Modeling Cooperation with Self-regarding Agents

The n-player public goods game, the basic model of decentralized social cooperation in non-market settings, has a unique Nash equilibrium in which all players defect. The Folk Theorem asserts that near-Pareto-optimal pay-offs can be supported if the game is indefinitely repeated and the discount factor is sufficiently near unity. This paper advances the view that the Folk Theorem does not explain why or how individuals cooperate in these set-tings. First, with imperfect public signaling, the Folk Theorem’s implication that near-optimal payoffs do not depend on the number of players, given a fixed finite upper limit on the informational processing capacity of players, is based on an impermissible order of taking limits. Second, the Folk the-orem demonstrates the existence of an equilibrium, but does not show that this equilibrium can be implemented; i.e., that there is some plausible social process by means of which it can be instantiated. We offer a social imple-mentation mechanism using focal rules. This mechanism uses public signals that agents treat as common knowledge, so instances of cooperation based on the repeated public goods game must be publicly observable. The fact that no examples of cooperation based on the n-player public goods game (n> 2) with public focal rules has been observed suggests that modeling cooperation with self-regarding agents remains unsolved problem.