Nonzero-Sum Stochastic Games with Unbounded Discounted Payoff

Discrete time two-person nonzero-sum stochastic games with the discounted payoff criterion and a countable state space is studied,here the payoff functions might have neither upper nor lower bounds.The existence of Nash equilibria is proved in randomized stationary strategies by using the Fan's fixed-point theorem under the "drift" and the standard "continuous-compact" conditions,which are usually used in zero-sum stochastic games.