whitney test is robust to the distribution of the population, but with the cost of weaker test power. As shown in the lower panel of Figure 2, the ordinary t-test gives support for the hypothesis that average contributions are higher in red than in blue groups from period 2 onward, at a 5% significance level. Since individual contributions cannot be expected to be independent between periods, however, this tells us only that contributions are significantly higher in red groups, and does not necessarily indicate that subjects in red and blue groups are drawn from different populations. The clustered t-test and the non-parametric Mann-Whitney test give support for the hypothesis of higher contributions from period 4 onwards. Utilizing the whole panel of observations further strengthens these findings. This is done in Table 2, where we regress contribution on group choice using different specifications. In Columns (1) to (3), we study the partner and stranger games separately and jointly. All specifications include period dummies.22 Column (1) shows that in the partner game, contributions to the local public good is on average NOK 15 higher in red than blue groups. This difference is significant. As members of one group play against each other in ten consecutive periods, we might worry about correlation between players. To solve this potential problem, all regressions are clustered at the group level.23 The stranger game, where players can choose group type in each period, is analyzed in Column (2). Here the results are even stronger: Contributions in red groups are about NOK 21 higher than in the blue groups, and still statistically significant. Finally Column (3) uses data from both parts of the experiment; the difference between red and blue groups is here NOK 19. This leads us to the following result: Result 3. In any given period, average contributions to the local public good are higher in red groups than in blue groups. 22

Excluding the period dummies have only small effects on the estimates parameters and make them more significant. 23 For the stranger game and the joint analysis, groups do not keep together, so we instead cluster on the group-period.

20

Table 2: Contribution by group type (1)

(2)

(3)

(4)

(5)

Red group

15.35*** (3.08)

21.10*** (19.45)

19.09*** (20.01)

12.27*** (5.25)

9.881*** (4.38)

Cluster level Game Individual FE R2 Obs

Group Partner No 0.146 870

Group×Period Stranger No 0.189 1740

Group×Period Both No 0.197 2610

Individual Stranger Yes 0.115 1740

Individual Both Yes 0.146 2610

Notes: The dependent variable is contribution; Red group is a dummy for currently being in a red group. All specifications contain period dummies. t-values clustered at indicated levels are reported in parentheses. *, **, and *** denote significance at the 10%, 5%, and 1% levels. If subjects strive towards some ideal which is positively affected by other group members’ expected contributions, then the same individual will contribute (weakly) more to the local public good as a member of a red group than if she is in a blue group. This follows from Proposition 4. To analyze this, we again regress contributions on group type, but now including individual fixed effects, in practice comparing changes in group choice to changes in contribution levels. The results are shown in Columns (4) and (5) of Table 2. Column (4) uses data from the stranger game where groups choices are made every period, whereas Column (5) also include data from the partner game. It is clearly seen that an individual who changes group type contributes more when in red groups than when in blue groups, and the difference is statistically significant. The estimated differences are, however, smaller than when we do not condition on the individual. This indicates that a major part of the differences unveiled above were due to selection of individuals into red and blue groups. Still, we have the following result: Result 4. A given individual will contribute more to the local public good when member of a red group than when member of a blue group.

4.3

Evolution over time

Contributions in the red groups do not, in contrast to the blue groups, appear to decrease over time. From Proposition 1, we know that contributions should decline over time in groups with sufficiently low warm glow of giving β τ . This pattern is well-known and well21

documented in the literature (Ledyard, 1995). Column (1) of Table 3 shows that this pattern is also found in our data; contributions are lower in later periods, and the F-test shows that this difference is statistically significant. From Figure 2, we see that this is mostly driven by the decline in the blue groups. This is in line with Proposition 3. In specification (2) of Table 3, we investigate this by introducing group type specific period dummies. We see that declining contributions are, indeed, mostly found in blue groups. The interaction term between period and a dummy for being in a red group is substantially and significantly higher in the last periods. Although the contributions are falling in red groups as well, this is only significant at the 10 % level, and the difference between the red and blue groups is significantly increasing over time. This leads us to the following result: Result 5. The difference in contributions between red and blue groups increases over time.

