Leading with(out) sacrifice? A public-goods experiment with a privileged player.

Glockner, Andreas ; Irlenbusch, Bernd ; Kube, Sebastian 等

I. INTRODUCTION

Suppose several academics are working together on a research project: providing input to the joint project usually much resembles contributing to a public good, and therefore reciprocity and conditional cooperation may affect the team members. But now assume that, for a certain team member, working on the project pays privately. For example, this researcher might have to accomplish a task required for the project (e.g., gathering data or acquiring knowledge about a new research method) for some closely related and profitable consultancy work anyway. How will the collaborators on the project respond to the work input of this team member? Will they regard it as an example to follow or rather neglect any reciprocity motive because of the private profitability of the work?

We analyze this situation by introducing a public-goods experiment where one privileged player (1) has a higher marginal per capita rate of return (MPCR) from the public good than have the other players. In our baseline treatment, the privileged player has an MPCR larger than one, that is, he/she has a net benefit from contributing to the public good. (2) In the other treatment, the privileged player has a high per capita rate, but the rate is smaller than one, such that contributions are relatively cheap for this player but still constitute a sacrifice.

Our data show that the presence of a privileged player with an MPCR smaller than one has a positive impact on the contributions of the other players. However, if the privileged player has an MPCR larger than one, the other group members contribute less than they do in the first treatment. This is striking as the privileged players with an MPCR larger than one contribute almost their entire endowments.

The results contribute to the literature on conditional cooperation, reciprocity, and leadership. There is substantial evidence that subjects are conditional cooperators, that is, they cooperate only if other players of the group do the same (Fischbacher, Gachter, and Fehr 2001). This robust finding has initiated public-goods experiments in which group members choose sequentially. Some player becomes the first mover--either voluntarily or exogenously imposed--who can give a positive example to the other group members (Clark and Sefton 2001; Gachter and Renner 2003; Guth et al. 2007; Levati, Sutter, and van der Heijden 2007; Potters, Sefton, and Vesterlund 2005, 2007). These studies find that participants indeed reciprocate to first movers who provide an example. A recent study compares cooperation in normal and privileged groups in simultaneous-move public-good games with and without punishment (Reuben and Riedl 2009). Consistent with our findings, the increased contributions of players with an MPCR larger than one are not necessarily reciprocated by other players. This can be due to the fact that other players take into account intentions and that the high contributions of the privileged player with an MPCR larger than one are interpreted as a merely selfish act. In line with this interpretation, leadership research suggests that self-sacrifice might be a crucial mediating factor to generate increased cooperation and reciprocity.

In hypothetical public-good scenarios, it has been shown that leaders' nonmonetary sacrifices increase cooperation (De Cremer and van Knippenberg 2002; see also Choi and Mai-Dalton 1998) and, particularly, if distributive justice is low (De Cremer, van Dijke, and Bos 2004). Elaborating on these findings, we are the first to show that, in a public-good situation with different MPCRs, a privileged player's sacrifice considerably supports the emergence of reciprocating behavior in other players.

II. THE EXPERIMENT

A. Experimental Design In our experiment, subjects participate in two x ten periods of a typical linear public-goods game in constant groups of four players with a surprise restart (3) after Period 10. Each group consists of one player of Type A and three players of Type B. The subjects' types are randomly determined at the beginning and kept constant throughout the experiment. Players interact anonymously, but player types are common knowledge.

Players receive an endowment of 20 tokens per period and simultaneously decide how to share this endowment between their private and a joint group account. Subsequently, they are informed about the individual contributions of each player in the group and their own payoff. Players receive one point for each token they put in their private account. Additionally, all players in the group earn points for each token that is put in the group account either by themselves or by any other player. Players of Type B receive 0.4 points per group account token. The MPCR for players of Type A differs across treatments: in our baseline treatment IT 1.4] their MPCR equals 1.4, whereas it is 0.9 in our sacrifice treatment [T 0.9]. Consequently, player i's individual period payoff, [[pi].sub.i], equals

