Voluntarily Separable Prisoner's Dilemma

We develop a general framework to analyze endogenous relationships. To consider relationships in the modern society, neither one-shot games nor repeated games are appropriatemodelsbecausethe formationand dissolutionofa relationship is not an option. We formulate voluntarily separable repeated games, in which players are randomly matched t oplay acomponentgameaswellastochoose whether to play the game again with the same partner. There is no information flow across matches, and players are boundedly rational. We extend the notion of Neutrally Stable Distribution (NSD) to fit for our model. When the component game is a prisoner's dilemma, NSD requires some trust-building periods to defect at the beginning of a partnership. We ?nd that polymorphic NSDs with voluntary breakups include strategies with shorter trust-building periods than any monomorphic NSD with no voluntary separation, and hence the average payo? ofpolymorphic NSD is higher.