5

Alternative explanations

The theory outlined in Section 2 explained higher contribution in red groups as a result of selection: If some individuals are generally more cooperative than others, these individuals are more likely to donate to the Red Cross and also to make large contributions to their group. However, other explanations to our experimental results could also be envisaged. Choosing red groups is not necessarily motivated by altruism. First, recall that with our experimental design, it is possible that private earnings are higher in red than in blue groups. Self-interested subjects might choose red because they (for whatever reason) expect average contributions to be sufficiently higher in red groups to make this privately profitable. Figure 3 shows the average profit in each group type, as well as the profit in red groups plus the contribution to the Red Cross. One can see that it is never privately profitable to join a red group.24 Thus, this explanation does not seem too plausible. Another reason for choosing red groups could be related to signalling. Some high contributors may prefer to be matched with other high contributors because they dislike the sense of being taken advantage of by free-riders. While earnings in red groups are lower than in blue groups, the utility loss from feeling that one is being taken advantage of may outweigh this difference, even if there is no warm glow of giving to the Red Cross. The cost of contributing to the Red Cross can thus be considered simply a costly signal that one is a high contributor. 24

Contributing 0 yields an average profit of 87 in blue groups and 62 in red groups, and the difference is positive although declining in all periods.

22

Table 3: Contributions by period (1)

2 3 4 5 6 7 8 9 10 F(9,28)

R2 N

(2)

All

Blue

Red

Difference

-1.092 (-0.76) -2.115 (-1.06) -3.276 (-1.59) -3.299 (-1.33) -3.736* (-1.83) -5.276** (-2.34) -6.184** (-2.66) -9.966*** (-3.46) -17.24*** (-6.22)

-2.875 (-1.53) -3.708 (-1.22) -8.500*** (-3.02) -8.583*** (-2.84) -7.271** (-2.39) -8.688*** (-2.97) -10.69*** (-3.78) -17.52*** (-4.56) -23.75*** (-7.77)

1.103 (0.53) -0.154 (-0.07) 3.154 (1.22) 3.205 (1.30) 0.615 (0.30) -1.077 (-0.36) -0.641 (-0.20) -0.667 (-0.25) -9.231** (-2.28)

3.978 (1.40) 3.554 (0.97) 11.65*** (2.83) 11.79*** (3.42) 7.886** (2.15) 7.611* (1.82) 10.05** (2.26) 16.85*** (3.69) 14.52*** (2.84)

5.764*** [0.000]

12.42*** [0.000]

1.927* [0.089]

2.240** [0.050]

0.115 870

0.146 870

Notes: Dependent variable is contribution. Both specifications include individual fixed effects. Specification (1) includes dummies for each period in the partner game. Specification (2) includes separate period dummies for members of red and blue groups. The last column indicates the difference between the estimated coefficients. F(9,28) is a F-test of no time varying coefficients with p-values in square brackets, and tvalues clustered at the group level are reported in parentheses. *, **, and *** denote significance at the 10%, 5%, and 1% levels.

23

100

120

Profit

140

160

Figure 3: Average profit by group type

0

10

20

30

Period Blue

Red

Red and Red Cross

Notes: Red and Red Cross is average personal profit pluss NOK 50 given to the Red Cross. Data from mixed groups are excluded. To distinguish this possible explanation from that of correlated contribution behavior and self-selection, we conducted a placebo version of the experiment described in Section 3. The placebo treatment is identical to the experiment described above, except that subjects in red groups no longer donate to the Red Cross. As before, there is an extra private gain of NOK 50 by joining a blue groups; a such extra gain is given neither to members of red groups nor to the Red Cross. The NOK 50 loss by joining a red group could thus still act as a signalling device, but would no longer be of particular interest to agents who value charitable giving. We conducted two sessions with a total of 39 participants and 13 groups. Figure 4, which mimics Figure 1, shows the groups that formed and the individual choices. There were very few red groups. In the partner game there were no red groups; one blue group, however, was mixed. In the stranger game, there were sometimes one and once two red groups. This is obviously because few participants opted for red groups. In the partner game there was a single person choosing a red group, and in most of the stranger game at most one or two players chose red. This lack of enthusiasm for red groups is a first indication that their function is not mainly that of a signalling device. The next question we need to ask is whether contributions in red groups were higher than in blue group in this version of the experiment. As there were no red groups in the partner 24

