{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ZGUHVHJ63OEC4H4GOIP2QEMZ37","short_pith_number":"pith:ZGUHVHJ6","schema_version":"1.0","canonical_sha256":"c9a87a9d3edb882e1f86721fa81199dfe1c76d65c4378768c1d53e732f5fb7c1","source":{"kind":"arxiv","id":"1707.09090","version":1},"attestation_state":"computed","paper":{"title":"Asymptotic Analysis of Mean Field Games with Small Common Noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Saran Ahuja, Tzu-Wei Yang, Weiluo Ren","submitted_at":"2017-07-28T02:39:39Z","abstract_excerpt":"In this paper, we consider a mean field game (MFG) model perturbed by small common noise. Our goal is to give an approximation of the Nash equilibrium strategy of this game using a solution from the original no common noise MFG whose solution can be obtained through a coupled system of partial differential equations. We characterize the first order approximation via linear mean-field forward-backward stochastic differential equations whose solution is a centered Gaussian process with respect to the common noise. The first order approximate strategy can be described as follows: at time $t \\in ["},"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":"1707.09090","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-28T02:39:39Z","cross_cats_sorted":[],"title_canon_sha256":"f02b277afba5553ffd75142f8dab0c97421e5b6a6cec0ede04196e970eb52200","abstract_canon_sha256":"17111194f77875f3901c926844dbee5268108581f01e290940e2f76254c61871"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:17.138007Z","signature_b64":"XsOnYEFYLzx87VsfFraIyG/X3Ybd7x/Mj6fS3Q5ps1iBjheTEDDHBj6I89XuBPDWGdj3jQ6OB11TxtuD5fXmBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9a87a9d3edb882e1f86721fa81199dfe1c76d65c4378768c1d53e732f5fb7c1","last_reissued_at":"2026-05-18T00:39:17.137387Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:17.137387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic Analysis of Mean Field Games with Small Common Noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Saran Ahuja, Tzu-Wei Yang, Weiluo Ren","submitted_at":"2017-07-28T02:39:39Z","abstract_excerpt":"In this paper, we consider a mean field game (MFG) model perturbed by small common noise. Our goal is to give an approximation of the Nash equilibrium strategy of this game using a solution from the original no common noise MFG whose solution can be obtained through a coupled system of partial differential equations. We characterize the first order approximation via linear mean-field forward-backward stochastic differential equations whose solution is a centered Gaussian process with respect to the common noise. The first order approximate strategy can be described as follows: at time $t \\in ["},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.09090","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":"1707.09090","created_at":"2026-05-18T00:39:17.137491+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.09090v1","created_at":"2026-05-18T00:39:17.137491+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.09090","created_at":"2026-05-18T00:39:17.137491+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZGUHVHJ63OEC","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZGUHVHJ63OEC4H4G","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZGUHVHJ6","created_at":"2026-05-18T12:31:59.375834+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/ZGUHVHJ63OEC4H4GOIP2QEMZ37","json":"https://pith.science/pith/ZGUHVHJ63OEC4H4GOIP2QEMZ37.json","graph_json":"https://pith.science/api/pith-number/ZGUHVHJ63OEC4H4GOIP2QEMZ37/graph.json","events_json":"https://pith.science/api/pith-number/ZGUHVHJ63OEC4H4GOIP2QEMZ37/events.json","paper":"https://pith.science/paper/ZGUHVHJ6"},"agent_actions":{"view_html":"https://pith.science/pith/ZGUHVHJ63OEC4H4GOIP2QEMZ37","download_json":"https://pith.science/pith/ZGUHVHJ63OEC4H4GOIP2QEMZ37.json","view_paper":"https://pith.science/paper/ZGUHVHJ6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.09090&json=true","fetch_graph":"https://pith.science/api/pith-number/ZGUHVHJ63OEC4H4GOIP2QEMZ37/graph.json","fetch_events":"https://pith.science/api/pith-number/ZGUHVHJ63OEC4H4GOIP2QEMZ37/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZGUHVHJ63OEC4H4GOIP2QEMZ37/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZGUHVHJ63OEC4H4GOIP2QEMZ37/action/storage_attestation","attest_author":"https://pith.science/pith/ZGUHVHJ63OEC4H4GOIP2QEMZ37/action/author_attestation","sign_citation":"https://pith.science/pith/ZGUHVHJ63OEC4H4GOIP2QEMZ37/action/citation_signature","submit_replication":"https://pith.science/pith/ZGUHVHJ63OEC4H4GOIP2QEMZ37/action/replication_record"}},"created_at":"2026-05-18T00:39:17.137491+00:00","updated_at":"2026-05-18T00:39:17.137491+00:00"}