Discrete-time Risk-sensitive Mean-field Games

TL;DR

This paper analyzes discrete-time mean-field games with risk-sensitive costs, establishing the existence of equilibria and their approximation properties as the number of agents grows large.

Contribution

It introduces a risk-sensitive framework into mean-field games and proves the existence of equilibria and their approximation to Nash equilibria in large populations.

Findings

Existence of mean-field equilibrium under mild assumptions

Approximate Nash equilibrium for large populations

Extension of mean-field game theory to risk-sensitive settings

Abstract

In this paper, we study a class of discrete-time mean-field games under the infinite-horizon risk-sensitive discounted-cost 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 then show that the policy obtained from the mean-field equilibrium constitutes an approximate Nash equilibrium when $N$ is sufficiently large.