10 5

Blue groups

0

Number of groups

13

Figure 4: Group choice by period in placebo experiment

10

20

30

20

30

.75 .25

.5

Blue

0

Fraction of agents

1

1

1

10 Period

Notes: The first panel shows the number of red (hatched) and blue (solid) groups by period. Mixed groups in light colors, homogeneous groups in dark colors. The second panel shows the fraction of agents who choose red (hatched) and blue (solid) groups by period. The dark colored areas show the fraction of agents who consistently choose either red or blue groups in all the 20 periods in the stranger game.

25

Table 4: Contribution by group type

Red group Clustered at Game Period dummies R2 Obs

(1)

(2)

3.831 (1.36)

2.432 (0.79)

Group×Period Stranger No 0.000986 780

Group×Period Stranger Yes 0.0297 780

Notes: The dependent variable is contribution. Z-values clustered at group or group-period level are reported in parentheses. *, **, and *** denote significance at the 10%, 5%, and 1% levels. game, this question cannot be answered for this part of the experiment. In the stranger game, however, we can analyze it. Table 4 replicates the analyzes from Columns (3) and (4) of Table 2 in this version of the experiment. Whereas members of red groups contributed about NOK 21 more than members of blue groups in the original version of the experiment, the difference is now only about NOK 3, and this number is not significantly different from zero at any conventional level of significance.25 This implies that there are no signs of higher contributions in red groups in the placebo version of the experiment, so there is no evidence of red groups being used successfully as signaling devices in this case.

6

Conclusion

The ability to sustain high contributions to local public goods is important for many types of groups. One important example is firms whose production is characterized by unobservable teamwork effort. In this paper we have shown, theoretically and experimentally, that groups may use costly social responsibility measures, such as a commitment to charity donations, as a device to attract more cooperative individuals. Conditional cooperation, if present, will reinforce the initial effect of such self-selection. Our predictions were tested by means of a public good game with endogenous group formation. Before making their contribution choice, subjects could choose which type of group they preferred to be a member of. The difference between group types was that a fixed extra 25

The reduction in the level of significance is mostly due to the lower coefficient, although the standard error is also increased.

26

amount of money was donated either to the Red Cross (red groups) or to individual subjects (blue groups). Throughout the periods, the share of red groups was always between 30 and 45 percent, with no clear trend in either direction. High contributors in an initial one-shot public good game with exogenous groups were significantly more likely than others to choose red groups in subsequent parts of the experiment. Average contributions were significantly higher in red groups, although not high enough to make red group membership as profitable as blue group membership. Moreover, while contributions in blue groups decreased substantially over time, contributions stayed high in the red groups. In line with previous experimental evidence, we thus have shown both theoretically and empirically that it is possible to sustain cooperation provided that the group consists of the right people: “the good guys”. In addition, we have shown that pre-commitment to charitable giving is one possible way for these good guys to find each other. Our theoretical model assumes that some individuals are generally more cooperative than others. The experimental findings presented here are consistent with this hypothesis. If correct, this idea has several interesting implications; one of them is that corporate social responsibility may pay off because it attracts responsible employees who work harder when not monitored. To our knowledge, however, this is the first attempt within experimental economics to test explicitly for correlated cooperativeness. Achieving a thorough understanding of the possible existence and implications of correlated cooperativeness requires, obviously, further studies.

