Speaker: Lucrezia Zorzi (Universita' degli studi di Verona)
Title: Trembling-Hand Perfection in Mean Field Games
Abstract: Mean field games may admit multiple equilibria, which naturally raises the question of equilibrium selection. In this talk, we introduce a trembling-hand perfection refinement for stochastic mean field games formulated through relaxed controlled martingale problems. Perturbations are imposed at the level of population controls: they have full support and are required to remain admissible for the state laws they generate. Trembling-hand perfection is then defined by requiring both the perturbed population behavior and the corresponding optimal responses to converge to the same equilibrium. We prove existence under general continuity, growth, and coercivity assumptions, without requiring compact control spaces or bounded coefficients. Finally, a one-dimensional example shows that the refinement is genuinely selective.
Joint work with Luciano Campi (University of Milan) and Luca Di Persio (University of Verona).
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