Exponentially many steps for finding a Nash equilibrium in a bimatrix game

@article{Savani2004ExponentiallyMS,
  title={Exponentially many steps for finding a Nash equilibrium in a bimatrix game},
  author={Rahul Savani and Bernhard von Stengel},
  journal={45th Annual IEEE Symposium on Foundations of Computer Science},
  year={2004},
  pages={258-267}
}
The Lemke-Howson algorithm is the classical algorithm for the problem NASH of finding one Nash equilibrium of a bimatrix game. It provides a constructive and elementary proof of existence of an equilibrium, by a typical "directed parity argument", which puts NASH into the complexity class PPAD. This paper presents a class of bimatrix games for which the Lemke-Howson algorithm takes, even in the best case, exponential time in the dimension d of the game, requiring /spl Omega/((/spl theta//sup 3… CONTINUE READING

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