On Optimal Social Convention in Voluntary Continuation Prisoner's Dilemma Games

Abstract

The option to leave unilaterally serves as a double-edged sword for cooperation in the repeated prisoner’s dilemma game, so that trigger strategies that use breakup as punishment threats generically may not yield optimally sustainable social outcome in this paradigm. In this study, we construct simple Markov strategy equilibria that, for a large set of parameters, achieve the maximal upper bound of expected lifetime payoff among all social conventions of simple symmetry with eternal mutual cooperation, defection, or (matched) alternation on the equilibrium path. Players have no need to punish defectors by leaving their partners. As a means of smooth transition towards eternal mutual cooperation, the defector is to compensate the cooperator he exploited by cooperating more in the next period of their ongoing partnership. It also turns out that our optimal equilibrium strategies are belief-free and thus can be considered robust to noises. All other well-known designs of social conventions in the literature are also of simple symmetry but are shown to reach the optimum only in degenerate parameter cases in contrast.