Games with costly endogenous separation are repeated games where players have
the option to leave their current partnership (with some cost) and keep on playing
in a newly-formed partnership. Players can also be separated by exogenous factors.
We study equilibria in these games. As a relevant case of application, cooperation in
a repeated Prisoner’s Dilemma is compromised in environments where individuals
are free to leave their partners, since defectors can exploit cooperators and move
on. Previous studies have explored diverse mechanisms to prevent defect-and-leave
strategies from taking hold. We show that, for large enough separation costs, not
only full cooperation, but actually any symmetric sequence of outcomes can be sup-
ported as a (path-protecting) neutrally stable state, which is Lyapunov stable under
the replicator dynamics.
