Monotonicity and Robust Implementation under Forward-Induction Reasoning

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 (M & uuml;ller (2016))-is indeed robust in the sense of Bergemann and Morris (2009).