## 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 language | English (US) |
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Pages (from-to) | 1596-1620 |

Number of pages | 25 |

Journal | Mathematics of Operations Research |

Volume | 45 |

Issue number | 4 |

DOIs | |

State | Published - Nov 2020 |

## Keywords

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

## ASJC Scopus subject areas

- General Mathematics
- Computer Science Applications
- Management Science and Operations Research