Dynamic commitment games, efficiency and coordination

An important form of commitment is the ability to restrict the set of future actions from which choices can be made. We study a simple two player dynamic game of complete information which incorporates this type of commitment. For a given initial game, the players engage in an endogenously determined number of commitment periods before choosing from the remaining actions. We show the existence of equilibria with pure strategies in the commitment periods. Partial characterization results for general games capture the tradeoff between commitment and deterrence. The equilibrium outcome is unique and efficient for two classes of games, including pure coordination and stag-hunt games.