On the Complexity of Approximating a Nash Equilibrium

@article{Daskalakis2011OnTC,
  title={On the Complexity of Approximating a Nash Equilibrium},
  author={Constantinos Daskalakis},
  journal={ACM Trans. Algorithms},
  year={2011},
  volume={9},
  pages={23:1-23:35}
}
We show that computing a relatively (i.e., multiplicatively as opposed to additively) 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 Nash equilibrium, since the original results on the computational complexity of the problem [Daskalakis et al. 2006a; Chen and Deng 2006]. Moreover, it provides an apparent---assuming that PPAD is not contained in TIME(nO(log n… CONTINUE READING
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