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Brekke, K. A., K. Nyborg, and M. Rege. 2007. “The Fear of Exclusion: Individual Effort when Group Formation is Endogenous.” Scandinavian Journal of Economics 109 (3):531– 550. Brekke, Kjell Arne, Karen Evelyn Hauge, Jo Thori Lind, and Karine Nyborg. 2009. “Playing with the good guys. A public good game with endogeneous group formation.” CESifo Working Paper 2647. Brekke, Kjell Arne and Karine Nyborg. 2008. “Attracting Responsible Employees: Green Production as Labor Market Screening.” Resource and Energy Economics 30:509–526. Brekke, Kjell Arne, Karine Nyborg, and Snorre Kverndokk. 2003. “An economic model of moral motivation.” Journal of Public Economics 87:337–3354. Cornes, Richard and Todd Sandler. 1986. The Theory of Externalities, Public Goods, and Club Goods. New York: Cambridge Unversity Press. Croson, R. 2007. “Theories of Commitment, Altruism and Reciprocity: Evidence from Linear Public Goods Games.” Economic Inquiry 45:199–216. Croson, R., E. Fatas, and T. Neugebauer. 2006. “Reciprocity, Matching and Conditional Cooperation in Two Public Goods Games.” Economics Letters 87:95–101. Croson, Rachel T. A. 1996. “Partners and strangers revisited.” Economics Letters 53 (1):25– 32. Ehrhart, Karl-Martin and Claudia Keser. 1999. “Mobility and cooperation: On the run.” Working Paper 99s-24, CIRANO, Montreal. Fehr, Ernst and Simon G¨achter. 2000. “Cooperation and Punishment in Public Goods Experiments.” The American Economic Review 90 (4):980–994. ———. 2002. “Altruistic punishment in humans.” Nature 415 (6868):137–140. Festinger, L. 1957. A Theory of Cognitive Dissonance. Stanford, CA: Stanford University Press. Fischbacher, Urs. 2007. “z-Tree: Zurich toolbox for ready-made economic experiments.” Experimental Economics 10 (2):171–178. Fischbacher, Urs and Simon G¨achter. 2006. “Heterogeneous social preferences and the dynamics of free riding in public goods.” IZA Discussion Papers 2011. 28

———. forthcoming. “Social Preferences, Beliefs, and the Dynamics of Free Riding in Public Goods.” American Economic Review . Fischbacher, Urs, Simon G¨achter, and Ernst Fehr. 2001. “Are people conditionally cooperative? Evidence from a public goods experiment.” Economics Letters 71:397–404. G¨achter, Simon and Christian Th¨oni. 2005. “Social learning and voluntary cooperation among like-minded people.” Journal of the European Economic Association 3 (2-3):303– 314. Gunnthorsdottir, Anna, Daniel Houser, and Kevin McCabe. 2007. “Disposition, history and contributions in public goods experiments.” Journal of Economic Behavior and Organization 62 (2):304–315. ¨ ur, Bernd Irlenbusch, and Bettina Rockenbach. 2006. “The competetive AdvanG¨ urerk, Ozg¨ tage of Sanctioning Institutions.” Science 312:108–111. Hartshorne, H. and M.A. May. 1929. Studies in the Nature of Character, Studies in Service and Self-Control, vol. 2. New York: Macmillan. Hauge, Karen Evelyn. 2009. “Eliciting moral ideals in a public good game experiment.” In Morality and economic decisions: An experimental approach. PhD dissertation submittet to the University of Oslo. Holmstr¨om, Bengt. 1982. “Moral Hazard in Teams.” Bell Journal of Economics 13:324–340. Johnson, Norman L. and Samuel Kotz. 1972. Distributions in Statistics: Continuous Multivariate Distributions. New York: John Wiley & Sons. Johnson, Tim, Christopher T. Dawes, James H. Fowler, Richard McElreath, and Oleg Smirnov. 2009. “The role of egalitarian motives in altruistic punishment.” Economics Letters 102:192–94. Keser, Claudia and Frans van Winden. 2000. “Conditional Cooperation and Voluntary Contributions to Public Goods.” Scandinavian Journal of Economics 102 (1):23–39. Konow, James. 2009. “Mixed Feelings: Theories and Evidence of Altruism.” Mimeo, Loyola Marymount University. Ledyard, John O. 1995. “Public goods: A Survey of Experimental Research.” In The Handbook of Experimental Economics, edited by John H. Kagel and Alvin E. Roth. Princeton, New Jersey: Princeton University Press, 111–194. 29

