On the convergence of finite state mean-field games through Γ-convergence

Abstract In this study, we consider the long-term convergence (trend toward an equilibrium) of finite state mean-field games using Γ -convergence. Our techniques are based on the observation that an important class of mean-field games can be viewed as the Euler–Lagrange equation of a suitable functional. Therefore, using a scaling argument, one can convert a long-term convergence problem into a Γ -convergence problem. Our results generalize previous results related to long-term convergence for finite state problems.

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