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
Descripción
Sumario: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).