Large Supports are Required for Well-Supported Nash Equilibria

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 graphtheoretic 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 [13].

• Type: Journal
• Year: 2015
• Where: APPROX
• Authors: Yogesh Anbalagan, Hao Huang, Shachar Lovett, Sergey Norin, Adrian Vetta, Hehui Wu
• Keywords: Algorithms, APPROX 2015