License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2022.41
URN: urn:nbn:de:0030-drops-169790
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16979/
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Deligkas, Argyrios ; Fasoulakis, Michail ; Markakis, Evangelos

A Polynomial-Time Algorithm for 1/3-Approximate Nash Equilibria in Bimatrix Games

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Abstract

Since the celebrated PPAD-completeness result for Nash equilibria in bimatrix games, a long line of research has focused on polynomial-time algorithms that compute ε-approximate Nash equilibria. Finding the best possible approximation guarantee that we can have in polynomial time has been a fundamental and non-trivial pursuit on settling the complexity of approximate equilibria. Despite a significant amount of effort, the algorithm of Tsaknakis and Spirakis [Tsaknakis and Spirakis, 2008], with an approximation guarantee of (0.3393+δ), remains the state of the art over the last 15 years. In this paper, we propose a new refinement of the Tsaknakis-Spirakis algorithm, resulting in a polynomial-time algorithm that computes a (1/3+δ)-Nash equilibrium, for any constant δ > 0. The main idea of our approach is to go beyond the use of convex combinations of primal and dual strategies, as defined in the optimization framework of [Tsaknakis and Spirakis, 2008], and enrich the pool of strategies from which we build the strategy profiles that we output in certain bottleneck cases of the algorithm.

BibTeX - Entry

@InProceedings{deligkas_et_al:LIPIcs.ESA.2022.41,
  author =	{Deligkas, Argyrios and Fasoulakis, Michail and Markakis, Evangelos},
  title =	{{A Polynomial-Time Algorithm for 1/3-Approximate Nash Equilibria in Bimatrix Games}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{41:1--41:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16979},
  URN =		{urn:nbn:de:0030-drops-169790},
  doi =		{10.4230/LIPIcs.ESA.2022.41},
  annote =	{Keywords: bimatrix games, approximate Nash equilibria}
}

Keywords: bimatrix games, approximate Nash equilibria
Collection: 30th Annual European Symposium on Algorithms (ESA 2022)
Issue Date: 2022
Date of publication: 01.09.2022

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