A Theory of Endogenous Commitment

Commitment is typically modeled by giving one of the players the opportunity to take an initial binding action. The drawback to this approach is that the fundamental question of who has the opportunity to commit is driven by a modeling decision. This paper presents a framework in which commitment power arises naturally from the fundamentals of the model. We construct a finite dynamic game in which players are given the option to change their minds as often as they want, but pay a switching cost if they do so. We show that for games with two players and two actions there is a unique subgame perfect equilibrium with a simple structure. This equilibrium is independent of the order of moves and robust to other protocol specifications. Moreover, despite the perfect information nature of the model and the costly switches, strategic delays may arise in equilibrium. The flexibility of the model allows us to apply it to many different environments. In particular, we study an entry-deterrence situation. Its equilibrium is intuitive and illustrative of how commitment power is endogenously determined.