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...
| Autores: | , , |
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| 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 |
| 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). |
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