Foundations for Cooperation in the Prisoners ’ Dilemma

We provide axiomatic foundations for a simple model of play in prisoners’ dilemma games. The model accommodates cooperation and suggests that players behave as if their expectations about their opponents’ behavior vary with their own choice. We refer to this nonstandard updating as magical thinking. The degree to which players exhibit magical thinking may be heterogeneous in the population and is captured by a uniquelyidentified parameter for each player. Further, it is as if all players perceive these parameters to be i.i.d. draws from a common distribution. The model’s identification allows for tractable comparative statics. We investigate how our theory extends to all symmetric 2×2 games.