Existence of equilibrium stationary strategies in discounted stochastic games

Abstract

In this paper we show that the existence of p-equilibrium stationary strategies imply the existence of equilibrium stationary strategies when the state space is uncountable under the condition that the reward functions and transition probabilities are continuous. Using this and a theorem of Himmelberg et al we are able to give a set of sufficient conditions for the existence of an equilibrium pair. This answer partially a question raised by Ward Whitt recently.