Pure Nash Equilibria: Hard and Easy Games

@article{Gottlob2005PureNE,
  title={Pure Nash Equilibria: Hard and Easy Games},
  author={Georg Gottlob and Gianluigi Greco and Francesco Scarcello},
  journal={J. Artif. Intell. Res.},
  year={2005},
  volume={24},
  pages={357-406}
}
We investigate complexity issues related to pure Nash equilibria of strategic games. We show that, even in very restrictive settings, determining whether a game has a pure Nash Equilibrium is NP-hard, while deciding whether a game has a strong Nash equilibrium is Σ2P-complete. We then study practically relevant restrictions that lower the complexity. In particular, we are interested in quantitative and qualitative restrictions of the way each player's payoff depends on moves of other players… CONTINUE READING

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