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On the Complexity of Two-PlayerWin-Lose Games
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The complexity of computing a Nash equilibrium
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Settling the Complexity of Two-Player Nash Equilibrium
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On the Complexity of Nash Equilibria and Other Fixed Points (Extended Abstract)
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How hard is it to approximate the best Nash equilibrium?
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On a Network Generalization of the Minmax Theorem
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Polynomial algorithms for approximating nash equilibria of bimatrix games
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A note on approximate nash equilibria
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Efficient algorithms for constant well supported approximate equilibria in bimatrix games
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The complexity of decision problems about nash equilibria in win-lose games
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We show that computing a relative---that is, multiplicative as opposed to additive---approximate Nash equilibrium in two-player games is PPAD-complete, even for constant values of the approximation. Our result is the first constant inapproximability result for the problem, since the appearance of the original results on the complexity of the Nash equilibrium [8, 5, 7]. Moreover, it provides an apparent---assuming that PPAD ⊈ TIME(nO(log n))---dichotomy between the complexities of additive and relative notions of approximation, since for constant values of additive approximation a quasi-polynomial-time algorithm is known [22]. Such a dichotomy does not arise for values of the approximation that scale with the size of the game, as both relative and additive approximations are PPAD-complete [7]. As a byproduct, our proof shows that the Lipton-Markakis-Mehta sampling lemma is not applicable to relative notions of constant approximation, answering in the negative direction a question posed to us by Shang-Hua Teng [26].