Large Supports are Required for Well-Supported Nash Equilibria

Yogesh Anbalagan, Hao Huang, Shachar Lovett, Sergey Norin, Adrian Vetta, Hehui Wu
We prove that for any constant k and any < 1, there exist bimatrix win-lose games for which every-WSNE requires supports of cardinality greater than k. To do this, we provide a graph-theoretic characterization of win-lose games that possess-WSNE with constant cardinality supports. We then apply a result in additive number theory of Haight [8] 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 [7] and Myers [10].