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.
