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.
Acknowledgments
We are greatly indebted to the reviewers for their valuable comments and suggestions.
Disclosure statement
No potential conflict of interest was reported by the author(s).