License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CONCUR.2015.268
URN: urn:nbn:de:0030-drops-53802
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5380/
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Gutierrez, Julian ; Harrenstein, Paul ; Wooldridge, Michael

Expresiveness and Complexity Results for Strategic Reasoning

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Abstract

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.

BibTeX - Entry

@InProceedings{gutierrez_et_al:LIPIcs:2015:5380,
  author =	{Julian Gutierrez and Paul Harrenstein and Michael Wooldridge},
  title =	{{Expresiveness and Complexity Results for Strategic Reasoning}},
  booktitle =	{26th International Conference on Concurrency Theory (CONCUR 2015)},
  pages =	{268--282},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-91-0},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{42},
  editor =	{Luca Aceto and David de Frutos Escrig},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5380},
  URN =		{urn:nbn:de:0030-drops-53802},
  doi =		{10.4230/LIPIcs.CONCUR.2015.268},
  annote =	{Keywords: Temporal logic, Nash equilibrium, game models, formal verification}
}

Keywords: Temporal logic, Nash equilibrium, game models, formal verification
Collection: 26th International Conference on Concurrency Theory (CONCUR 2015)
Issue Date: 2015
Date of publication: 26.08.2015

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