Expressiveness and complexity results for strategic reasoning

Conference item

This paper presents a range of expressiveness and complexity results for the specification, computation, and verification of Nash equilibria in multi-player non-zero-sum concurrent games in which players have goals expressed as temporal logic formulae. Our results are based on a novel approach to the characterisation of equilibria in such games: a semantic characterisation based on winning strategies and memoryful reasoning. This characterisation allows us to obtain a number of other results relating to the analysis of equilibrium properties in temporal logic.

We show that, up to bisimilarity, reasoning about Nash equilibria in multi-player non-zero-sum concurrent games can be done in ATL^* and that constructing equilibrium strategy profiles in such games can be done in 2EXPTIME using finite-memory strategies. We also study two simpler cases, two-player games and sequential games, and show that the specification of equilibria in the latter setting can be obtained in a temporal logic that is weaker than ATL^*. Based on these results, we settle a few open problems, put forward new logical characterisations of equilibria, and provide improved answers and alternative solutions to a number of questions.

Authors: Gutierrez, J; Harrenstein, P; Wooldridge, M

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Schloss Dagstuhl
• Host title: 26th International Conference on Concurrency Theory (CONCUR 2015)
• Volume: 42
• Pages: 268-282
• Publication date: 2015-08-26
• Acceptance date: 2015-06-15
• Event title: Concur 2015, 26th Conference on Concurrency Theory
• Event location: Madrid, Spain
• Event website: http://mafalda.fdi.ucm.es/concur2015/
• Event start date: 2015-09-01
• Event end date: 2015-09-04
• DOI: 10.4230/LIPIcs.CONCUR.2015.268
• ISSN: 1868-8969
• ISBN: 9783939897910
• Language: English
• Keywords: game models; formal verification; temporal logic; Nash equilibrium