Games with Costly Endogenous Separation

Introduction
Games with costly endogenous separation (GCESs) are repeated games where players have the option to leave their current partnership and form a new one with a random partner, incurring a cost in the process. Thus, in these games, partnerships may be broken not only due to causes that are not related to the players’ choices (exogenous separation), but also due to players’ decisions (endogenous separation). We extend the framework of symmetric two-player games with endogenous separation by adding costs to the separation process and studying its influence on the existence of stable equilibria.

Methods
We study the existence of Nash and Neutrally Stable (NS) equilibria in the general case of symmetric two-player games with costly endogenous separation, with applications to the GCES version of the prisoner’s dilemma and the hawk–dove game.

Results
Fully cooperative strategies can support an NS equilibrium in both the prisoner’s dilemma and the hawk–dove game when the cost of endogenous separation is large enough. However, in order to achieve a fully cooperative equilibrium, a considerably large cost is needed.

Conclusions
GCESs may provide a good approach to modelling many real scenarios with freedom of association and search costs and can help explain cooperative or partially cooperative equilibria in social dilemmas.