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Monotonicity and Robust Implementation Under Forward‐Induction Reasoning

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  • Pierpaolo Battigalli
  • Emiliano Catonini

Abstract

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).

Suggested Citation

  • Pierpaolo Battigalli & Emiliano Catonini, 2026. "Monotonicity and Robust Implementation Under Forward‐Induction Reasoning," Econometrica, Econometric Society, vol. 94(2), pages 505-536, March.
    • Handle: RePEc:wly:emetrp:v:94:y:2026:i:2:p:505-536
    DOI: 10.3982/ECTA23709
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    References listed on IDEAS

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