{"paper":{"title":"The complexity of approximate Nash equilibrium in congestion games with negative delays","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DS"],"primary_cat":"cs.GT","authors_text":"Frederic Magniez, Michel de Rougemont, Miklos Santha, Xavier Zeitoun","submitted_at":"2011-02-06T15:46:36Z","abstract_excerpt":"We extend the study of the complexity of finding an $\\eps$-approximate Nash equilibrium in congestion games from the case of positive delay functions to delays of arbitrary sign. We first prove that in symmetric games with $\\alpha$-bounded jump the $\\eps$-Nash dynamic converges in polynomial time when all delay functions are negative, similarly to the case of positive delays. We then establish a hardness result for symmetric games with $\\alpha$-bounded jump and with arbitrary delay functions: in that case finding an $\\eps$-Nash equilibrium becomes $\\PLS$-complete."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1161","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"}