Discrete-time Risk-sensitive Mean-field Games
It extends mean-field game theory to risk-sensitive agents with exponential utility, providing theoretical foundations for large-scale multi-agent systems under risk aversion.
This paper establishes the existence of a mean-field equilibrium for discrete-time risk-sensitive mean-field games under the infinite-horizon discounted-cost criterion, and shows that the resulting policy provides an approximate Nash equilibrium for finite-agent systems.
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.