{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:VLTR543GU5T55BMLGUDERUQR6Z","short_pith_number":"pith:VLTR543G","schema_version":"1.0","canonical_sha256":"aae71ef366a767de858b350648d211f6481ab16e382ba004b7d1fd0f3bd6b9a5","source":{"kind":"arxiv","id":"2605.14363","version":1},"attestation_state":"computed","paper":{"title":"Equilibrium for Time-inconsistent Mean Field Games: A Systematic Analysis by Entropy Regularization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Entropy regularization establishes existence of equilibria for time-inconsistent mean field games via convergence of regularized solutions.","cross_cats":[],"primary_cat":"math.OC","authors_text":"Erhan Bayraktar, Keyu Zhang, Xiang Yu, Zhenhua Wang","submitted_at":"2026-05-14T04:45:34Z","abstract_excerpt":"This paper studies the existence and approximation of equilibria for general time-inconsistent mean field game (MFG) problems in the continuous-time setting. To handle the intricate nonlocal equilibrium Hamilton-Jacobi-Bellman (EHJB) system arising from initial-time dependence, such as non-exponential discounting, we develop a vanishing entropy regularization approach for solving the MFG. With entropy regularization, we first characterize the regularized equilibrium via a coupled exploratory equilibrium HJB (EEHJB) equation and a law-dependent stochastic differential equation. By exploiting Sc"},"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":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2605.14363","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-05-14T04:45:34Z","cross_cats_sorted":[],"title_canon_sha256":"22efcea9b2393a8d8d3774cbc78eec7ace67230d916caa2437b55508a8c2e0c7","abstract_canon_sha256":"66de6614abc3ce524599ee634ade8a44960eb370b9b9fb4670447cb4c7950ea2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:07.926702Z","signature_b64":"pDYbQUhfLC177JPGfiZL2eU2IZJwnYr2fK3ZVpQYrX9MjofbaEZgUtxjjwL41S0sAsOM8TwnYf1MlfqqIzviBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aae71ef366a767de858b350648d211f6481ab16e382ba004b7d1fd0f3bd6b9a5","last_reissued_at":"2026-05-17T23:39:07.925886Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:07.925886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equilibrium for Time-inconsistent Mean Field Games: A Systematic Analysis by Entropy Regularization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Entropy regularization establishes existence of equilibria for time-inconsistent mean field games via convergence of regularized solutions.","cross_cats":[],"primary_cat":"math.OC","authors_text":"Erhan Bayraktar, Keyu Zhang, Xiang Yu, Zhenhua Wang","submitted_at":"2026-05-14T04:45:34Z","abstract_excerpt":"This paper studies the existence and approximation of equilibria for general time-inconsistent mean field game (MFG) problems in the continuous-time setting. To handle the intricate nonlocal equilibrium Hamilton-Jacobi-Bellman (EHJB) system arising from initial-time dependence, such as non-exponential discounting, we develop a vanishing entropy regularization approach for solving the MFG. With entropy regularization, we first characterize the regularized equilibrium via a coupled exploratory equilibrium HJB (EEHJB) equation and a law-dependent stochastic differential equation. By exploiting Sc"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"By employing compactness arguments, Young measure techniques, and a duality tool for divergence-form Fokker-Planck equations, we prove that the regularized equilibria converge, up to subsequences, to an equilibrium of the original time-inconsistent MFG.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"Mild assumptions on the data for global existence of regularized equilibria; short time horizon and weak terminal interaction conditions for convergence of the policy iteration algorithm.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Entropy regularization establishes existence and convergence of equilibria for time-inconsistent mean field games via fixed-point arguments and compactness techniques.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Entropy regularization establishes existence of equilibria for time-inconsistent mean field games via convergence of regularized solutions.