Markov-Nash equilibria in mean-field games with discounted cost

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In this paper, we consider discrete-time dynamic games of the mean-field type with a finite number N of agents subject to an infinite-horizon discounted-cost optimality criterion. The state space of each agent is a Polish space. At each time, the agents are coupled through the empirical distribution of their states, which affects both the agents' individual costs and their state transition probabilities. We introduce a new solution concept of the Markov-Nash equilibrium, under which a policy is player-by-player optimal in the class of all Markov policies. Under mild assumptions, we demonstrate the existence of a mean-field equilibrium in the infinite-population limit N → ∞, and then show that the policy obtained from the mean-field equilibrium is approximately Markov-Nash when the number of agents N is sufficiently large.

Original languageEnglish (US)
Pages (from-to)4256-4287
Number of pages32
JournalSIAM Journal on Control and Optimization
Issue number6
StatePublished - 2018


  • Discounted cost
  • Mean-field games
  • Nash equilibrium

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


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