The Robustness of Sequential Implementation under Information Perturbations

2026-09-24

AI Summary

This study addresses whether the additional implementation power of multi-stage mechanisms under sequential equilibrium is robust to information perturbations. By integrating game theory with Bayesian mechanism design, this work constructs arbitrarily small information perturbations for non-Bayesian monotonic social choice functions and systematically analyzes the robustness boundaries of their sequential implementation. It demonstrates that any infinitesimal information perturbation leads to unacceptable outcomes with significant probability, revealing the fragile nature of the implementation advantage of multi-stage mechanisms. Furthermore, it identifies conditional independence and known payoff types as sufficient conditions for preserving robustness. Ultimately, this research establishes the theoretical conclusion that multi-stage mechanisms cannot withstand minor information perturbations in non-Bayesian monotonic settings.

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.''

Problem

• Sequential Implementation
• Information Perturbations
• Bayesian Monotonicity
• Multi-stage Mechanisms
• Robustness

Innovation

• Sequential Implementation
• Information Perturbations
• Bayesian Monotonicity
• Sequential Equilibrium
• Multi-stage Mechanisms