# Settling the complexity of computing approximate two-player Nash equilibria

Settling the complexity of computing approximate two-player Nash equilibria In our recent paper [Rubinstein 2016] we rule out a PTAS for the 2-Player Nash Equilibrium Problem. More precisely, 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 time nlog1o(1) n. This matches (up to the o (1) term) the algorithm of Lipton, Markakis, and Mehta [Lipton et al. 2003]. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM SIGecom Exchanges Association for Computing Machinery

# Settling the complexity of computing approximate two-player Nash equilibria

, Volume 15 (2): 5 – Feb 24, 2017
5 pages

/lp/association-for-computing-machinery/settling-the-complexity-of-computing-approximate-two-player-nash-7yFA20hAVj
Publisher
Association for Computing Machinery
ISSN
1551-9031
eISSN
1551-9031
DOI
10.1145/3055589.3055596
Publisher site
See Article on Publisher Site

### Abstract

In our recent paper [Rubinstein 2016] we rule out a PTAS for the 2-Player Nash Equilibrium Problem. More precisely, 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 time nlog1o(1) n. This matches (up to the o (1) term) the algorithm of Lipton, Markakis, and Mehta [Lipton et al. 2003].

### Journal

ACM SIGecom ExchangesAssociation for Computing Machinery

Published: Feb 24, 2017

Keywords: Nash equilibrium