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In this paper, we investigate the robustness of stationary mean-fieldequilibria in the presence of model uncertainties, specifically focusing oninfinite-horizon discounted cost functions. To achieve this, we initiallyestablish convergence conditions for value iteration-based algorithms inmean-field games. Subsequently, utilizing these results, we demonstrate thatthe mean-field equilibrium obtained through this value iteration algorithmremains robust even in the face of system dynamics misspecifications. We thenapply these robustness findings to the finite model approximation problem inmean-field games, showing that if the state space quantization is fine enough,the mean-field equilibrium for the finite model closely approximates thenominal one.

Robustness and Approximation of Discrete-time Mean-field Games under Discounted Cost Criterion