Self-enforcing agreements and forward induction reasoning
In dynamic games, players may observe a deviation from a pre-play, possibly incomplete, non-binding agreement before the game is over. The attempt to rationalize the deviation may lead players to revise their beliefs about the deviator’s behavior in the continuation of the game. This instance of forward induction reasoning is based on interactive beliefs about not just rationality, but also the compliance with the agreement itself. I study the effects of such rationalization on the self-enforceability of the agreement. Accordingly, outcomes of the game are deemed implementable by some agreement or not. Conclusions depart substantially from what the traditional equilibrium refinements suggest. A non subgame perfect equilibrium outcome may be induced by a self-enforcing agreement, while a subgame perfect equilibrium outcome may not. The incompleteness of the agreement can be crucial to implement an outcome.