Algorithms for uniform optimal strategies in two-player zero-sum stochastic games with perfect information

In stochastic games with perfect information, in each state at most one player has more than one action available. We propose two algorithms which find the uniform optimal strategies for zero-sum two-player stochastic games with perfect information. Such strategies are optimal for the long term average criterion as well. We prove the convergence for one algorithm, which presents a higher complexity than the other one, for which we provide numerical analysis.