Cooperation in temporary partnerships

Abstract

The literature on cooperation in infinitely repeated Prisoner's Dilemmas covers the extreme opposites of the matching spectrum: partners, a player's opponent never changes, and strangers, a player's opponent randomly changes in every period. Here, we extend the analysis to settings where the opponent changes, but not in every period. In these temporary partnerships, players can deter some deviations by directly sanctioning their partner. Hence, relaxing the extreme assumption of one-period matchings can support some cooperation also off equilibrium because a class of strategies emerges that are less extreme than the typical “grim” strategy. We establish conditions supporting full cooperation as a subgame perfect equilibrium under a social norm that complements direct sanctions with a cyclical community sanction. Though this strategy less effectively incentivizes cooperation, it more effectively incentivizes punishment after a deviation, hence, can be preferable to the grim strategy under certain conditions.