CIRJE-F-415. Fujiwara-Greve, Takako and Masahiro Okuno-Fujiwara, "Voluntarily Separable Prisoner's Dilemma", April 2006.

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 playersarerandomlymatchedtoplay acomponentgameaswellastochoose whether to play the game again with the same partner. There is no information ?ow across matches, and players areboundedly rational. We extend the notion of Neutrally Stable Distribution (NSD) to ?t 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.