(1) [[pi].sub.i] = [e.sub.i] - [g.sub.i] + (0.4 + [[delta].sub.i]) [summation over (j)][g.sub.j]

where [e.sub.i] denotes player i's endowment, [g.sub.i] player i's contribution to the joint group account, and [[delta].sub.i] equals 1/2 if player i is of Type A in [T 0.9], [[delta].sub.i] equals 1 if player i is of Type A in the [T 1.4], and 0 otherwise. The computerized experiments (4) were conducted at the EconLab at the University of Bonn in December 2007. We ran 4 sessions with a total of 21 matching groups (84 subjects), leaving us with 10 independent observations in treatment [T 0.9] and 11 independent observations in treatment [T 1.4]. At the beginning of each session, instructions were distributed and read out aloud. (5) Afterwards, participants could pose clarifying questions in private and had to answer a set of control questions to ensure that everybody had understood the game. A session lasted for about 45 min. Points earned were accumulated over all periods and converted at an exchange rate of 1 [euro] per 85 points. Subjects earned on average 10.93 [euro] (SD 1.78 [euro]) including a show-up fee of 4 [euro].

B. Behavioral Predictions

In our sacrifice treatment [T 0.9], zero contributions are the unique subgame-perfect Nash equilibrium in each stage game of the finitely repeated linear public-goods game, if one assumes players who are rational and only interested in their own monetary payoff. Also players of Type B in the baseline treatment [T 1.4] contribute nothing in the Nash equilibrium. Due to the MPCR being greater than one, Type-A players in IT 1.4] have a dominant strategy to contribute their entire endowment to the public good. Thus, under standard assumptions, we should expect to observe a treatment effect only in the decision of Type-A players.

Once we move away from the standard assumptions and introduce, for example, reciprocity or conditional cooperation, B players' behavior might also be affected by the treatment manipulation. The high contributions of the privileged player A in [T 1.4] could possibly motivate them to cooperate and contribute a substantial amount, too. However, if it is not A's contribution per se that matters, but rather the assumed underlying motivation, the incentive structure in [T 1.4] might hamper conditional cooperation--simply because high contributions of player A cannot be identified as being a clearly cooperative action. As a consequence, Type-B players might then be unsure about whether to reciprocate or not. In fact, contributions by player A in [T 1.4] would not necessarily be seen as a nice act in reciprocity models like Rabin (1993) and Levine (1998). Models of inequity aversion concerning earnings (Bolton and Ockenfels 2000; Fehr and Schmidt 1999) make a similar prediction. Although contributions of the A player in [T 0.9] change the differences in payoffs between A and B players to the advantage of the B players, A players' contributions in [T 1.4] leave the payoff differences unaffected. In [T 1.4], full contribution of the Type-A player and complete free-riding of the Type-B players, for example, leads to equal earnings for all players (i.e., 28 tokens). In [T 0.9] for each contributed unit of an A player symmetric contributions of 0.2 by each of the three Type-B players are needed to equalize the payoff of all players. For example, a full contribution of 20 of Type-A player and contributions of 4 for each Type-B player leads to equal payoffs. Therefore, inequality may cause some (rather small) contributions by Type-B players in [T 0.9]. However, the social benefits of contribution of player B are higher in [T 1.4], so unconditional altruism or concerns for efficiency would point in the direction of higher contributions of B players in the baseline treatment [T 1.4].

[FIGURE 1 OMITTED]

C. Results

Figure 1 illustrates the average contributions in both treatments and for both types of player types (for average contributions per groups and periods, see Appendix Table 1). The effect of increasing the MPCR of player

A is strong and significant. When their MPCR equals 1.4 instead of 0.9, they contribute on average about 50% (40%) more in the first (second) phase of the experiment (rank sum test, p = 0.02 and p = 0.01, one-sided). (6) The difference remains stable and significant over time (cf. Table 1).

In contrast, the contributions of Type-B players are higher in the presence of a privileged player with an MPCR smaller than one. Compared with treatment [T 1.4], Type-B players contribute approximately 34% (93%) more to the public good in the first (second) phase of treatment [T 0.9]. Except for the beginning, this difference reaches significance over time (e.g., p < 0.05, rank sum test on Periods 11-20, cf. Table 1).

