Sensitive equilibria for ergodic stochastic games with countable state spaces (Q1806281)

The author considers stochastic games with countable state spaces, unbounded immediate payoff functions and some natural stochastic stability assumptions on the transition structure based on a recent work by \textit{S. P. Meyn} and \textit{R. L. Tweedie} [Ann. Appl. Prob. 4, 981--1011 (1994; Zbl 0812.60059)] and studies the existence of sensitive optimal strategies(overtaking or 1-optimality) in some classes of zero-sum stochastic games. The paper also contains a new equilibrium theorem for a class of ergodic non-zero sum stochastic games.