Robustness and Approximation of Discrete-Time Mean-Field Games Under Discounted Cost Criterion
研究了模型不确定下离散时间平均场博弈的鲁棒性，证明值迭代算法得到的均衡对系统动态误设具有鲁棒性，并应用于有限模型近似问题。
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.