The tendency of higher contributions from B players in IT 0.9] is despite the fact that Type A players contribute more in [T 1.4] than in [T 0.9]. Our data thus suggest that the unambiguousness of A's motivation to contribute is an important factor for conditional cooperation.

This can also be seen by calculating the Spearman correlation between Type-B players' average contributions and Type-A players' contributions in the previous period for each independent group separately, and then comparing the coefficients between treatments. (7) This descriptive measure of the reaction of B players' to A's behavior equals 0.18 in [T 0.9] and -0.07 in [T 1.4], the difference being significant (rank sum test, p = 0.04, two-sided). Correspondingly, after the A player has contributed more than zero in the previous period, the mean contribution of B players is 6.1 in the sacrifice treatment [T 0.9], but only 3.7 in the baseline treatment [T 1.4]. In both treatments, B players' contributions are more in line with the average contributions of the other B players in the previous period (the average Spearman correlation coefficient is 0.27 in both treatments). Notice that in [T 0.9] B players' contributions in Periods 1-10 (Periods 11-20) are on average 184% (155%, respectively) higher than symmetric Bs' contributions yielding equal payoffs among both types of players.

Additional evidence for our hypothesis that contributions of Type-A and Type-B players are interdependently related in [T 0.9], but not in [T 1.4], can be shown by calculating the Spearman correlation between Type-A players' average contributions and Type-B players' contributions in the previous period; this descriptive measure of the reaction of Type-A players to Bs' behavior equals 0.21 in [T 0.9] and 0.09 in [T 1.4]. (8) Thus, it seems that there is positive reinforcement of contributions in [T 0.9] imposing some kind of leadership on Type-A players; contributions by those players trigger Type-B players' contributions in the consecutive period, while this response again causes positive reciprocity by the Type-A players. However, in [T 1.4], there is little evidence for the positive reinforcement of contributions.

In treatment [T 0.9], we observe a typical restart effect, that is, contribution levels in Periods 1 and 11 are virtually the same. This is true for both player types. Yet, in treatment [T 1.4], although A players' contributions are relatively stable during the first ten periods, Type-B players exhibit a less cooperative attitude; in the second phase they start at a lower level than in the first phase (signed rank test, p = 0.07, two-tailed, on average 7.94 in Period 1 and 4.88 in Period 11).

Total contributions to the public good do not differ between treatments (rank sum test, p = 0.95 for the first ten periods, on average 28.2 in [T 0.9] and 28.8 in [T 1.4] and p = 0.48 for the last ten periods, 27.6 in [T 0.9] and 26.8 in [T 1.4], both two-sided). Thus, the higher contributions of players A in [T 1.4]--due to the higher MPCR--are compensated by higher contributions of players B in [T 0.9]. Note that this ultimately depends on our parameterization of having only three B players. The difference in contributions would probably change to the advantage of [T 0.9] if the number of B players in the group were increased.

III. CONCLUSION

Our results refine the previous evidence on conditional cooperation in public-goods environments and show that others tend to follow a high contributing player if they know that her example requires a sacrifice. However, if contributing can be attributed to a different motive, for example, individual payoff maximization, others feel less inclined to follow the example. In this respect, our findings underline the importance of intentions for cooperation (Blount 1995; Charness 2004; Falk, Fehr, and Fischbacher 2008) in public-goods environments also, confirming the intuition that a sacrifice provides an encouraging signal to followers (Hermalin 1998). Our findings extend and strengthen previous findings from leadership research (De Cremer and van Knippenberg 2002, 2005) by analyzing a standardized environment in which leadership is not just induced by scenario instructions but by differences in players' MPCRs. Arguably, we cannot distinguish between the relative effects of self-sacrifice and inequity aversion. However, if inequity aversion was the main driving force of our results, Type-B players should not contribute more than four tokens in IT 0.9]. As they do contribute more, we consider it unlikely that inequity aversion alone is causing the difference in contributions of B players in [T 0.9] and [T 1.41.

Regarding our introductory example, we conclude that a team member who has a personal motive to contribute, for example, because it privately pays off for her to do so, might be well advised to disguise this fact and present her contributions as costly and truly cooperative choices in order to foster conditional cooperation among her collaborators.

