Identifying Preferences for Conditional Cooperation Using Individual Beliefs

Abstract

The relationship between contributions and elicited beliefs in a repeated two-person public good experiment is modeled with the help of a parsimounious random-utility function that allows for conditionally cooperative, opportunistic, and altruistic patterns of behavior. Under standard assumptions, a latent-class mixed logit specification with three sub-populations is shown to capture well heterogeneity in individual contribution levels over time, while also accomodating for different degrees of heteroscedasticity. The estimation results are consistent with the conjecture that the majority of players in public goods games are strongly conditional cooperators, with smaller fractions of the population leaning to opportunistic or altruistic behavior.

Keywords:

• Conditional cooperation
• Finite Mixture
• Latent class logit
• Quantal response equilibrium

Mathematics Subject Classification:

• Primary 62 F
• Secondary 91

Acknowledgments

The points of view expressed in this article are not necessarily endorsed by the authors’ institutions of affiliation. This investigation was funded by the Max Planck Institute of Economics, Germany, and partially supported by Spanish Ministerio de Ciencia e Innovación, grant SEJ2007-63098-ECON. Torsten Weiland wrote the computer program used in the laboratory experiment. We would like to thank the Associate Editor and the reviewer for their many helpful comments and suggestions. We are also grateful to Antonio Costilla for his help on the revision of the methodological and theoretical discussions of the present work.

Notes

Fischbacher et al. (2000) suggested that conditional cooperation can be considered as a motivation in its own right or result from fairness preferences like inequity aversion or reciprocity.

We are thankful to an anonymous referee who pointed this out.

In what follows, we specifically assume that is not a function of c _i . Nevertheless, there might be situations in which this assumption is too strong, for instance, when subjects experience cognitive dissonance due to the presence of normative expectations (i.e., beliefs regarding what constitutes a “socially appropriate behavior” in the sense of Bicchieri and Xiao, 2009; Cason and Mui, 1998). One option for tackling this potential endogeneity problem would be to explicitly model elicited beliefs as a function of demographic and other control variables (see, e.g., Bellemare et al., 2008). As an alternative, one could take elicited beliefs as part of an individual's choice rather than as exogenous explanatory variables. In this case, the (subjective) expected utility function in Eq. (3) could be written as , with possible extensions in the specification of the utility function to capture the notion of norms regarding what constitutes socially acceptable expectations.

This interpretation does not preclude ρ from also capturing sources of heteroscedasticity other than learning effects. For instance, it may also account for strategic reputation effects in which opportunistic players try to mimic conditionally cooperative behavior in earlier rounds in order to (indirectly) induce higher cooperation levels from later partners through contagion.

Notice that the belief-elicitation mechanism implemented in the experiment was not a quadratic scoring rule (QSR) in the sense of Murphy and Winkler (1970), as this would have required eliciting subjective probabilities for the whole action space (i.e., ,…, ). As has been shown in Sec. 2, only the first moment of each player's beliefs determines his ordering of preferences; therefore, using a QSR would have introduced unnecessary complexity in the instructions to the participants. Moreover, one cannot ex ante rule out the possibility that experimental subjects are risk-averse or engage in probability weighting, in which case the QSR would not be incentive-compatible.

Note. Dependent variable is the proportion of endowment contributed in each period. Standard deviations appear in parenthesis.

Note. Dependent variable is the proportion of endowment contributed in each period. Standard deviations appear in parenthesis.