Efficiency may improve when defectors exist

Abstract

Voluntarily Separable Repeated Prisoner's Dilemma (Fujiwara-Greve and Okuno-Fujiwara, 2009) has many kinds of equilibria. Focusing on monomorphic and bimorphic equilibria, we show that a bimorphic equilibrium consisting of cooperators and defectors is most efficient, under a mild payoff condition. This is a striking contrast to ordinary repeated Prisoner's Dilemma, where the symmetric efficient payoff is achieved by the symmetric C-trigger equilibrium. Our result indicates that behavioral diversity can be beneficial for the society, when players are free to escape from personalized punishments.