Constrained average stochastic games with continuous-time independent state processes

Abstract

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.