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- W2057913812 abstract "We prove that Bimatrix, the problem of finding a Nash equilibrium in a two-player game, is complete for the complexity class PPAD (Polynomial Parity Argument, Directed version) introduced by Papadimitriou in 1991. Our result, building upon the work of Daskalakis et al. [2006a] on the complexity of four-player Nash equilibria, settles a long standing open problem in algorithmic game theory. It also serves as a starting point for a series of results concerning the complexity of two-player Nash equilibria. In particular, we prove the following theorems: —Bimatrix does not have a fully polynomial-time approximation scheme unless every problem in PPAD is solvable in polynomial time. —The smoothed complexity of the classic Lemke-Howson algorithm and, in fact, of any algorithm for Bimatrix is not polynomial unless every problem in PPAD is solvable in randomized polynomial time. Our results also have a complexity implication in mathematical economics: —Arrow-Debreu market equilibria are PPAD -hard to compute." @default.
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- W2057913812 date "2009-05-01" @default.
- W2057913812 modified "2023-10-17" @default.
- W2057913812 title "Settling the complexity of computing two-player Nash equilibria" @default.
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- W2057913812 doi "https://doi.org/10.1145/1516512.1516516" @default.
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