Neugebauer, Tibor, Javier Perote, Ulrich Schmidt, and Malte Loos. 2009. “Selfish-biased conditional cooperation: On the decline of contributions in repeated public goods experiments.” Journal of Economic Psychology 30:52–60. Nyborg, K. and M. Rege. 2003. “Does Public Policy Crowd Out Private Contributions to Public Goods?” Public Choice 115 (3):397–418. Ones, Umut and Louis Putterman. 2007. “The ecology of collective action: A public goods and sanctions experiment with controlled group formation.” Journal of Economic Behavior and Organization 62 (4):495–521. Page, Talbot, Louis Putterman, and Bulent Unel. 2005. “Voluntary Association in Public Goods Experiments: Reciprocity, Mimicry and Efficiency.” The Economic Journal 115 (October):1032–1053. Piliavin, J. A. and H-W. Charng. 1990. “Altruism: A Review of Recent Theory and Research.” Annual Review of Sociology 16:27–65. Scotchmer, Suzanne. 2002. “Local Public Goods and Clubs.” In Handbook of Public Economics, vol. 4, edited by A. J. Auerbach and M. Feldstein. Amsterdam: Elsevier, 1997– 2042. Sugden, Robert. 1984. “Reciprocity: The supply of Public Goods Through Voluntary Contributions.” The Economic Journal 94 (dec):1281–1302. ¨ Thøgersen, John and Folke Olander. 2006. “To what degree are environmentally beneficial choices reflective of a general conservation stance?” Environment and Behavior 38:550– 568. Zelmer, J. 2003. “Linear Public Good Games: A Meta-Analysis.” Experimental Economics 6:299–310.

30

A A.1

Proofs Proof of Theorem 1

h
0 i Assume first (bi , yi )0 ∼ N µb , µy , Σ . Then it follows from standard results on conditional normal distributions (see e.g. Johnson and Kotz, 1972, Ch 35.3) that   
σ 212 σ 12 2 bi |yi = Y ∼ N µb + 2 Y − µy , σ 1 − 2 σ2 σ2 where σ 21 σ 12 σ 12 σ 22

Σ=

!

Hence bi |yi > Y has a distribution function Z+∞

fY+ (b) =

x=Y

  
  x−µ b − µb + σσ122 x − µy φ σ2 y  2  dx q 2 2 φ Y −µy σ 2 12 1 − Φ σ 1 − σ2 σ 22 

2

whereas bi |yi < Y has a distribution function 

ZY

fY− (b) =

φ x=−∞



σ 12 σ 22

b − µb + x − µy q σ2 σ 21 − σ122


  

2

φ



x−µy σ 22

Φ



Y −µy σ 22

  dx

where φ and Φ denote the pdf and cdf of the standard normal distribution. Hence the former Rz − stochastically dominates the latter if −∞ fY− (b) − f−∞ (b) db > 0 for all z, which holds when

Z+∞

ZY

Zz

x+ =Y x− =−∞ b=−∞

  
 
  b − µb + σσ122 x− − µy b − µb + σσ122 x+ − µy φ   − φ  db q 2 2 q 2 2 σ σ 12 2 2 12 σ 1 − σ2 σ 1 − σ2  

2

2

(17) φ



× 1−Φ

x−µy σ 22





Y −µy σ 22



φ



x−µy σ 22

Φ



Y −µy σ 22

  dx− dx+ > 0.

31

As we always have x− < x+ , Zz b=−∞

  
 
  b − µb + σσ122 x+ − µy b − µb + σσ122 x− − µy  − φ  db > 0. q 2 2 q 2 2 φ σ σ 12 2 2 12 σ 1 − σ2 σ 1 − σ2 

2

2

It follows that (17) always holds, and hence that bi |yi > Y , will stochastically dominate bi |yi < Y . It trivially follows that we can replace yi and Y with θi = g (yi ) and ˆθ = g (Y ) for any monotonically increasing function g, so bi |red stochastically dominates bi |blue. Finally stochastic dominance is preserved by monotonically increasing relations, so β i |red stochastically dominates β i |blue for β i = h (bi ) for any monotonically increasing function h.

