The Complexity of pure Nash equilibria in weighted Max-Congestion Games

We study Network Max-Congestion Games (NMC games, for short), a class of network games where each player tries to minimize the most congested edge along the path he uses as strategy. We focus our study on the complexity of computing a pure Nash equilibria in weighted NMC games. We show that, for sin...

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Detalhes bibliográficos
Autores: Álvarez Faura, M. del Carme|||0000-0003-2352-0546, Francès Medina, Guillem
Tipo de documento: relatório científico
Data de publicação:2008
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositório:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglês
OAI Identifier:oai:upcommons.upc.edu:2117/81965
Acesso em linha:https://hdl.handle.net/2117/81965
Access Level:Acceso aberto
Palavra-chave:Nash Equilibria
PLS
Complexity
Maximum Congestion
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
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spelling The Complexity of pure Nash equilibria in weighted Max-Congestion GamesÁlvarez Faura, M. del Carme|||0000-0003-2352-0546Francès Medina, GuillemNash EquilibriaPLSComplexityMaximum CongestionÀrees temàtiques de la UPC::Informàtica::Informàtica teòricaWe study Network Max-Congestion Games (NMC games, for short), a class of network games where each player tries to minimize the most congested edge along the path he uses as strategy. We focus our study on the complexity of computing a pure Nash equilibria in weighted NMC games. We show that, for single-commodity games with non-decreasing delay functions, this problem is in P when either all the paths from the source to the target node are disjoint or all the delay functions are equal. For the general case, we prove that the computation of a PNE belongs to the complexity class PLS through a new technique based on semi-potential functions and a slightly modified definition of the usual local search neighborhood. We further apply this technique to a different class of games (which we call Pareto-efficient) with restricted cost functions. Finally, we also prove some PLS-hardness results, showing that computing a PNE for Pareto-efficient NMC games is indeed a PLS- complete problem.Universitat Politècnica de Catalunya. Departament de Llenguatges i Sistemes Informàtics20082008-03-0420162016-01-25reporthttp://purl.org/coar/resource_type/c_93fcVoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/reportapplication/pdfhttps://hdl.handle.net/2117/81965reponame: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:2117/819652026-05-27T15:37:01Z
dc.title.none.fl_str_mv The Complexity of pure Nash equilibria in weighted Max-Congestion Games
title The Complexity of pure Nash equilibria in weighted Max-Congestion Games
spellingShingle The Complexity of pure Nash equilibria in weighted Max-Congestion Games
Álvarez Faura, M. del Carme|||0000-0003-2352-0546
Nash Equilibria
PLS
Complexity
Maximum Congestion
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
title_short The Complexity of pure Nash equilibria in weighted Max-Congestion Games
title_full The Complexity of pure Nash equilibria in weighted Max-Congestion Games
title_fullStr The Complexity of pure Nash equilibria in weighted Max-Congestion Games
title_full_unstemmed The Complexity of pure Nash equilibria in weighted Max-Congestion Games
title_sort The Complexity of pure Nash equilibria in weighted Max-Congestion Games
dc.creator.none.fl_str_mv Álvarez Faura, M. del Carme|||0000-0003-2352-0546
Francès Medina, Guillem
author Álvarez Faura, M. del Carme|||0000-0003-2352-0546
author_facet Álvarez Faura, M. del Carme|||0000-0003-2352-0546
Francès Medina, Guillem
author_role author
author2 Francès Medina, Guillem
author2_role author
dc.subject.none.fl_str_mv Nash Equilibria
PLS
Complexity
Maximum Congestion
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
topic Nash Equilibria
PLS
Complexity
Maximum Congestion
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
description We study Network Max-Congestion Games (NMC games, for short), a class of network games where each player tries to minimize the most congested edge along the path he uses as strategy. We focus our study on the complexity of computing a pure Nash equilibria in weighted NMC games. We show that, for single-commodity games with non-decreasing delay functions, this problem is in P when either all the paths from the source to the target node are disjoint or all the delay functions are equal. For the general case, we prove that the computation of a PNE belongs to the complexity class PLS through a new technique based on semi-potential functions and a slightly modified definition of the usual local search neighborhood. We further apply this technique to a different class of games (which we call Pareto-efficient) with restricted cost functions. Finally, we also prove some PLS-hardness results, showing that computing a PNE for Pareto-efficient NMC games is indeed a PLS- complete problem.
publishDate 2008
dc.date.none.fl_str_mv 2008
2008-03-04
2016
2016-01-25
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/2117/81965
url https://hdl.handle.net/2117/81965
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/pdf
dc.publisher.none.fl_str_mv Universitat Politècnica de Catalunya. Departament de Llenguatges i Sistemes Informàtics
publisher.none.fl_str_mv Universitat Politècnica de Catalunya. Departament de Llenguatges i Sistemes Informàtics
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 15.301603

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