Does stake size matter for cooperation and punishment?
Introduction
While some experimental economists argue that one of the concerns with data from the laboratory—the effect of stake size—has largely been put to rest, others provide evidence that this issue is still largely in dispute. Several studies that have explicitly tested for stake effects have found that an increase in monetary stakes does not significantly affect the average behavior of decision-makers. It could, however, reduce the variance of the subjects' behavior in certain environments (e.g., Camerer, 2003, Camerer and Hogarth, 1999, Smith and Walker, 1993). Further evidence in line with this general conclusion has been provided, for instance, by Cameron (1999) for ultimatum games, Carpenter et al. (2005) for dictator and ultimatum games, Clark and Sefton (2001) for a sequential prisoner's dilemma game, and Fehr et al. (2002) for the gift-exchange game. In contrast, critical remarks and counter-evidence can be found in Parco et al. (2002), Slonim and Roth (1998), who report fewer rejections in ultimatum games with higher stakes, and Johansson-Stenman et al. (2005) for trust games.1 Thus, it would be premature to conclude that the effects of stake size should be neglected in experimental economics in general.
The objective of this paper is to test whether stake size has an impact on cooperation and sanctioning behavior. We study both a standard linear public goods game and a public goods game that is augmented by a punishment stage after the contribution stage. Punishment takes the form of informal individual sanctions and is costly both to the punisher and the punished as in, e.g., Fehr and Gächter (2000).
To the best of our knowledge, we are the first to analyze the effects of stake size on both voluntary contributions to a public good and, particularly, on punishment in the context of public good provision. Most existing experimental evidence on stake size refers to bargaining games as discussed above. Since social dilemmas are almost ubiquitous in everyday life, and since they often involve an option to sanction other decision-makers, we think that this is a worthwhile endeavor.
We are aware of only one other paper that explicitly deals with a test of stakes on the private provision of a public good. Marwell and Ames (1980) report that people invest less money in the public good when stakes are higher. Their findings are, however, partly confounded by an experimenter effect.2
Section snippets
The public good and our experimental design
Let I = {1, 2, ..., n} denote a group of n subjects who interact only once in a one-shot simultaneous public goods game without punishment. Individual i ∈ I receives an endowment E, which can be allocated either to a private good and/or to a public good. The voluntary contribution of individual i to the public good, ci, must satisfy 0 ≤ ci ≤ E. Let C denote the sum of all group members' contributions (i.e. ). Individual member is payoff from his or her contribution is thus given by
Results
In Table 1, we show the mean contribution levels to the public good in Part I and Part II, separately for the LOW and the HIGH treatment. As can easily be seen in the table, there are only small differences between the two treatments. In Part I, the average contribution level was 34.4% in LOW and 32.9% in HIGH, while in Part II it was 41.2% and 40.9% for LOW and HIGH, respectively. Punishment in Part II was used by 25% of participants in LOW and by 17% of participants in HIGH. The average
Conclusion
This paper analyzes the effects of a stake size variation in a one-shot public goods experiment without and with punishment. The increase in stake does neither have a significant effect on the mean nor on the variance of the level of contributions in our experiment. It also has an insignificant effect on punishment. Our results suggest that findings of public goods experiments with standard laboratory stakes can be extrapolated to situations with higher stakes. Evidence from a game show (Friend
Acknowledgments
We would like to thank Martin Dufwenberg, Olof Johansson-Stenman, an anonymous referee and participants of the ESA World Meeting 2006 in Atlanta for helpful comments as well as Benedikt Herrmann for the suggestions regarding the research design. We are also indebted to the Western Cape Department of Education in South Africa for facilitating this research. Financial assistance from the Swedish Research Council (Vetenskapsrådet), the Swedish International Development Cooperation Agency (SIDA) at
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