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Expresiveness and Complexity Results for Strategic Reasoning Gutierrez, Julian Harrenstein, Paul Wooldridge, Michael Temporal logic Nash equilibrium game models formal verification 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Julian Gutierrez and Paul Harrenstein and Michael Wooldridge 2015 Is Part Of LIPIcs, Volume 42, 26th International Conference on Concurrency Theory (CONCUR 2015) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CONCUR.2015.268 urn:nbn:de:0030-drops-53802 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2015.268 eng https://creativecommons.org/licenses/by/3.0/legalcode