科研之友
微信
新浪微博
Facebook
分享链接
摘要
In this paper, we consider discrete-time -person constrained stochastic games with discounted cost criteria. The state space is denumerable and the action space is a Borel set, while the cost functions are admitted to be unbounded from below and above. Under suitable conditions weaker than those in (Alvarez-Mena and Hernandez-Lerma, Math Methods Oper Res 63:261-285, 2006) for bounded cost functions, we also show the existence of a Nash equilibrium for the constrained games by introducing two approximations. The first one, which is as in (Alvarez-Mena and Hernandez-Lerma, Math Methods Oper Res 63:261-285, 2006), is to construct a sequence of finite games to approximate a (constrained) auxiliary game with an initial distribution that is concentrated on a finite set. However, without hypotheses of bounded costs as in (Alvarez-Mena and Hernandez-Lerma, Math Methods Oper Res 63:261-285, 2006), we also establish the existence of a Nash equilibrium for the auxiliary game with unbounded costs by developing more shaper error bounds of the approximation. The second one, which is new, is to construct a sequence of the auxiliary-type games above and prove that the limit of the sequence of Nash equilibria for the auxiliary-type games is a Nash equilibrium for the original constrained games. Our results are illustrated by a controlled queueing system.
- 出版日期2014-10
- 单位中山大学
