Nonzero-sum risk-sensitive finite-horizon continuous-time stochastic games

Abstract

This paper concerns the nonzero-sum games for continuous-time jump processes with unbounded transition rates under the risk-sensitive finite-horizon cost criterion. The state space is a countable set and the costs are allowed to be unbounded in the game model. Under the suitable optimality conditions, by introducing an appropriate topology for the set of all randomized Markov multi-strategies and employing the risk-sensitive finite-horizon optimality equations of the players, we prove the existence of a randomized Markov Nash equilibrium in the class of all randomized history-dependent multi-strategies.