Risk-sensitive first passage stochastic games with unbounded costs

Abstract

ABSTRACT This paper studies discrete-time nonzero-sum stochastic games under the risk-sensitive first passage discounted cost criterion. The state space is a countable set and the costs are allowed to be unbounded. Under the suitable optimality conditions, we prove that the risk-sensitive first passage discounted optimal value function of each player is a unique solution to the risk-sensitive first passage optimality equation via an approximation method. Moreover, by the risk-sensitive first passage discounted optimality equation, we show the existence of a randomized Markov Nash equilibrium. Finally, three examples are given to illustrate the results.