Decidability Results for Multi-objective Stochastic Games

BRENGUIER, Romain and Vojtěch FOREJT. Decidability Results for Multi-objective Stochastic Games. In Artho C., Legay A., Peled D. International Symposium on Automated Technology for Verification and Analysis. Germany: Springer, 2016, p. 227-243. ISBN 978-3-319-46519-7. Available from: https://dx.doi.org/10.1007/978-3-319-46520-3_15.

Basic information

Original name

Decidability Results for Multi-objective Stochastic Games

Authors

BRENGUIER, Romain (250 France) and Vojtěch FOREJT (203 Czech Republic, guarantor, belonging to the institution)

Edition

Germany, International Symposium on Automated Technology for Verification and Analysis, p. 227-243, 17 pp. 2016

Publisher

Springer

---

Other information

Language

English

Type of outcome

Stať ve sborníku

Field of Study

10201 Computer sciences, information science, bioinformatics

Country of publisher

Germany

Confidentiality degree

není předmětem státního či obchodního tajemství

Publication form

printed version "print"

Impact factor

Impact factor: 0.402 in 2005

RIV identification code

RIV/00216224:14330/16:00094154

Organization unit

Faculty of Informatics

ISBN

978-3-319-46519-7

ISSN

DOI

http://dx.doi.org/10.1007/978-3-319-46520-3_15

Keywords in English

stochastic games; multi-criteria optimisation

Tags

core_A, firank_A

---

Abstract

V originále

We study stochastic two-player turn-based games in which the objective of one player is to ensure several infinite-horizon total reward objectives, while the other player attempts to spoil at least one of the objectives. The games have previously been shown not to be determined, and an approximation algorithm for computing a Pareto curve has been given. The major drawback of the existing algorithm is that it needs to compute Pareto curves for finite horizon objectives (for increasing length of the horizon), and the size of these Pareto curves can grow unboundedly, even when the infinite-horizon Pareto curve is small. By adapting existing results, we first give an algorithm that computes the Pareto curve for determined games. Then, as the main result of the paper, we show that for the natural class of stopping games and when there are two reward objectives, the problem of deciding whether a player can ensure satisfaction of the objectives with given thresholds is decidable. The result relies on an intricate and novel proof which shows that the Pareto curves contain only finitely many points. As a consequence, we get that the two-objective discounted-reward problem for unrestricted class of stochastic games is decidable.