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.
