LIPIcs.APPROX-RANDOM.2015.78.pdf
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Large Supports are Required for Well-Supported Nash Equilibria
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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Conference on Randomization and Computation (RANDOM)
Conference: International Conference on Approximation Algorithms for Combinatorial Optimization Problems (APPROX) - License:
Creative Commons Attribution 3.0 Unported license
- Publication date: 2015-08-13
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Yogesh Anbalagan, Hao Huang, Shachar Lovett, Sergey Norin, Adrian Vetta, and Hehui Wu. Large Supports are Required for Well-Supported Nash Equilibria. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 40, pp. 78-84, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2015)
https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2015.78
https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2015.78
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.
Keywords
- bimatrix games
- well-supported Nash equilibria
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