Expressiveness and complexity results for strategic reasoning

Julian Gutierrez, Paul Harrenstein, Michael Wooldridge

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

14 Citations (Scopus)


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-zerosum 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.

Original languageEnglish
Title of host publication26th International Conference on Concurrency Theory
EditorsLuca Aceto, David de Frutos Escrig
Place of PublicationSaarbrücken/Wadern Germany
PublisherLIPIcsSchloss Dagstuhl – Leibniz Center for Informatics
Number of pages15
ISBN (Electronic)9783939897910
Publication statusPublished - 2015
Externally publishedYes
EventInternational Conference on Concurrency Theory 2015 - Madrid, Spain
Duration: 1 Sep 20154 Sep 2015
Conference number: 26th

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


ConferenceInternational Conference on Concurrency Theory 2015
Abbreviated titleCONCUR 2015
Internet address


  • Formal verification
  • Game models
  • Nash equilibrium
  • Temporal logic

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