Conventions and Coalitions in Repeated Games

Abstract

This paper develops a theory of repeated games for settings where coalitions may choose actions. We assume that members of coalitions cannot commit to long-run be- havior (on and o↵ the path) but coalitions can engage in short-term deviations. Players are farsighted and recognize that behavior is history-dependent. A convention reflects players’ shared understanding of how history influences future behavior. We say that a convention is stable if at every history, no coalition of players can find profitable one- shot deviations. We prove that when monitoring is perfect in both non-transferable and transferable utility games, stable conventions can implement any payo↵ that is feasible and strictly individually rational so long as players are arbitrarily patient. Accordingly, coalitional deviations do not refine behavior beyond the folk theorem for sub-game perfect equilibria. By contrast, if members of a deviating coalition can transfer utility to each other secretly, a stable convention implements payo↵s only within the -core of the stage- game, and all such outcomes can be implemented as players become arbitrarily patient. We use these results to interpret how legal institutions can shape the behavior of individ- uals and coalitions through their expectations of future behavior, and why laws may be undermined when transfers are secret.