{"paper":{"title":"The Complexity of Computational Problems about Nash Equilibria in Symmetric Win-Lose Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT"],"primary_cat":"cs.CC","authors_text":"Marios Mavronicolas, Vittorio Bil\\`o","submitted_at":"2019-07-24T14:42:24Z","abstract_excerpt":"We revisit the complexity of deciding, given a {\\it bimatrix game,} whether it has a {\\it Nash equilibrium} with certain natural properties; such decision problems were early known to be ${\\mathcal{NP}}$-hard~\\cite{GZ89}. We show that ${\\mathcal{NP}}$-hardness still holds under two significant restrictions in simultaneity: the game is {\\it win-lose} (that is, all {\\it utilities} are $0$ or $1$) and {\\it symmetric}. To address the former restriction, we design win-lose {\\it gadgets} and a win-lose reduction; to accomodate the latter restriction, we employ and analyze the classical {\\it ${\\maths"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.10468","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"}