ABBREVIATION

MPCR: Marginal Per Capita Rate of Return

doi: 10.1111/j.1465-7295.2010.00314.x

APPENDIX

Instructions for the Experiment

(Treatment variations are indicated with {})

General Introductory Information

* Each participant is endowed with a starting capital of 340 points credited on his private account independent from the behavior in the experiment.

* The experiment consists of two parts. In the following, the course of action of the first part is explained. The instructions of the second part will be handed out later.

Part 1

Course of Action

* During Part 1, you belong to a group consisting of four participants. The identity of the other participants remains unknown to you. The composition of the group does not change. During Part 1 of the experiment you will exclusively interact with the participants in your group.

* In each group, there are two roles: one Type-A player and three Type-B players. The roles will be randomly awarded at the beginning and do not change.

* Part 1 consists of ten periods.

As soon as you know your type, please write the type into the following box:

[ILLUSTRATION OMITTED]

Contribution to the Common Project. In each period, each group member receives an endowment of 20 points. You have to decide how many of the 20 points you want to contribute to a common project. You can keep the remaining points.

Calculation of the Payoff of a Type-A Player in One Period. In a period your payoff consists of two components:

* tokens you keep = endowment--your contribution to the project;

* earnings from the project = 1.4 {0.9} x sum of the contributions of all group members.

Thus, if you are a Type-A player, your payoff is: 20 - your contribution to the project ++ 1.4 {0.9} x sum of the contributions of all group members.

Calculation of the Payoff of a Type-B Player in One Period.

In a period your payoff consists of two components:

* tokens you keep = endowment - your contribution to the project;

* earnings from the project = 0.4 x sum of the contributions of all group members.

Thus, if you are a Type-B player, your payoff is: 20 - your contribution to the project + 0.4 x sum of the contributions of all group members.

Information at the End of a Period. At the end of a period, you will receive an overview of the contributions of each player in the current period.

Total Payoff. The total payoff from the experiment is composed of the starting capital of 340 points plus the sum of payoffs from all ten periods. At the end of the experiment, your total payoff will be paid out to you, with an exchange rate of 1 [euro] per 85 tokens.

Please Notice. Communication is not allowed during the whole experiment. If you have any questions, please raise your hand. All decisions are made anonymously, that is, no other participant is informed about the identity of someone who made a certain decision. The payment is anonymous too, that is, no participant gets to know the payoff of another participant.

Part 2

Groups and Roles

* You belong to the same group as in Part 1. Also, during Part 2 of the experiment, you will exclusively interact with the participants in your group.

* You have the same role as in Part 1.

Periods and Course of Action in a Period

* Part 2 also consists of ten periods.

* In each period in Part 2, you also have to decide about your contribution to the common project.

* The calculations of payoffs and the information at the end of a period are also the same as in Part 1 of the experiment.

* The payoff of a period is again added to your total payoff.

APPENDIX TABLE A1
Average Contributions by Group and Periods

 1-10
 Period
 Type A 0.9 A 1.4 B 0.9 B 1.4

Group 1 9 18 7.3 7.6
 2 13.3 12.1 3.6 5.6
 3 7 20 7.3 8.9
 4 11.8 20 10.5 9.7
 5 16 7.7 5.2 0.4
 6 14.7 16.9 3.4 2.8
 7 4.5 17.9 8.3 2.6
 8 17.2 5.1 6.4 3.8
 9 10.9 19.3 2.8 0.6
 10 0 20 4.4 4.6
 11 16 1.4

 11-20
 Period
 Type A 0.9 A 1.4 B 0.9 B 1.4

Group 1 9.6 19 5.6 7.3
 2 12.4 14.7 4.1 2.3
 3 9.6 20 8.7 1.6
 4 8.5 20 4.7 6.3
 5 8 15.6 2.7 0.1
 6 18 19.9 7.8 3.9
 7 3.1 19.4 4.4 0.1
 8 18.8 8.9 2.9 3.6
 9 14.4 19.7 3.9 0
 10 7.2 20 10.6 7.4
 11 16 0.1

REFERENCES

Andreoni, J. "Why Free Ride? Strategies and Learning in Public-Goods Experiments." Journal of Public Economics, 37, 1988, 291-304.

