Non-Binding 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 co-players ’behavior in the continuation of the game. This instance of forward induction reasoning is based on interactive beliefs not just about rationality, but also about the compliance with the agreement itself. Here I study the effects of such rationalization on the self-enforceability of the agreement. Accordingly, outcomes of the game are deemed to be enforceable by some agreement or not. Conclusions depart substantially from what the equilibrium refinement tradition suggests. A subgame imperfect Nash equilibrium may represent a self-enforcing agreement, while a subgame perfect equilibrium may not. The incompleteness of the agreement may be crucial to implement an equilibrium outcome. However, every game possesses an outcome which is compatible with both forward induction and subgame perfection.

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