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SIAMCOMP

2010

2010

We reexamine what it means to compute Nash equilibria and, more generally, what it means to compute a ﬁxed point of a given Brouwer function, and we investigate the complexity of the associated problems. Speciﬁcally, we study the complexity of the following problem: given a ﬁnite game, Γ, with 3 or more players, and given > 0, compute an approximation within of some (actual) Nash equilibrium. We show that approximation of an actual Nash Equilibrium, even to within any non-trivial constant additive factor < 1/2 in just one desired coordinate, is at least as hard as the long standing square-root sum problem, as well as a more general arithmetic circuit decision problem that characterizes P-time in a unit-cost model of computation with arbitrary precision rational arithmetic; thus placing the approximation problem in P, or even NP, would resolve major open problems in the complexity of numerical computation. We show similar results for market equilibria: it is hard to estima...

Related Content

Added |
30 Jan 2011 |

Updated |
30 Jan 2011 |

Type |
Journal |

Year |
2010 |

Where |
SIAMCOMP |

Authors |
Kousha Etessami, Mihalis Yannakakis |

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