Continuous-time zero-sum games with probability criterion

Abstract

In this article, we investigate a zero-sum stochastic game for continuous-time Markov chain with denumerable state space and unbounded transition rates, under the probability criterion. Under suitable assumptions, we show the existence of value of the game and also characterize it as the unique solution of a pair of Shapley equations. We also establish the existence of a randomized stationary saddle point equilibrium.

Keywords:

• Zero-sum game
• probability criterion
• Shapley equations
• value of the game
• optimal policies