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"79ba4fdfe19ce32963b653fa0e6c9361478fc909d5ec0e99bb0a7c8d3c72faf9"},"source":{"id":"2605.14363","kind":"arxiv","version":1},"verdict":{"id":"5e3c24d8-65ab-4e64-82d7-42f087d7d422","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:09:12.877005Z","strongest_claim":"By employing compactness arguments, Young measure techniques, and a duality tool for divergence-form Fokker-Planck equations, we prove that the regularized equilibria converge, up to subsequences, to an equilibrium of the original time-inconsistent MFG.","one_line_summary":"Entropy regularization establishes existence and convergence of equilibria for time-inconsistent mean field games via fixed-point arguments and compactness techniques.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"Mild assumptions on the data for global existence of regularized equilibria; short time horizon and weak terminal interaction conditions for convergence of the policy iteration algorithm.","pith_extraction_headline":"Entropy regularization establishes existence of equilibria for time-inconsistent mean field games via convergence of regularized solutions."},"references":{"count":60,"sample":[{"doi":"","year":2025,"title":"Bayraktar, E. and Huang, Y.-J. and Wang, Z. and Zhou, Z. , title =. Mathematics of Operations Research , volume =. 2025 , pages =","work_id":"d093b4ff-5b90-4e90-9051-839b9ccefbbb","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"SIAM Journal on Financial Mathematics , volume =","work_id":"7ee26a97-4126-4b74-bb77-50acc7464b9d","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Mathematics of Operations Research , year =","work_id":"296ce239-9412-4e30-8b87-d3ce1f7ef586","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2017,"title":"On time-inconsistent stochastic control in continuous time , journal =","work_id":"1cdd903d-6eba-47df-a135-7a862fad626a","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Extended hjb equation for mean-variance stopping problem: Vanishing regularization method.Preprint, available at arXiv:2510.24128, 2025","work_id":"c01a2704-b761-4553-b3ed-03da4cfdc7a4","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":60,"snapshot_sha256":"a644c1afc9c1599ac47e05d40ea30b8dc0205fc5a722d54f2297f2f9f128319f","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"db3552ca9fda607a2acc66fea7b72bc1d4f5472b9274f927963cf0e719838225"},"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":"2605.14363","created_at":"2026-05-17T23:39:07.926048+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.14363v1","created_at":"2026-05-17T23:39:07.926048+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.14363","created_at":"2026-05-17T23:39:07.926048+00:00"},{"alias_kind":"pith_short_12","alias_value":"VLTR543GU5T5","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"VLTR543GU5T55BML","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"VLTR543G","created_at":"2026-05-18T12:33:37.589309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":2,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VLTR543GU5T55BMLGUDERUQR6Z","json":"https://pith.science/pith/VLTR543GU5T55BMLGUDERUQR6Z.json","graph_json":"https://pith.science/api/pith-number/VLTR543GU5T55BMLGUDERUQR6Z/graph.json","events_json":"https://pith.science/api/pith-number/VLTR543GU5T55BMLGUDERUQR6Z/events.json","paper":"https://pith.science/paper/VLTR543G"},"agent_actions":{"view_html":"https://pith.science/pith/VLTR543GU5T55BMLGUDERUQR6Z","download_json":"https://pith.science/pith/VLTR543GU5T55BMLGUDERUQR6Z.json","view_paper":"https://pith.science/paper/VLTR543G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.14363&json=true","fetch_graph":"https://pith.science/api/pith-number/VLTR543GU5T55BMLGUDERUQR6Z/graph.json","fetch_events":"https://pith.science/api/pith-number/VLTR543GU5T55BMLGUDERUQR6Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VLTR543GU5T55BMLGUDERUQR6Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VLTR543GU5T55BMLGUDERUQR6Z/action/storage_attestation","attest_author":"https://pith.science/pith/VLTR543GU5T55BMLGUDERUQR6Z/action/author_attestation","sign_citation":"https://pith.science/pith/VLTR543GU5T55BMLGUDERUQR6Z/action/citation_signature","submit_replication":"https://pith.science/pith/VLTR543GU5T55BMLGUDERUQR6Z/action/replication_record"}},"created_at":"2026-05-17T23:39:07.926048+00:00","updated_at":"2026-05-17T23:39:07.926048+00:00"}