Monotonicity and Robust Implementation Under Forward-Induction Reasoning

doi:10.3982/ECTA23709

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Monotonicity and Robust Implementation Under Forward-Induction Reasoning

2026-04-01

Pierpaolo Battigalli *

Emiliano Catonini *

DOI：10.3982/ECTA23709

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Abstract

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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).

Keywords:

Incomplete information

forward induction

strong rationalizability

path monotonicity

robust implementation

sequential mechanisms

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