A.2

Proof of footnote 16

Suppose that the claim t

gˆRt+1

−

gˆBt+1

1−λX ¯ (β (ˆ g s ) − β¯ B (ˆ gBs )) = α s=1 R R

holds for t + 1 ≤ k. We want to show that it holds for t + 1 = k + 1 as well. Note first that the average contribution is given by g¯τt = gˆτt +

β¯ R (ˆ gRt ) n − M − for τ ∈ {R, B} α nα

so


β¯ (ˆ g t ) − β¯ B (ˆ gBt ) g¯Rt − g¯Bt = gˆRt − gˆBt + R R α Combining the two equations above with equation (8), we find that

gˆRk+1 − gˆBk+1 = (1 − λ) g¯Rk − g¯Bk + λ gˆRk − gˆBk  
β¯ R (ˆ
gRk ) − β¯ B (ˆ gBk ) k k = (1 − λ) gˆR − gˆB + + λ gˆRk − gˆBk α
1−λ ¯ gBk )) + gˆRk − gˆBk = (β R (ˆ gRk ) − β¯ B (ˆ α k 1−λX ¯ = (β R (ˆ gRs ) − β¯ B (ˆ gBs )) α s=1 Since we know from the text that the claim is true for k = 2, the general claim follows by induction.

32

A.3

Details of group choice when ideals depend on group type

Proposition 5. Individuals are more likely to choose red groups the higher the observed t t difference in contributions g¯iR − g¯iB . Utility will be ( uti =

t+1 2 Y + θi + M (n − 1)¯ gRt + (β i − n−M )gi − α2 (git+1 − gˆiR ) if τ i = R n n t+1 2 M α t+1 n−M t Y + D + n (n − 1)¯ gB + (β i − n )gi − 2 (gi − gˆiB ) if τ i = B

Inserting the optimal contribution git

=

t gˆiτ

1 + α

  n−M βi − n

we see that i will chose red if θi

 

M n−M t t t t ≥ D + (n − 1) g¯iB − g¯iR + β i − giB − giR n n  

M n−M t t t t gˆiR = D − (n − 1) g¯iR − g¯iB − β i − − gˆiB . n n

Note that individual i is more likely to choose red the higher the difference in contributions t t ) is, as claimed in Proposition 6. − g¯iB (¯ giR The condition can also be rewritten as
n−M t

M t t t gˆiR − gˆiB θi + β i gˆiR − gˆiB ≥ D − (n − 1) g¯Rt − g¯Bt + n n In expectations gˆRt > gˆBt , and thus we see that both a high θi as well as a high value of β i increase the likelihood that individual i will choose the red group. We can thus expect a high value of β i in red groups both because of the correlation with θi but also due to the direct impact of β i . The intuitive reason why β i enters directly here is that those with a high β i have an additional motive to enter a group where they will be expected to make high contribution, and that is the warm glow they derive from high contributions. This only matters when expected contributions are different between different group types.

B

Instructions

Welcome to this experiment in economics. The results from this experiment will be used in a research project. Therefore, it is important that you follow certain rules. It is important 33

that you do not talk or in other ways communicate with any of the other participants during the experiment. Please turn off mobile phones, and use only pre-opened software on the computer. In the experiment, there will be full anonymity, which means that no other participants in this room will know which decisions you in particular make during the experiment. In addition, it is not possible to track the decisions made during the experiments back to individuals. You will be notified when the experiment starts, and when you can start entering your answers on the computer in front of you. If you have any questions during the experiment, please raise your hand, and an experimenter will come to you and answer your question in private. You will receive money in compensation for participating in this experiment. How much money you receive will depend on the decisions you make during the experiment. After the experiment is over, you will be informed about your total payment. The person who organizes the practical payments will not now the details of the experiment and can therefore not know which decisions you have made.

Instructions Part 1 This experiment consists of three parts. Your choices in part 1 will not influence what happens, or what payment you can receive from part 2 and 3. In part 1 of the experiment, you will be part of a group consisting of 3 people (yourself and 2 others). All three members of the group will receive an endowment of 60 NOK each. Your task is to decide how you want to allocate the money. You shall choose how many NOK you want to keep, and how much you want to contribute to an account which belongs to your group. Your compensation for participating in the experiment, depends on how much of the endowment you choose to keep, how much you contribute to the group account, and how much the others in your group contribute to the group account. When all members of your group have decided how they wish to contribute to the group account, the total amount contributed to your group’s account will be doubled and then divided equally between the three of you. For each NOK you keep, you (and only you) will earn 1 NOK. For each NOK you contribute to the group account, you and all the others in your group will earn 2/3 NOK. The same applies for the others in your group. Examples: If for instance you contribute all your 60 NOK to the group account and the others in your group keep all for themselves, you will be paid 40 NOK (2/3 x the 60 NOK you contributed to the group account =40), while the two others will be paid 100 NOK each (the 60 NOK they kept + 2/3 x the 60 NOK you contributed to the group account). If