Blount, S. "When Social Outcomes Aren't Fair: The Effect of Causal Attributions on Preferences." Organizational Behavior and Human Decision Process, 63, 1995, 131-44.

Bolton, G. E., and A. Ockenfels. "'ERC: A Theory of Equity, Reciprocity, and Competition." American Economic Review, 90, 2000, 166-93.

Charness, G. "Attribution and Reciprocity in an Experimental Labor Market.'" Journal of Labor Economics, 22, 2004, 665-88.

Choi, Y., and R. R. Mai-Dalton. "On the Leadership Function of Self-Sacrifice." Leadership Quarterly, 9, 1998, 475 501.

Clark, K., and M. Sefton. "The Sequential Prisoners Dilemma: Evidence on Reciprocation." Economic Journal, 111, 2001.51-68.

Croson, R. "Partners and Strangers Revisited." Economic Letters, 53, 1996, 25-32.

De Cremer, D., M. van Dijke, and A. Bos. "Distributive Justice Moderating the Effects of Self-Sacrificial Leadership." The Leadership & Organization Development Journal, 25, 2004, 466-75.

De Cremer, D., and D. van Knippenberg. "How Do Leaders Promote Cooperation? The Effects of Charisma and Procedural Fairness." Journal of Applied Psychology, 87, 2002, 858-66.

--. "Cooperation as a Function of Leader Self-Sacrifice, Trust, and Identification." Leadership & Organization Development Journal, 26, 2005, 355-69.

Falk, A., E. Fehr, and U. Fischbacher. "Testing Theories of Fairness--Intentions Matter." Games and Economic Behavior, 62, 2008, 287-303.

Fehr, E., and K. M. Schmidt. "A Theory of Fairness, Competition, and Cooperation." The Quarterly Journal of Economics, 114, 1999, 817-68.

Fischbacher, U. "z-Tree: Zurich Toolbox for Ready-Made Economic Experiments." Experimental Economics, 10, 2007, 171-78.

Fischbacher, U., S. Gachter, and E. Fehr. "Are People Conditionally Cooperative? Evidence from a Public Goods Experiment." Economics Letters, 71, 2001, 397 -404.

Gachter, S., and E. Renner. "Leading by Example in the Presence of Free-Rider Incentives." Paper presented at a Conference on Leadership, Lyon, France, March 2003.

Greiner, B. "An Online Recruitment System for Economic Experiments," in Forschung und Wissenschafiliches Rechnen 2003. GWDG Bericht, Vol. 63, edited by K. Kremer and V. Macho. Goettingen: Gesellschaft fuer Wissenschaftliche Datenverarbeitung, 2004, 79-93.

Gtith, W., V. Levati, M. Sutter, and Eline van der Heijden. "Leading by Example with and without Exclusion Power in Voluntary Contribution Experiments." Journal of Public Economics, 91, 2007, 1023 42.

Hermalin, B. "Toward an Economic Theory of Leadership:

Leading by Example." American Economic Review, 88, 1998, 1188-206.

Levati, V., M. Sutter, and E. van der Heijden. "Leading by Example in a Public Goods Game with Heterogeneity and Incomplete Information." Journal of Conflict Resolution, 51, 2007, 793-818.

Levine, D. "Modeling Altruism and Spitefulness in Experiments." Review of Economic Dynamics, 1, 1998, 593-622.

Olson, M.. The Logic of Collective Action. Cambridge: Harvard University Press, 1980 (1965).

Potters, J., M. Sefton, and L. Vesterlund. "After You--Endogenous Sequencing in Voluntary Contribution Games." Journal of Public Economics, 89, 2005, 1399-419.

--. "Leading-by-Example and Signaling in Voluntary Contribution Games: An Experimental Study." Economic Theory, 33, 2007, 169-82.

Rabin, M. "Incorporating Fairness into Game Theory and Economics." American Economic Review, 83, 1993, 1281-302.

Reuben, E., and A. Riedl. "Public Goods Provision and Sanctioning in Privileged Groups." Journal of Conflict Resolution, 53, 2009, 72-93.

