Risk-Sensitive Average Equilibria for Discrete-Time Stochastic Games

Abstract

In this paper, we study the risk-sensitive average payoff criterion for the nonzero-sum discrete-time stochastic games with a denumerable state space. The risk-sensitivity coefficient can take positive values and negative values. Under the suitable conditions, we show the existence of a solution to the coupled equations by a technique of the discounted approximation, and obtain the existence of a stationary Nash equilibrium. Moreover, we present some verifiable sufficient conditions imposed on the primitive data of the model for the verification of our assumption and use an example to illustrate that our conditions are weaker than those in the existing literature.