Pure Nash Equilibria in Games with a Large Number of Actions

@article{lvarez2005PureNE,
  title={Pure Nash Equilibria in Games with a Large Number of Actions},
  author={Carme {\`A}lvarez and Joaquim Gabarr{\'o} and Maria J. Serna},
  journal={Electron. Colloquium Comput. Complex.},
  year={2005},
  volume={TR05}
}
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… 

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