Playing stochastic games precisely

Authors:
Taolue Chen;Vojtěch Forejt;Marta Kwiatkowska;Aistis Simaitis;Ashutosh Trivedi;Michael Ummels
Affiliations:
Department of Computer Science, University of Oxford, Oxford, UK;Department of Computer Science, University of Oxford, Oxford, UK;Department of Computer Science, University of Oxford, Oxford, UK;Department of Computer Science, University of Oxford, Oxford, UK;University of Pennsylvania, Philadelphia;Technische Universität Dresden, Germany
Venue:
CONCUR'12 Proceedings of the 23rd international conference on Concurrency Theory
Year:
2012

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Abstract

We study stochastic two-player games where the goal of one player is to achieve precisely a given expected value of the objective function, while the goal of the opponent is the opposite. Potential applications for such games include controller synthesis problems where the optimisation objective is to maximise or minimise a given payoff function while respecting a strict upper or lower bound, respectively. We consider a number of objective functions including reachability, ω-regular, discounted reward, and total reward. We show that precise value games are not determined, and compare the memory requirements for winning strategies. For stopping games we establish necessary and sufficient conditions for the existence of a winning strategy of the controller for a large class of functions, as well as provide the constructions of compact strategies for the studied objectives.