Perfect Information Stochastic Games and Related Classes

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 for two-person switching control stochastic games. The orderfield property holds for each of the classes mentioned, and algorithms to compute equilibria are pointed out.