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arXiv · 2609.05083

Trembling-Hand Perfection in Mean Field Games

Luciano Campi·Luca Di Persio·Lucrezia Zorzi
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Abstract

We introduce an admissible trembling-hand refinement for stochastic mean field games formulated through relaxed controlled martingale problems. A relaxed MFG equilibrium is perfect if it is the common Wasserstein limit of two sequences of joint control-state laws. The first consists of full-support population perturbations admissible for the state laws they generate; the second consists of exact optimal responses to those perturbed state laws. This admissibility condition prevents the control and state coordinates of a perturbation from being varied independently. Under the standing continuity, growth, and coercivity assumptions, we prove existence without requiring compact controls or bounded coefficients. The proof combines a perturbed fixed-point argument in the compact-bounded case with truncation, uniform moment estimates, compactness, and stability of controlled martingale problems. A one-dimensional model with exactly two relaxed mean field game equilibria shows that the refinement is genuinely selective: only one equilibrium is trembling-hand perfect.

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Luciano Campi, Luca Di Persio, Lucrezia Zorzi. 2026-09-04. Trembling-Hand Perfection in Mean Field Games. https://arxiv.org/abs/2609.05083

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