Nonzero-sum games for continuous-time Markov chains with unbounded discounted payoffs

作者：Guo, XP^*; Hernandez Lerma, O

来源：Journal of Applied Probability, 2005, 42(2): 303-320.

DOI：10.1239/jap/1118777172

• nonzero-sum game
• discounted payoff criterion
• Nash equilibrium
• controlled Q-process

In this paper, we study two-person nonzero-sum games for continuous-time Markov chains with discounted payoff criteria and Borel action spaces. The transition rates are possibly unbounded, and the payoff functions might have neither upper nor lower bounds. We give conditions that ensure the existence of Nash equilibria in stationary strategies. For the zero-sum case, we prove the existence of the value of the game, and also provide a recursive way to compute it, or at least to approximate it. Our results are applied to a controlled queueing system. We also show that if the transition rates are uniformly bounded, then a continuous-time game is equivalent, in a suitable sense, to a discrete-time Markov game.

• 出版日期2005-6
• 单位中山大学