Settling the Complexity of Computing Approximate Two-Player Nash Equilibria

@article{Rubinstein2016SettlingTC,
  title={Settling the Complexity of Computing Approximate Two-Player Nash Equilibria},
  author={Aviad Rubinstein},
  journal={2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)},
  year={2016},
  pages={258-265}
}
  • A. Rubinstein
  • Published 14 June 2016
  • Computer Science
  • 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)
We prove that there exists a constant ε > 0 such that, assuming the Exponential Time Hypothesis for PPAD, computing an ε-approximate Nash equilibrium in a two-player (n × n) game requires quasi-polynomial time, nlog1-o(1) n. This matches (up to the o(1) term) the algorithm of Lipton, Markakis, and Mehta [54]. Our proof relies on a variety of techniques from the study of probabilistically checkable proofs (PCP), this is the first time that such ideas are used for a reduction between problems… 
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We prove that there exists a constant e > 0 such that, assuming the Exponential Time Hypothesis for PPAD, computing an e-approximate Nash equilibrium in a two-player (n × n) game requires
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