Approximating Values of Generalized-Reachability Stochastic Games

08/14/2019

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by   Pranav Ashok, et al.

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Simple stochastic games are turn-based 2.5-player games with a reachability objective. The basic question asks whether player Max can win a given game with at least a given probability. A natural extension are games with a conjunction of such conditions as objective. Despite a plethora of recent results on analysis of systems with multiple objectives, decidability of this basic problem remains open. In this paper, we show the Pareto frontier of the achievable values can be approximated to a given precision. In particular, our algorithm is not limited to stopping games and can be run as an anytime algorithm, always returning the current approximation and its error bound.