The Robustness of Sequential Implementation under Information Perturbations

Ian Ball, Drew Fudenberg and Stephen Morris

Papers from arXiv.org

Abstract: Bayesian monotonicity is a necessary condition for full implementation in Bayes-Nash equilibrium. Under the sequential equilibrium refinement, however, multi-stage mechanisms can expand the scope for implementation. We show that this additional implementation power is fragile. Whenever a multi-stage mechanism sequentially implements a social choice correspondence that is not Bayesian monotone, we construct arbitrarily small "information perturbations" and show that there are sequential equilibria under these perturbations that yield inadmissible decisions with probability bounded away from zero. Under these perturbations, players' types are not independent conditional on the state and some player is sometimes uncertain of their payoff type. We show by example that the general result fails if perturbations are required to satisfy conditional independence or "known payoff types."

Date: 2026-09, Revised 2026-10
New Economics Papers: this item is included in nep-des, nep-gth and nep-mic
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