We examine a three-person stochastic game where the only existing equilibria consist of cyclic Markov strategies. Unlike in two-person games of a similar type, stationary $\epsilon $-equilibria $(\epsilon 0)$ do not exist for this game. Besides we characterize the set of feasible equilibrium...

For n-person perfect information stochastic games and for n-person stochastic games with Additive Rewards and Additive Transitions (ARAT) we show the existence of pure limiting average equilibria. Using a similar approach we also derive the existence of limiting average $ \epsilon $-equilibria...