Robustness and Approximation of Discrete-time Mean-field Games under Discounted Cost Criterion
Provides theoretical guarantees for robustness and approximation in mean-field games, relevant to researchers working on multi-agent systems and game theory.
The paper establishes convergence conditions for value iteration in mean-field games and shows that the resulting equilibrium is robust to model misspecifications. It also proves that finite model approximations with fine enough state space quantization closely approximate the nominal equilibrium.
In this paper, we investigate the robustness of stationary mean-field equilibria in the presence of model uncertainties, specifically focusing on infinite-horizon discounted cost functions. To achieve this, we initially establish convergence conditions for value iteration-based algorithms in mean-field games. Subsequently, utilizing these results, we demonstrate that the mean-field equilibrium obtained through this value iteration algorithm remains robust even in the face of system dynamics misspecifications. We then apply these robustness findings to the finite model approximation problem in mean-field games, showing that if the state space quantization is fine enough, the mean-field equilibrium for the finite model closely approximates the nominal one.