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[CFK+13c] Taolue Chen, Vojtech Forejt, Marta Kwiatkowska, Aistis Simaitis and Clemens Wiltsche. On Stochastic Games with Multiple Objectives. In Proc. 38th International Symposium on Mathematical Foundations of Computer Science (MFCS'13), volume 8087 of LNCS, pages 266-277, Springer. August 2013. [pdf] [bib] [Studies strategy synthesis and Pareto set approximation for multiple reward objectives in stochastic 2-player games.]
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Abstract. We study two-player stochastic games, where the goal of one player is to satisfy a formula given as a positive boolean combination of expected total reward objectives and the behaviour of the second player is adversarial. Such games are important for modelling, synthesis and verification of open systems with stochastic behaviour. We show that finding a winning strategy is PSPACE-hard in general and undecidable for deterministic strategies. We also prove that optimal strategies, if they exist, may require infinite memory and randomisation. However, when restricted to disjunctions of objectives only, memoryless deterministic strategies suffice, and the problem of deciding whether a winning strategy exists is NP-complete. We also present algorithms to approximate the Pareto sets of achievable objectives for the class of stopping games.

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