Approximate markov-nash equilibria for discrete-time risk-sensitive mean-field games

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)1596-1620
Number of pages25
JournalMathematics of Operations Research
Volume45
Issue number4
DOIs
StatePublished - Nov 2020

Keywords

  • Approximate Nash equilibrium
  • Mean-field games
  • Risk-sensitive stochastic control

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research

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