## Abstract

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 language | English (US) |
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Pages (from-to) | 4256-4287 |

Number of pages | 32 |

Journal | SIAM Journal on Control and Optimization |

Volume | 56 |

Issue number | 6 |

DOIs | |

State | Published - 2018 |

## Keywords

- Discounted cost
- Mean-field games
- Nash equilibrium

## ASJC Scopus subject areas

- Control and Optimization
- Applied Mathematics