Stable strategies in repeated games with endogenous separation

Abstract

Games with endogenous separation are repeated games where players have the option to leave their current partnership and keep on playing in a newly- formed partnership. Arguably, most repeated interactions in real life fall into this category. We present a general framework to analyze equilibria in games with endogenous separation, extending concepts from evolutionary game the- ory, and with a focus on neutrally stable strategies, i.e., stable strategies that are resistant to direct invasion by any alternative strategy. We introduce path- protecting strategies, which play a similar role to trigger strategies in standard (fixed-partnership) repeated games, and we provide a constructive proof of their existence. We also present a Folk Theorem for path-protecting strategies in these games.