On Optimal and Neutrally Stable Population Equilibrium in Voluntary Partnership Prisoner's Dilemma Games

37 Pages Posted: 25 Jan 2010 Last revised: 25 Mar 2012

See all articles by Filip Vesely

Filip Vesely

University of Wisconsin at Milwaukee - Economics

Chun-Lei Yang

Date Written: May 1, 2010

Abstract

In a voluntary partnership prisoner's dilemma, equilibrium discounted payoff at the origin of a partnership also serves as the worst feasible threat with which to sustain cooperation. In a population model, we introduce the Markov strategy and characterize neutrally stable equilibrium. We construct simple Markov strategies that achieve the highest discounted payoff at the origin among all subgame perfect equilibrium distributions that have either eternal cooperation or eternal (matched) alternation on their equilibrium paths. Partnerships past the first strangers’ phase never break up, and potential punishments are all performed within the partnership. With this feature, our optimal Markov equilibria prove to be neutrally stable, while many commonly known ones in the literature are not.

Keywords: Voluntary Partnership, Prisoner's Dilemma, Markov Strategy, Neutral Stability, Eternal Cooperation, Eternal Alternation

JEL Classification: C73

Suggested Citation

Vesely, Filip and Yang, Chun-Lei, On Optimal and Neutrally Stable Population Equilibrium in Voluntary Partnership Prisoner's Dilemma Games (May 1, 2010). Available at SSRN: https://ssrn.com/abstract=1541684 or http://dx.doi.org/10.2139/ssrn.1541684

Filip Vesely (Contact Author)

University of Wisconsin at Milwaukee - Economics ( email )

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