{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:EK3JI6AOIC7X3DF4CHORKSEJ5D","short_pith_number":"pith:EK3JI6AO","schema_version":"1.0","canonical_sha256":"22b694780e40bf7d8cbc11dd154889e8d542caa844b7263a305c8b23585c0453","source":{"kind":"arxiv","id":"1703.10211","version":8},"attestation_state":"computed","paper":{"title":"Connections between Mean-Field Game and Social Welfare Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Lin Zhao, Sen Li, Wei Zhang","submitted_at":"2017-03-29T19:36:52Z","abstract_excerpt":"This paper studies the connection between a class of mean-field games and a social welfare optimization problem. We consider a mean-field game in function spaces with a large population of agents, and each agent seeks to minimize an individual cost function. The cost functions of different agents are coupled through a mean-field term that depends on the mean of the population states. We show that although the mean-field game is not a potential game, under some mild condition the $\\epsilon$-Nash equilibrium of the mean-field game coincides with the optimal solution to a social welfare optimizat"},"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":"1703.10211","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-03-29T19:36:52Z","cross_cats_sorted":[],"title_canon_sha256":"dab4cf0ccb8699b3fd8d9c928c21857be4fb4d92405a5de3356d4f6a26112eb6","abstract_canon_sha256":"c64ab000f46a6ae564530dbcb13b926344f758fc4d0e8fa82d9004a4b386d777"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:23.337755Z","signature_b64":"NbacWq6t5AsyGOL7rmQqUygF7ZQWRSWOrvq3N+R0zJ71SIyQS0+X9iD2lBkDawLD418zsX44cdgAxuVWKcWDCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22b694780e40bf7d8cbc11dd154889e8d542caa844b7263a305c8b23585c0453","last_reissued_at":"2026-05-18T00:23:23.337140Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:23.337140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Connections between Mean-Field Game and Social Welfare Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Lin Zhao, Sen Li, Wei Zhang","submitted_at":"2017-03-29T19:36:52Z","abstract_excerpt":"This paper studies the connection between a class of mean-field games and a social welfare optimization problem. We consider a mean-field game in function spaces with a large population of agents, and each agent seeks to minimize an individual cost function. The cost functions of different agents are coupled through a mean-field term that depends on the mean of the population states. We show that although the mean-field game is not a potential game, under some mild condition the $\\epsilon$-Nash equilibrium of the mean-field game coincides with the optimal solution to a social welfare optimizat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10211","kind":"arxiv","version":8},"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":"1703.10211","created_at":"2026-05-18T00:23:23.337269+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.10211v8","created_at":"2026-05-18T00:23:23.337269+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10211","created_at":"2026-05-18T00:23:23.337269+00:00"},{"alias_kind":"pith_short_12","alias_value":"EK3JI6AOIC7X","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"EK3JI6AOIC7X3DF4","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"EK3JI6AO","created_at":"2026-05-18T12:31:12.930513+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/EK3JI6AOIC7X3DF4CHORKSEJ5D","json":"https://pith.science/pith/EK3JI6AOIC7X3DF4CHORKSEJ5D.json","graph_json":"https://pith.science/api/pith-number/EK3JI6AOIC7X3DF4CHORKSEJ5D/graph.json","events_json":"https://pith.science/api/pith-number/EK3JI6AOIC7X3DF4CHORKSEJ5D/events.json","paper":"https://pith.science/paper/EK3JI6AO"},"agent_actions":{"view_html":"https://pith.science/pith/EK3JI6AOIC7X3DF4CHORKSEJ5D","download_json":"https://pith.science/pith/EK3JI6AOIC7X3DF4CHORKSEJ5D.json","view_paper":"https://pith.science/paper/EK3JI6AO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.10211&json=true","fetch_graph":"https://pith.science/api/pith-number/EK3JI6AOIC7X3DF4CHORKSEJ5D/graph.json","fetch_events":"https://pith.science/api/pith-number/EK3JI6AOIC7X3DF4CHORKSEJ5D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EK3JI6AOIC7X3DF4CHORKSEJ5D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EK3JI6AOIC7X3DF4CHORKSEJ5D/action/storage_attestation","attest_author":"https://pith.science/pith/EK3JI6AOIC7X3DF4CHORKSEJ5D/action/author_attestation","sign_citation":"https://pith.science/pith/EK3JI6AOIC7X3DF4CHORKSEJ5D/action/citation_signature","submit_replication":"https://pith.science/pith/EK3JI6AOIC7X3DF4CHORKSEJ5D/action/replication_record"}},"created_at":"2026-05-18T00:23:23.337269+00:00","updated_at":"2026-05-18T00:23:23.337269+00:00"}