{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:2OBY3GPXQMUH4G4ZUKNBCEUNPZ","short_pith_number":"pith:2OBY3GPX","schema_version":"1.0","canonical_sha256":"d3838d99f783287e1b99a29a11128d7e6e7869483b1b0e2b212a072c0ac6e332","source":{"kind":"arxiv","id":"1811.02811","version":1},"attestation_state":"computed","paper":{"title":"Remarks on Nash equilibria in mean field game models with a major player","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alessio Porretta (DIPMAT), Marco Cirant, Pierre Cardaliaguet (CEREMADE)","submitted_at":"2018-11-07T09:51:03Z","abstract_excerpt":"For a mean field game model with a major and infinite minor players, we characterize a notion of Nash equilibrium via a system of so-called master equations, namely a system of nonlinear transport equations in the space of measures. Then, for games with a finite number N of minor players and a major player, we prove that the solution of the corresponding Nash system converges to the solution of the system of master equations as N tends to infinity."},"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":"1811.02811","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-11-07T09:51:03Z","cross_cats_sorted":[],"title_canon_sha256":"a4e0075632cc80a0f7df68903626712314272b233ba7f3fc08f5a8eb8d3263bb","abstract_canon_sha256":"4186e1013c8283e9fc48d9a58a6e78e96fc6631a70c4d80359966cfa3bc84d30"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:20.704345Z","signature_b64":"ikEIbJLfV8iYBkqMO4iXjvd8x+CPj59PWTCUMwfiwaxB7AusJ6OrrMAzIfoyePKarVTxsYiNvMQzqlD+1ygeCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3838d99f783287e1b99a29a11128d7e6e7869483b1b0e2b212a072c0ac6e332","last_reissued_at":"2026-05-18T00:01:20.703775Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:20.703775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Remarks on Nash equilibria in mean field game models with a major player","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alessio Porretta (DIPMAT), Marco Cirant, Pierre Cardaliaguet (CEREMADE)","submitted_at":"2018-11-07T09:51:03Z","abstract_excerpt":"For a mean field game model with a major and infinite minor players, we characterize a notion of Nash equilibrium via a system of so-called master equations, namely a system of nonlinear transport equations in the space of measures. Then, for games with a finite number N of minor players and a major player, we prove that the solution of the corresponding Nash system converges to the solution of the system of master equations as N tends to infinity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.02811","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":"1811.02811","created_at":"2026-05-18T00:01:20.703865+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.02811v1","created_at":"2026-05-18T00:01:20.703865+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.02811","created_at":"2026-05-18T00:01:20.703865+00:00"},{"alias_kind":"pith_short_12","alias_value":"2OBY3GPXQMUH","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"2OBY3GPXQMUH4G4Z","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"2OBY3GPX","created_at":"2026-05-18T12:32:02.567920+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/2OBY3GPXQMUH4G4ZUKNBCEUNPZ","json":"https://pith.science/pith/2OBY3GPXQMUH4G4ZUKNBCEUNPZ.json","graph_json":"https://pith.science/api/pith-number/2OBY3GPXQMUH4G4ZUKNBCEUNPZ/graph.json","events_json":"https://pith.science/api/pith-number/2OBY3GPXQMUH4G4ZUKNBCEUNPZ/events.json","paper":"https://pith.science/paper/2OBY3GPX"},"agent_actions":{"view_html":"https://pith.science/pith/2OBY3GPXQMUH4G4ZUKNBCEUNPZ","download_json":"https://pith.science/pith/2OBY3GPXQMUH4G4ZUKNBCEUNPZ.json","view_paper":"https://pith.science/paper/2OBY3GPX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.02811&json=true","fetch_graph":"https://pith.science/api/pith-number/2OBY3GPXQMUH4G4ZUKNBCEUNPZ/graph.json","fetch_events":"https://pith.science/api/pith-number/2OBY3GPXQMUH4G4ZUKNBCEUNPZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2OBY3GPXQMUH4G4ZUKNBCEUNPZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2OBY3GPXQMUH4G4ZUKNBCEUNPZ/action/storage_attestation","attest_author":"https://pith.science/pith/2OBY3GPXQMUH4G4ZUKNBCEUNPZ/action/author_attestation","sign_citation":"https://pith.science/pith/2OBY3GPXQMUH4G4ZUKNBCEUNPZ/action/citation_signature","submit_replication":"https://pith.science/pith/2OBY3GPXQMUH4G4ZUKNBCEUNPZ/action/replication_record"}},"created_at":"2026-05-18T00:01:20.703865+00:00","updated_at":"2026-05-18T00:01:20.703865+00:00"}