families can be solved in deterministic polynomial time. Policy iteration is one of the most important algorithmic schemes for solving infinitary payoff games. It is parameterized by an improvement rule that determines how to proceed in the iteration from one policy to the next. It is a major open problem

of deciding whether the System can ensure that the probability to satisfy the mean-payoff parity objective is at least a given threshold is in NP∩coNP, matching the best known bound in the special case of 2-player games (where all transitions are deterministic). We present an algorithm running in timeO(d·n 2d

equivalent to the problem of deciding the winner in mean-payoff parity games, which can thus be solved in NP ∩ coNP. As a consequence we also obtain a conceptually simple algorithm to solve mean-payoff parity games.

This paper presents a new exponential lower bound for the two most popular deterministic variants of the strategy improvement algorithm for solving parity, mean payoff, discounted payoff and simple stochastic games. The first variant improves every node in each step maximizing the current

is polynomial-time reducible to solving stochastic parity games. We construct practical algorithms for solving the occurring nested fixpoint equations based on strategy iteration. As a corollary we obtain that solving deterministic total-payoff games and solving stochastic liminf-payoff games is in UP ∩ co−UP.

is not more difficult than LTL realizability: it is 2ExpTime-Complete. This is done by reduction to two-player mean-payoff parity games. While infinite memory strategies are required to realize LTLMP specifications in general, we show that -optimality can be obtained with finite memory strategies, for any >

We generalise the hyperplane separation technique (Chatterjee and Velner, 2013) from multi-dimensional mean-payoff to energy games, and achieve an algorithm for solving the latter whose running time is exponential only in the dimension, but not in the number of vertices of the game graph

an additional means to investigate the kinds of information contained in the representations evoked by CSs. Time apparently plays a major role in behavioral learning, as demonstrated by the unblocking effects of temporal variations of reinforcement The uncertainty of reward is a major factor for generating

of turn-based Stochastic Mean Payoff Games. It is a major open problem whether these game families can be solved in polynomial time. The currently fastest algorithms for the solution of all these games are adaptations of the randomized generalizationof linear programming. We refer to the algorithm of

Massively multiplayer online games (MMOGs) have become increasingly popular in the recent years, particularly in the form of online role-playing games (MMORPGs). These games support up to several ten thousand players interacting in a virtual game world. The current commercially successful games