Zelmer, J. "Linear Public Goods Experiments: A MetaAnalysis." Experimental Economics, 6, 2003, 299-310.

(1.) With "privileged player" we refer to the group member with an MPCR higher than that of the other players. Olson (1965), see also Reuben and Riedl (2009), introduced the somewhat different notation of "privileged groups" which, however, refers to groups that contain one player with an MPCR larger than one (i.e., our baseline treatment).

(2.) Zelmer (2003) reviews linear public-goods games with asymmetric MPCR, none of which involves players with a rate larger than one.

(3.) The restart was announced only at the end of the first ten periods, and group composition and players" types were kept constant across all periods (see Andreoni 1988 or Croson 1996 for similar restart designs).

(4.) Subjects were recruited with the online recruiting system ORSEE (Greiner 2004), and the experimental software was developed with the z-Tree software package (Fischbacher 2007).

(5.) The English translations of the instructions are provided in the Appendix. The original German ones are available from the authors upon request.

(6.) All rank sum tests except those for the first period are performed with groups as independent observations to take the dependency of decisions within a group into account.

(7.) Three matching groups in 1.4 are excluded, because their players A always contributed their entire endowment, resulting in too many ties to calculate a correlation coefficient.

(8.) Correlation in [T 0.9] is significantly different from zero (p = 0.003, two-sided test), while the corresponding correlation in IT 1.4] is not (p = 0.17, two-sided test).

Glockner: Head Research Group Intuitive Experts, Max Planck Institute for Research on Collective Goods, Kurt-Schumacher Str.10, D-53113 Bonn, Germany. Phone +49 (0) 228 91416 857, Fax +49 (0) 228 91416 858, E-mail gloeckner@coll.mpg.de

Irlenbusch: Professor of Corporate Development and Business Ethics, University of Cologne, Herbert-LewinStr. 2, D-50931 Koln, Germany. Phone +49 (0)221 470 1848, Fax +49 (0) 221 470 1849, E-mail bernd. irlenbusch@uni-koeln.de

Kube: Professor of Economics, Adenauerallee 24-42, D-53113 Bonn, Germany. Phone +49 (0) 228 73 9240, Fax +49 (0) 228 73 9239, E-mail kube@uni-bonn.de

Nicklisch: Senior Research Fellow, Max Planck Institute for Research on Collective Goods, Kurt-Schumacher Str. 10, D-53113 Bonn, Germany. Phone +49 (0) 228 91416 79, Fax +49 (0) 228 91416 62, E-mail nicklisch@coll. mpg.de

Normann: Professor of Economics, Dusseldorf Institute for Competition Economics (DICE), Heinrich-Heine-Universitat Dusseldorf, Universitatsstr. 1, D-40225 Dusseldorf, Germany. Phone +49 (0) 211 81 15 297, Fax +49 (0) 211 81 15 499, E-mail normann@dice.uniduesseldorf.de

TABLE 1
Contributions by Periods

Period 1 1-5 6-10 10 1-10

Type A 0.9 12.8 12.4 8.5 5.2 10.4
Type A 1.4 15.2 16.0 15.5 16.2 15.7
Prob > [absolute value of z] 0.66 0.13 0.01 0.01 0.02

 11 11-15 16-20 20 11-20

Type A 0.9 13.6 12.3 9.6 5.2 11.0
Type A 1.4 15.8 17.5 18.3 19.1 17.9
Prob > [absolute value of z] 0.43 0.02 0.01 0.01 0.01

 1 1-5 6-10 10 1-10

Type B 0.9 8.7 7.7 4.2 4.1 5.9
Type B 1.4 7.9 6.1 2.6 1.5 4.4
Prob > [absolute value of z] 0.39 0.25 0.09 0.09 0.26

 11 11-15 16-20 20 11-20

Type B 0.9 7.6 7.6 3.5 2.3 5.6
Type B 1.4 4.9 4.1 1.9 1.2 2.9
Prob > [absolute value of z] 0.22 0.13 0.08 0.28 0.05

Notes: The table reports average contribution to the public good
for treatment [T 0.9] and [T 1.4] (first two rows). The third row
reports p-values (two-sided) from a nonparametric Wilcoxon rank
sum test.