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arXiv · 1504.03602

Large Supports are required for Well-Supported Nash Equilibria

Yogesh Anbalagan·Hao Huang·Shachar Lovett·Sergey Norin·Adrian Vetta·Hehui Wu
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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.

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Yogesh Anbalagan, Hao Huang, Shachar Lovett, Sergey Norin, Adrian Vetta, Hehui Wu. 2015-04-14. Large Supports are required for Well-Supported Nash Equilibria. https://arxiv.org/abs/1504.03602

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