Non-zero-sum stochastic games with recursive utilities of risk-sensitive players

Recursive utilities constructed by conditional entropic risk measures have recently been considered in various stochastic models and their applications, e.g., in economic dynamics. We study countable state discounted stochastic games played by risk-sensitive players. More precisely, we assume that the players evaluate their payoffs in a recursive way with the aid of the certainty equivalent of an exponential utility function. Under typical continuity and compactness conditions we prove that a stationary Nash equilibrium exists.