{"paper":{"title":"Solving Matrix Games with Near-Optimal Matvec Complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.GT"],"primary_cat":"math.OC","authors_text":"Aaron Sidford, Ishani Karmarkar, Liam O'Carroll","submitted_at":"2026-01-05T18:44:27Z","abstract_excerpt":"We study the problem of computing an $\\epsilon$-approximate Nash equilibrium of a two-player, bilinear game with a bounded payoff matrix $A \\in \\mathbb{R}^{m \\times n}$, when the players' strategies are constrained to lie in simple sets. We provide algorithms which solve this problem in $\\tilde{O}(\\epsilon^{-2/3})$ matrix-vector multiplies (matvecs) in two well-studied cases: $\\ell_1$-$\\ell_1$ (or zero-sum) games, where the players' strategies are both in the probability simplex, and $\\ell_2$-$\\ell_1$ games (encompassing hard-margin SVMs), where the players' strategies are in the unit Euclidea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.02347","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2601.02347/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}