Robustness and Approximation of Discrete-Time Mean-Field Games Under Discounted Cost Criterion

• 成果类型: Article; Early Access
• 署名作者: Aydin, Ugur; Saldi, Naci
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign; Ihsan Dogramaci Bilkent University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2023.0316
• 发表日期: 2025
• 关键词: markov decision-processes; incorrect priors; Nash equilibria; dynamic-games

摘要

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 iterationbased 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.