ABSTRACT

This paper attempts to study nonzero-sum continuous-time constrained average stochastic games with independent state processes. In these game models, each player independently controls a continuous-time Markov chain, but players are coupled by the immediate cost functions. The transition rates and immediate cost functions are allowed to be unbounded. Each player wants to minimize certain expected average cost, but constraints are imposed on other expected average costs. By introducing the average occupation measures, we establish the one-to-one relationship of constrained Nash equilibria and the fixed points of certain multifunction defined on the product space of average occupation measures. Then, by using the fixed point theorem, we show the existence of constrained Nash equilibria. Finally, we show that each stationary Nash equilibrium corresponds to a global minimizer of a certain mathematical program.

摘要

本文试图研究具有独立状态过程的非零和连续时间约束平均随机博弈。在这些博弈模型中，每个玩家独立控制一个连续时间马尔可夫链，但玩家通过直接成本函数耦合。允许转移率和直接成本函数是无界的。每个参与者都希望最小化某些预期平均成本，但对其他预期平均成本施加了限制。通过引入平均占用测度，我们建立了约束纳什均衡与定义在平均占用测度乘积空间上的某个多功能不动点的一一对应关系。然后，通过使用不动点定理，我们证明了约束纳什均衡的存在。最后，