Efficacy, Beliefs, and Investment in Step-Level Public Goods

Abstract

A central concept for understanding social dilemma behavior is the efficacy of an actor's cooperative behavior in terms of increasing group well-being. We report a decision and game theoretical analysis of efficacy in step-level public goods (SPGs). Previous research shows a positive relation between efficacy and contributions to SPGs and explains this relation by a purely motivational account. We show, however, that from a decision and game theory perspective an increasing relationship is not general, but only follows from very specific assumptions about players’ information and beliefs. We offer 3 examples of how the predicted efficacy–contribution relation depends on players’ information and beliefs. We discuss the implications of our results for the social psychology of efficacy in social dilemmas.

Keywords:

• Bayesian equilibrium
• beliefs
• efficacy
• information
• social dilemmas
• step-level public goods

Notes

¹Note that an SPG is strictly speaking not always a social dilemma, since individually rational choices can be collectively efficient if an individual investment pushes the group over the threshold of the production of the SPG. However, since there always also exists an inefficient equilibrium in which no one invests, there is a tension between individual and collective interests, as in pure social dilemmas.

²In the same intergroup competition context, Rapoport, Bornstein, and Erev (1989) report results of a first experiment that show a decreasing relationship between efficacy and investment probability. However, in this experiment higher efficacy was associated with higher costs of investment, so that for players with higher efficacy the monetary payoff to the investment was smaller. In a second experiment, in which higher efficacy is associated with proportionally larger costs and benefits of investment such that the ratio of benefits to costs is equal for all players, these authors report no relation between efficacy and investment.

³One could also argue that a player's strategy is a map from her share and her beliefs to the set of probability distributions over her actions. However, since P(·) is given and fixed, a player's posterior beliefs (i.e., beliefs after she learns her own share) are entirely determined by her share. Modeling strategies as depending only on players’ own shares is therefore equivalent to modeling strategies as depending on players’ own shares and her beliefs about the shares of others.

⁴Note that we assume independent strategies, although players’ shares are of course generally dependent, since they sum to 100.