Risk-sensitive first passage stochastic games with unbounded costs

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.

KEYWORDS:

• Nonzero-sum game
• risk-sensitive first passage discounted cost criterion
• Nash equilibrium

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 91A15
• 91A25

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).

Additional information

Funding

The research of the first author was supported by the National Natural Science Foundation of China [grant number 12171170] and the Natural Science Foundation of Fujian Province [grant number 2021J01308]. The research of the second author was supported by the National Natural Science Foundation of China [grant number 12271454].