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FOCS
2006
IEEE

Computing Nash Equilibria: Approximation and Smoothed Complexity

13 years 9 months ago
Computing Nash Equilibria: Approximation and Smoothed Complexity
We advance significantly beyond the recent progress on the algorithmic complexity of Nash equilibria by solving two major open problems in the approximation of Nash equilibria and in the smoothed analysis of algorithms. • We show that no algorithm with complexity poly(n, 1 ) can compute an -approximate Nash equilibrium in a two-player game, in which each player has n pure strategies, unless PPAD ⊆ P. In other words, the problem of computing a Nash equilibrium in a twoplayer game does not have a fully polynomial-time approximation scheme unless PPAD ⊆ P. • We prove that no algorithm for computing a Nash equilibrium in a two-player game can have smoothed complexity poly(n, 1 σ ) under input perturbation of magnitude σ, unless PPAD ⊆ RP. In particular, the smoothed complexity of the classic Lemke-Howson algorithm is not polynomial unless PPAD ⊆ RP. Instrumental to our proof, we introduce a new discrete fixed-point problem on a high-dimensional hypergrid with constant side...
Xi Chen, Xiaotie Deng, Shang-Hua Teng
Added 11 Jun 2010
Updated 11 Jun 2010
Type Conference
Year 2006
Where FOCS
Authors Xi Chen, Xiaotie Deng, Shang-Hua Teng
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