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[CFK+13c] T. Chen, V. Forejt, M. Kwiatkowska, A. Simaitis and C. Wiltsche. On Stochastic Games with Multiple Objectives. In Krishnendu Chatterjee and Jiri Sgall (editors), Proc. 38th International Symposium on Mathematical Foundations of Computer Science (MFCS'13), volume 8087 of Lecture Notes in Computer Science, pages 266-277, Springer. 2013. [pdf] [bib]
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Notes: An extended version of this paper, including proofs, can be found at http://www.cs.ox.ac.uk/files/5612/CS-RR-13-06.pdf. The original publication is available at link.springer.com.
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.