{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:3SLHS6ZUQ3DL4QMTOIWGQCXXRO","short_pith_number":"pith:3SLHS6ZU","schema_version":"1.0","canonical_sha256":"dc96797b3486c6be4193722c680af78bac9841fedebf6a217b1e0d534c163287","source":{"kind":"arxiv","id":"1608.07336","version":1},"attestation_state":"computed","paper":{"title":"Playing Anonymous Games using Simple Strategies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.PR"],"primary_cat":"cs.GT","authors_text":"Alistair Stewart, Ilias Diakonikolas, Yu Cheng","submitted_at":"2016-08-25T23:25:57Z","abstract_excerpt":"We investigate the complexity of computing approximate Nash equilibria in anonymous games. Our main algorithmic result is the following: For any $n$-player anonymous game with a bounded number of strategies and any constant $\\delta>0$, an $O(1/n^{1-\\delta})$-approximate Nash equilibrium can be computed in polynomial time. Complementing this positive result, we show that if there exists any constant $\\delta>0$ such that an $O(1/n^{1+\\delta})$-approximate equilibrium can be computed in polynomial time, then there is a fully polynomial-time approximation scheme for this problem.\n  We also present"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1608.07336","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2016-08-25T23:25:57Z","cross_cats_sorted":["cs.DS","math.PR"],"title_canon_sha256":"0c954cf367c38dc7030af2ab0a637d21b0479c42e7755f0c89f4f1f1453e9975","abstract_canon_sha256":"59ad6291e281ab151ceeb8459f28e252b8baaa4c3afff3f850f4085e9ef1144d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:53.340797Z","signature_b64":"KSMinQnYo6jtYg1Bu5pZ6eqMJCxqykU7ErSb97MJ8SpHHIwET9uhpWbmMFBdHY8XIJVIJ4hQ86qWbmxkKkFMCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc96797b3486c6be4193722c680af78bac9841fedebf6a217b1e0d534c163287","last_reissued_at":"2026-05-18T01:07:53.340220Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:53.340220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Playing Anonymous Games using Simple Strategies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.PR"],"primary_cat":"cs.GT","authors_text":"Alistair Stewart, Ilias Diakonikolas, Yu Cheng","submitted_at":"2016-08-25T23:25:57Z","abstract_excerpt":"We investigate the complexity of computing approximate Nash equilibria in anonymous games. Our main algorithmic result is the following: For any $n$-player anonymous game with a bounded number of strategies and any constant $\\delta>0$, an $O(1/n^{1-\\delta})$-approximate Nash equilibrium can be computed in polynomial time. Complementing this positive result, we show that if there exists any constant $\\delta>0$ such that an $O(1/n^{1+\\delta})$-approximate equilibrium can be computed in polynomial time, then there is a fully polynomial-time approximation scheme for this problem.\n  We also present"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07336","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1608.07336","created_at":"2026-05-18T01:07:53.340302+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.07336v1","created_at":"2026-05-18T01:07:53.340302+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07336","created_at":"2026-05-18T01:07:53.340302+00:00"},{"alias_kind":"pith_short_12","alias_value":"3SLHS6ZUQ3DL","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"3SLHS6ZUQ3DL4QMT","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"3SLHS6ZU","created_at":"2026-05-18T12:29:58.707656+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3SLHS6ZUQ3DL4QMTOIWGQCXXRO","json":"https://pith.science/pith/3SLHS6ZUQ3DL4QMTOIWGQCXXRO.json","graph_json":"https://pith.science/api/pith-number/3SLHS6ZUQ3DL4QMTOIWGQCXXRO/graph.json","events_json":"https://pith.science/api/pith-number/3SLHS6ZUQ3DL4QMTOIWGQCXXRO/events.json","paper":"https://pith.science/paper/3SLHS6ZU"},"agent_actions":{"view_html":"https://pith.science/pith/3SLHS6ZUQ3DL4QMTOIWGQCXXRO","download_json":"https://pith.science/pith/3SLHS6ZUQ3DL4QMTOIWGQCXXRO.json","view_paper":"https://pith.science/paper/3SLHS6ZU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.07336&json=true","fetch_graph":"https://pith.science/api/pith-number/3SLHS6ZUQ3DL4QMTOIWGQCXXRO/graph.json","fetch_events":"https://pith.science/api/pith-number/3SLHS6ZUQ3DL4QMTOIWGQCXXRO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3SLHS6ZUQ3DL4QMTOIWGQCXXRO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3SLHS6ZUQ3DL4QMTOIWGQCXXRO/action/storage_attestation","attest_author":"https://pith.science/pith/3SLHS6ZUQ3DL4QMTOIWGQCXXRO/action/author_attestation","sign_citation":"https://pith.science/pith/3SLHS6ZUQ3DL4QMTOIWGQCXXRO/action/citation_signature","submit_replication":"https://pith.science/pith/3SLHS6ZUQ3DL4QMTOIWGQCXXRO/action/replication_record"}},"created_at":"2026-05-18T01:07:53.340302+00:00","updated_at":"2026-05-18T01:07:53.340302+00:00"}