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DOI: 10.4230/LIPIcs.APPROX-RANDOM.2015.78
URN: urn:nbn:de:0030-drops-52959
URL: http://drops.dagstuhl.de/opus/volltexte/2015/5295/
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Anbalagan, Yogesh ; Huang, Hao ; Lovett, Shachar ; Norin, Sergey ; Vetta, Adrian ; Wu, Hehui

Large Supports are Required for Well-Supported Nash Equilibria

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Abstract

We prove that for any constant k and any epsilon < 1, there exist bimatrix win-lose games for which every epsilon-WSNE requires supports of cardinality greater than k. To do this, we provide a graph-theoretic characterization of win-lose games that possess epsilon-WSNE with constant cardinality supports. We then apply a result in additive number theory of Haight to construct win-lose games that do not satisfy the requirements of the characterization. These constructions disprove graph theoretic conjectures of Daskalakis, Mehta and Papadimitriou and Myers.

BibTeX - Entry

@InProceedings{anbalagan_et_al:LIPIcs:2015:5295,
  author =	{Yogesh Anbalagan and Hao Huang and Shachar Lovett and Sergey Norin and Adrian Vetta and Hehui Wu},
  title =	{{Large Supports are Required for Well-Supported Nash Equilibria}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)},
  pages =	{78--84},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-89-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{40},
  editor =	{Naveen Garg and Klaus Jansen and Anup Rao and Jos{\'e} D. P. Rolim},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5295},
  URN =		{urn:nbn:de:0030-drops-52959},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2015.78},
  annote =	{Keywords: bimatrix games, well-supported Nash equilibria}
}

Keywords: bimatrix games, well-supported Nash equilibria
Seminar: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)
Issue Date: 2015
Date of publication: 28.07.2015


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