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- W2108113998 abstract "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 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 3/4/)/sup d/) many steps, where /spl theta/ is the golden ratio. The parity argument for NASH is thus explicitly shown to be inefficient. The games are constructed using pairs of dual cyclic polytopes with 2d suitably labeled facets in d-space." @default.
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- W2108113998 date "2004-12-23" @default.
- W2108113998 modified "2023-09-23" @default.
- W2108113998 title "Exponentially Many Steps for Finding a Nash Equilibrium in a Bimatrix Game" @default.
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- W2108113998 doi "https://doi.org/10.1109/focs.2004.28" @default.
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