We show that the problem of finding optimal strategies for both players in a simple stochastic game reduces to the generalized linear complementarity problem (GLCP) with a P-matrix, a well-studied problem whose hardness would imply NP = co-NP. This makes the rich GLCP theory and numerous existing algorithms available for simple stochastic games. As a special case, we get a reduction from binary...

This paper deals with perturbed matrix games. The main result is that the sets of solutions of perturbed games converge to subsets of solutions of appropriate lexicographic games. We consider applications of these results to dynamic games. In particular, we consider applications to repeated games with weighted discounted criteria and to finite-horizon stochastic games with perturbed transition ...

We consider turn-based stochastic games on infinite graphs induced by game probabilistic lossy channel systems (GPLCS), the game version of probabilistic lossy channel systems (PLCS). We study games with Büchi (repeated reachability) objectives and almost-sure winning conditions. These games are pure memoryless determined and, under the assumption that the target set is regular, a symbolic repr...