Linear Mean-Field Games with Discounted Cost

• 成果类型: Article; Early Access
• 署名作者: Saldi, Naci
• 署名单位: Ihsan Dogramaci Bilkent University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2023.0148
• 发表日期: 2025
• 关键词: nash equilibria; dynamic-games; SPACES

摘要

In this paper, we introduce discrete-time linear mean-field games subject to an infinite-horizon discounted-cost optimality criterion. At every time, each agent is randomly coupled with another agent via their dynamics and one-stage cost function, where this randomization is generated via the empirical distribution of their states (i.e., the mean-field term). Therefore, the transition probability and the one-stage cost function of each agent depend linearly on the mean-field term, which is the key distinction between classical meanfield games and linear mean-field games. Under mild assumptions, we show that the policy obtained from infinite population equilibrium is epsilon(N)-Nash when the number of agents N is sufficiently large, where epsilon(N) is an explicit function of N. Then, using the linear programming formulation of Markov decision processes (MDPs) and the linearity of the transition probability in the mean-field term, we formulate the game in the infinite population limit as a generalized Nash equilibrium problem (GNEP) and establish an algorithm for computing equilibrium with a convergence guarantee.