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

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