{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:TAOMUDRTHRTOVUTILCGX32ROFG","short_pith_number":"pith:TAOMUDRT","schema_version":"1.0","canonical_sha256":"981cca0e333c66ead268588d7dea2e29a2003f34850beeb943a9da33286e2a28","source":{"kind":"arxiv","id":"1603.06312","version":3},"attestation_state":"computed","paper":{"title":"A rank based mean field game in the strong formulation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","q-fin.MF"],"primary_cat":"math.PR","authors_text":"Erhan Bayraktar, Yuchong Zhang","submitted_at":"2016-03-21T02:26:10Z","abstract_excerpt":"We discuss a natural game of competition and solve the corresponding mean field game with \\emph{common noise} when agents' rewards are \\emph{rank dependent}. We use this solution to provide an approximate Nash equilibrium for the finite player game and obtain the rate of convergence."},"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":"1603.06312","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-21T02:26:10Z","cross_cats_sorted":["math.OC","q-fin.MF"],"title_canon_sha256":"2a9432dedc0db7a5d7f819f1f05d00bbd5783a1f4bd50a5836db0e972a49d499","abstract_canon_sha256":"7ca676a91fd063c94f427fb681a37ab76e58e227fca5148d988934a335b1cc27"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:12.996271Z","signature_b64":"2Lfkl4fTaX4j4AVefdlsJl5woDj1coY4jvehhiCEJP8goXSjBy5ACHi1SZRAPX6SBXzuFwiO3bRJdJm0m2cpBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"981cca0e333c66ead268588d7dea2e29a2003f34850beeb943a9da33286e2a28","last_reissued_at":"2026-05-18T01:02:12.995535Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:12.995535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A rank based mean field game in the strong formulation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","q-fin.MF"],"primary_cat":"math.PR","authors_text":"Erhan Bayraktar, Yuchong Zhang","submitted_at":"2016-03-21T02:26:10Z","abstract_excerpt":"We discuss a natural game of competition and solve the corresponding mean field game with \\emph{common noise} when agents' rewards are \\emph{rank dependent}. We use this solution to provide an approximate Nash equilibrium for the finite player game and obtain the rate of convergence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06312","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":""},"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":"1603.06312","created_at":"2026-05-18T01:02:12.995657+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.06312v3","created_at":"2026-05-18T01:02:12.995657+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06312","created_at":"2026-05-18T01:02:12.995657+00:00"},{"alias_kind":"pith_short_12","alias_value":"TAOMUDRTHRTO","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_16","alias_value":"TAOMUDRTHRTOVUTI","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_8","alias_value":"TAOMUDRT","created_at":"2026-05-18T12:30:44.179134+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/TAOMUDRTHRTOVUTILCGX32ROFG","json":"https://pith.science/pith/TAOMUDRTHRTOVUTILCGX32ROFG.json","graph_json":"https://pith.science/api/pith-number/TAOMUDRTHRTOVUTILCGX32ROFG/graph.json","events_json":"https://pith.science/api/pith-number/TAOMUDRTHRTOVUTILCGX32ROFG/events.json","paper":"https://pith.science/paper/TAOMUDRT"},"agent_actions":{"view_html":"https://pith.science/pith/TAOMUDRTHRTOVUTILCGX32ROFG","download_json":"https://pith.science/pith/TAOMUDRTHRTOVUTILCGX32ROFG.json","view_paper":"https://pith.science/paper/TAOMUDRT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.06312&json=true","fetch_graph":"https://pith.science/api/pith-number/TAOMUDRTHRTOVUTILCGX32ROFG/graph.json","fetch_events":"https://pith.science/api/pith-number/TAOMUDRTHRTOVUTILCGX32ROFG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TAOMUDRTHRTOVUTILCGX32ROFG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TAOMUDRTHRTOVUTILCGX32ROFG/action/storage_attestation","attest_author":"https://pith.science/pith/TAOMUDRTHRTOVUTILCGX32ROFG/action/author_attestation","sign_citation":"https://pith.science/pith/TAOMUDRTHRTOVUTILCGX32ROFG/action/citation_signature","submit_replication":"https://pith.science/pith/TAOMUDRTHRTOVUTILCGX32ROFG/action/replication_record"}},"created_at":"2026-05-18T01:02:12.995657+00:00","updated_at":"2026-05-18T01:02:12.995657+00:00"}