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 behaviour 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.

In sequential games, the set of paths consistent with rationality and forward‐induction reasoning may change nonmonotonically when adding transparent restrictions on players' beliefs. Yet, we prove that—in an incomplete‐information environment—predictions become sharper when the restrictions only concern initial beliefs about types. Thus, strong rationalizability for games with payoff uncertainty characterizes the path predictions of forward‐induction reasoning across all possible restrictions on players' hierarchies of exogenous beliefs. With this, we can solve an open problem: the implementation of social choice functions through sequential mechanisms under forward‐induction reasoning—which considerably expands the realm of implementable functions compared with simultaneous mechanisms (Müller (2016))—is indeed robust in the sense of Bergemann and Morris (2009).