Equilibria-based probabilistic model checking for concurrent stochastic games

Kwiatkowska, M., Norman, G. , Parker, D. and Santos, G. (2019) Equilibria-based probabilistic model checking for concurrent stochastic games. In: ter Beek, M. H., McIver, A. and Oliveira, J. N. (eds.) Formal Methods - The Next 30 Years. Series: Lecture Notes in Computer Science (11800). Springer, pp. 298-315. ISBN 9783030309411 (doi: 10.1007/978-3-030-30942-8_19)

Abstract

Probabilistic model checking for stochastic games enables formal verification of systems that comprise competing or collaborating entities operating in a stochastic environment. Despite good progress in the area, existing approaches focus on zero-sum goals and cannot reason about scenarios where entities are endowed with different objectives. In this paper, we propose probabilistic model checking techniques for concurrent stochastic games based on Nash equilibria. We extend the temporal logic rPATL (probabilistic alternating-time temporal logic with rewards) to allow reasoning about players with distinct quantitative goals, which capture either the probability of an event occurring or a reward measure. We present algorithms to synthesise strategies that are subgame perfect social welfare optimal Nash equilibria, i.e., where there is no incentive for any players to unilaterally change their strategy in any state of the game, whilst the combined probabilities or rewards are maximised. We implement our techniques in the PRISM-games tool and apply them to several case studies, including network protocols and robot navigation, showing the benefits compared to existing approaches.

• Item Type: Book Sections
• Additional Information: Proceedings of the Third World Congress, FM 2019, Porto, Portugal, October 7–11, 2019
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Norman, Dr Gethin
• Authors: Kwiatkowska, M., Norman, G., Parker, D., and Santos, G.
• College/School: College of Science and Engineering > School of Computing Science
• Publisher: Springer
• ISSN: 0302-9743
• ISSN (Online): 0302-9743
• ISBN: 9783030309411
• Published Online: 23 September 2019
• Copyright Holders: Copyright © 2019 Springer Nature Switzerland AG
• First Published: First published in Lecture Notes in Computer Science 11800:289-215
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher