Approximate Markov-Nash Equilibria for Discrete-Time Risk-Sensitive Mean-Field Games

• 成果类型: Article
• 署名作者: Saldi, Naci; Basar, Tamer; Raginsky, Maxim
• 署名单位: Ozyegin University; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2019.1044
• 发表日期: 2020
• 页码: 1596-1620
• 关键词: dynamic-games

摘要

In this paper, we study a class of discrete-time mean-field games under the infinite-horizon risk-sensitive optimality criterion. Risk sensitivity is introduced for each agent (player) via an exponential utility function. In this game model, each agent is coupled with the rest of the population through the empirical distribution of the states, which affects both the agent's individual cost and its state dynamics. Under mild assumptions, we establish the existence of a mean-field equilibrium in the infinite-population limit as the number of agents (N) goes to infinity, and we then show that the policy obtained from the mean-field equilibrium constitutes an approximate Nash equilibrium when N is sufficiently large.