{"paper":{"title":"Large Supports are required for Well-Supported Nash Equilibria","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.GT","authors_text":"Adrian Vetta, Hao Huang, Hehui Wu, Sergey Norin, Shachar Lovett, Yogesh Anbalagan","submitted_at":"2015-04-14T16:07:57Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03602","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}