Pure Nash Equilibria in Games with a Large Number of Actions

  • Carme Àlvarez
  • Joaquim Gabarró
  • Maria Serna
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3618)

Abstract

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 a 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 a 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 Σ\(^{p}_{\rm 2}\)-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).

Keywords

Strategic games Nash equilibria complexity classes 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Carme Àlvarez
    • 1
  • Joaquim Gabarró
    • 1
  • Maria Serna
    • 1
  1. 1.ALBCOM Research Group.Universitat Politècnica de CatalunyaBarcelonaSpain

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