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

29 Pages Posted: 21 Nov 2012

See all articles by Filip Vesely

Filip Vesely

University of Wisconsin at Milwaukee - Economics

Chun-Lei Yang

Multiple version iconThere are 2 versions of this paper

Date Written: November 18, 2012


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.

Keywords: voluntary continuation, repeated prisoner’s dilemma, social convention, moral maxim, Markov strategy, eternal cooperation, eternal alternation, belief-free

JEL Classification: C73

Suggested Citation

Vesely, Filip and Yang, Chun-Lei, On Optimal Social Convention in Voluntary Continuation Prisoner's Dilemma Games (November 18, 2012). Available at SSRN: https://ssrn.com/abstract=2179063 or http://dx.doi.org/10.2139/ssrn.2179063

Filip Vesely (Contact Author)

University of Wisconsin at Milwaukee - Economics ( email )

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