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Smoothed Complexity of 2-player Nash Equilibria
[article]
2020
arXiv
pre-print
We prove that computing a Nash equilibrium of a two-player (n × n) game with payoffs in [-1,1] is PPAD-hard (under randomized reductions) even in the smoothed analysis setting, smoothing with noise of constant magnitude. This gives a strong negative answer to conjectures of Spielman and Teng [ST06] and Cheng, Deng, and Teng [CDT09]. In contrast to prior work proving PPAD-hardness after smoothing by noise of magnitude 1/poly(n) [CDT09], our smoothed complexity result is not proved via hardness
arXiv:2007.10857v1
fatcat:i7tgbussgrcwxk3rva6vzwhrwm