Monotone Equilibrium, Admissibility and Perfection

Wei He, Yeneng Sun and Hanping Xu

Papers from arXiv.org

Abstract: This paper studies monotone equilibrium, admissibility, and perfection in Bayesian games. Athey (2001), McAdams (2003), and Reny (2011) prove existence of pure-strategy monotone equilibria under single-crossing and quasi-supermodularity. We construct a counterexample satisfying these assumptions but with no admissible monotone equilibrium, showing these results cannot generally be strengthened without further conditions. To address this existence problem, we introduce perfect monotone equilibrium, combining monotonicity with trembling-hand robustness. We show that stronger assumptions such as increasing differences and supermodularity ensure existence of perfect (and hence admissible) monotone equilibria. We also demonstrate the practical relevance of our results through auctions and Bertrand competitions.

Date: 2025-09, Revised 2026-09
New Economics Papers: this item is included in nep-gth and nep-mic
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