Monotonicity and robust implementation under forward-induction reasoning

In sequential games, the set of paths consistent with rationality and forward-induction reasoning may change non-monotonically 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, J. Econ. Theory 2016)---is indeed robust in the sense of Bergemann and Morris (Theor. Econ. 2009).