Conventions 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, with a special focus on social conventions, i.e., stable strategies that are resistant to direct invasion by any conceivable strategy. Our search for conventions leads to path-protecting strategies, which play a similar role to trigger strategies in standard (fixed-partnership) repeated games. We provide a constructive proof of existence for path-protecting strategies, and a folk theorem for neutrally stable conventions.