  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.
