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

TL;DR

This paper studies the robustness of stationary mean-field equilibria under model uncertainties and demonstrates that finite model approximations can closely match the true equilibrium with sufficient state space quantization.

Contribution

It establishes convergence conditions for value iteration in mean-field games and proves the robustness of equilibria under system misspecifications.

Findings

Mean-field equilibrium remains robust despite system dynamics misspecifications.

Finite model approximations can closely match the true equilibrium with fine enough state space quantization.

Convergence conditions for value iteration algorithms are established.

Abstract

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.