34

all three group members contribute the entire endowment to the group account, each group member will be paid 120 NOK each (2/3 x 3 x 60 =120 NOK). If all three group members contribute 30 NOK, each group member will be paid 90 kroner each (the 30 NOK kept, plus 2/3 x 3 x 30 NOK = 60 NOK to each from the group account). If all three contribute zero to the group account, all three are paid the initial endowment of 60 kroner. Notice that what happens in your group does not influence participants in other groups. Likewise, the decisions of participants in other groups than your own does not influence you. It is important for the results of the experiment that there are no misunderstandings of the instructions. To ensure that the instructions are clear, we ask you to fill in the question sheet on the desk in front of you. This is not a test of your knowledge, but insurance for us that we have given you clear instructions. You will now get a couple of minutes to read through the instructions and answer the questions on the sheet. Raise your hand when you are finished, or if you have any questions.

Instructions Part 2 The experiment will now continue. Your decisions in part 2 will not influence what happens or the payment you can receive in part 3. Part 2 of the experiment is quite similar to part 1. In difference from part 1, there are now first choose the type of group you prefer being a member of: X or Z. When all participants have chosen their preferred group type, the computer will randomly create groups of 3 according to preferred group type. If the number of participants preferring one type is not divisible by three, there will be one mixed group. The type of the mixed group will be decided by the majority wish of the mixed group. All participants in all groups will be informed about what kind of group they are members of, and whether it is a homogenous or a mixed group. Part 2 consists of 10 periods. Your actual payment from part 2 will consist of your average payoff across these 10 periods. The group composition will be the same in all periods, and your group will NOT consist of the same individuals as in part 1 of the experiment. In each period each participant will receive an endowment of 60 NOK. Just as in part 1, your task is to decide how many NOK to keep, and how many NOK to contribute to the group account. After each period, you will receive feedback concerning how many units you yourself contributed to the group account, how many units the other two in your group on average contributed to the group account, and your calculated payoff from that period. Just like before, the total amount in the group account will be doubled, and then divided equally between the three group members. Your

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actual payoff from part 2 will be the average of your calculated payoffs from the 10 periods of part 2. What is the difference between the group types? Group type X: Those organizing the experiment have inserted an extra amount of money into the group account in advance, such that each participant in every X-group will receive an extra payoff of 50 NOK per period Group type Z: Here there is no extra payoff to the participants. Instead, those that organize the experiment in each period for each participant in each Z-group will reserve 50 NOK to the Norwegian Red Cross. Just as your payoff is the average of your calculated payoff over the 10 periods, the actual payment to the Red Cross will be equal to the average of the reserved for the Red Cross over the 10 periods. Again we ask you to fill in a sheet of questions. The sheet will be handed out, and you will get some minutes to read through the instructions on your own, and answer the questions. Raise your hand when you are finished, or if you have any questions.

Instructions Part 3 In this last part of the experiment there are 20 periods. In this part you will be able to choose group type between every period. In each period you will be part of a new group. Otherwise the rules are as they were in part 2. After every period you will receive feedback about your calculated payoff from the previous period, and how many units were contributed to the group account on average in your group. You will also be told how many units on average was contributed to the group account in one X- and one Z-group, and the average calculated payoff for the members of these two groups. The rules for payoff are as before: Contributions from group members are doubled and then divided equally between the group members. In X-groups each member will in addition receive a calculated payoff of 50 kroner each in each period. In Z-groups 50 kroner for each member in each period is reserved for the Red Cross. From part 3 your actual payoff is equal to the average of your calculated payoff in the 20 periods. The Norwegian Red Cross will receive an amount equal to the average of what is reserved over the 20 periods.

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