# 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} }

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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