We consider some well known families of two-player, zero-sum, turn-based, perfect information games that can be viewed as specical cases of Shapley’s stochastic games. We show that the following tasks are polynomial time equivalent: • Solving simple stochastic games, • solving stochastic mean-payoff games with rewards and probabilities given in unary, and • solving stochastic mean-payoff games ...

After a brief survey of iterative algorithms for general stochastic games, we concentrate on finite-step algorithms for two special classes of stochastic games. They are Single-Controller Stochastic Games and Perfect Information Stochastic Games. In the case of single-controller games, the transition probabilities depend on the actions of the same player in all states. In perfect information st...

The existence of the value for stochastic games with finitely many states and actions, as well as for a class of stochastic games with infinitely many states and actions, is proved in [2]. Here we use essentially the same tools to derive the existence of the minmax and maxmin for n-player stochastic games with finitely many states and actions, as well as for a corresponding class of n-person st...

A stochastic graph game is played by two players on a game graph with probabilistic transitions. We consider stochastic graph games with ω-regular winning conditions specified as Rabin or Streett objectives. These games are NP-complete and coNP-complete, respectively. The value of the game for a player at a state s given an objective Φ is the maximal probability that the player can guarantee th...

In this paper we consider two-player zero-sum payoff games on finite graphs, both in the deterministic as well as in the stochastic setting. In the deterministic setting, we consider total-payoff games which have been introduced as a refinement of mean-payoff games [18, 10]. In the stochastic setting, our class is a turn-based variant of liminf-payoff games [15, 16, 4]. In both settings, we pro...

A stochastic graph game is played by two players on a game graph with probabilistic transitions. We consider stochastic graph games with ω-regular winning conditions specified as parity objectives. These games lie in NP ∩ coNP. We present a strategy improvement algorithm for stochastic parity games; this is the first non-brute-force algorithm for solving these games. From the strategy improveme...