Pure Nash equilibria in games with a large number of actions

We study the computational complexity of deciding the existence of a Pure Nash Equilibrium in multi-player strategic games. We address two fundamental questions: how can we represent a game?, and how can we represent a game with polynomial pay-off functions? Our results show that the computational c...

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Detalles Bibliográficos
Autores: Álvarez Faura, M. del Carme|||0000-0003-2352-0546, Gabarró Vallès, Joaquim|||0000-0003-3771-2813, Serna Iglesias, María José|||0000-0001-9729-8648
Tipo de recurso: informe técnico
Fecha de publicación:2004
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/83903
Acceso en línea:https://hdl.handle.net/2117/83903
Access Level:acceso abierto
Palabra clave:Strategic games
Nash equilibria
Complexity classes
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
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spelling Pure Nash equilibria in games with a large number of actionsÁlvarez Faura, M. del Carme|||0000-0003-2352-0546Gabarró Vallès, Joaquim|||0000-0003-3771-2813Serna Iglesias, María José|||0000-0001-9729-8648Strategic gamesNash equilibriaComplexity classesÀrees temàtiques de la UPC::Informàtica::Informàtica teòricaWe study the computational complexity of deciding the existence of a Pure Nash Equilibrium in multi-player strategic games. We address two fundamental questions: how can we represent a game?, and how can we represent a game with polynomial pay-off functions? Our results show that the computational complexity of deciding the existence of a pure Nash equilibrium in an strategic game depends on two parameters: the number of players and the size of the sets of strategies. In particular we show that deciding the existence of a Nash equilibrium in an strategic game is NP-complete when the number of players is large and the number of strategies for each player is constant, while the problem is Sigma_2^p-complete when the number of players is a constant and the size of the sets of strategies is exponential (with respect to the length of the strategies).20042004-11-0120162016-03-07reporthttp://purl.org/coar/resource_type/c_93fcVoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/reportapplication/postscripthttps://hdl.handle.net/2117/83903reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/839032026-05-27T15:37:01Z
dc.title.none.fl_str_mv Pure Nash equilibria in games with a large number of actions
title Pure Nash equilibria in games with a large number of actions
spellingShingle Pure Nash equilibria in games with a large number of actions
Álvarez Faura, M. del Carme|||0000-0003-2352-0546
Strategic games
Nash equilibria
Complexity classes
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
title_short Pure Nash equilibria in games with a large number of actions
title_full Pure Nash equilibria in games with a large number of actions
title_fullStr Pure Nash equilibria in games with a large number of actions
title_full_unstemmed Pure Nash equilibria in games with a large number of actions
title_sort Pure Nash equilibria in games with a large number of actions
dc.creator.none.fl_str_mv Álvarez Faura, M. del Carme|||0000-0003-2352-0546
Gabarró Vallès, Joaquim|||0000-0003-3771-2813
Serna Iglesias, María José|||0000-0001-9729-8648
author Álvarez Faura, M. del Carme|||0000-0003-2352-0546
author_facet Álvarez Faura, M. del Carme|||0000-0003-2352-0546
Gabarró Vallès, Joaquim|||0000-0003-3771-2813
Serna Iglesias, María José|||0000-0001-9729-8648
author_role author
author2 Gabarró Vallès, Joaquim|||0000-0003-3771-2813
Serna Iglesias, María José|||0000-0001-9729-8648
author2_role author
author
dc.subject.none.fl_str_mv Strategic games
Nash equilibria
Complexity classes
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
topic Strategic games
Nash equilibria
Complexity classes
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
description We study the computational complexity of deciding the existence of a Pure Nash Equilibrium in multi-player strategic games. We address two fundamental questions: how can we represent a game?, and how can we represent a game with polynomial pay-off functions? Our results show that the computational complexity of deciding the existence of a pure Nash equilibrium in an strategic game depends on two parameters: the number of players and the size of the sets of strategies. In particular we show that deciding the existence of a Nash equilibrium in an strategic game is NP-complete when the number of players is large and the number of strategies for each player is constant, while the problem is Sigma_2^p-complete when the number of players is a constant and the size of the sets of strategies is exponential (with respect to the length of the strategies).
publishDate 2004
dc.date.none.fl_str_mv 2004
2004-11-01
2016
2016-03-07
dc.type.none.fl_str_mv report
http://purl.org/coar/resource_type/c_93fc
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/report
format report
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/83903
url https://hdl.handle.net/2117/83903
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/postscript
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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