{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:5DTTKGH2N6ECXNOCMFXYVXN5HM","short_pith_number":"pith:5DTTKGH2","schema_version":"1.0","canonical_sha256":"e8e73518fa6f882bb5c2616f8addbd3b104a8df0e9c9009407d243d642d1fc96","source":{"kind":"arxiv","id":"2507.09415","version":2},"attestation_state":"computed","paper":{"title":"Contracting a crowd of heterogeneous agents","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"econ.TH","authors_text":"Erhan Bayraktar, Guillermo Alonso Alvarez, Ibrahim Ekren","submitted_at":"2025-07-12T22:46:09Z","abstract_excerpt":"We study optimal contract design for large populations of heterogeneous agents whose actions generate network spillovers represented by an interaction function. In a linear-quadratic framework, we solve the finite-agent problem and its continuum limit, obtaining explicit optimal contracts and equilibrium efforts. We show that the continuum contract can be evaluated on a large finite sample of agents to obtain admissible contracts that achieve the finite-agent principal's value up to an error of order 1/N. This provides a scalable approximation for settings with many interacting agents. We also"},"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":"2507.09415","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"econ.TH","submitted_at":"2025-07-12T22:46:09Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"689e06265ea0bb2d1b91cc59e4fc6f75f12ca805ddb1374d113911c4d181b94f","abstract_canon_sha256":"c372c9b7c7e1514bf82de02c1a0fed117d7c58f871ef8d662c82f3b0e1efb385"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:05:30.563288Z","signature_b64":"SQ5XXRmLfqUMXrvTXTpvMyKR5hPDUNY54k85k/7pib0F5yZx+QLC5yzU4iUEE00Kq8yOnLxs6wSFfY9as6f4CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8e73518fa6f882bb5c2616f8addbd3b104a8df0e9c9009407d243d642d1fc96","last_reissued_at":"2026-05-20T00:05:30.562545Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:05:30.562545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Contracting a crowd of heterogeneous agents","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"econ.TH","authors_text":"Erhan Bayraktar, Guillermo Alonso Alvarez, Ibrahim Ekren","submitted_at":"2025-07-12T22:46:09Z","abstract_excerpt":"We study optimal contract design for large populations of heterogeneous agents whose actions generate network spillovers represented by an interaction function. In a linear-quadratic framework, we solve the finite-agent problem and its continuum limit, obtaining explicit optimal contracts and equilibrium efforts. We show that the continuum contract can be evaluated on a large finite sample of agents to obtain admissible contracts that achieve the finite-agent principal's value up to an error of order 1/N. This provides a scalable approximation for settings with many interacting agents. We also"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.09415","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.09415/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2507.09415","created_at":"2026-05-20T00:05:30.562664+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.09415v2","created_at":"2026-05-20T00:05:30.562664+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.09415","created_at":"2026-05-20T00:05:30.562664+00:00"},{"alias_kind":"pith_short_12","alias_value":"5DTTKGH2N6EC","created_at":"2026-05-20T00:05:30.562664+00:00"},{"alias_kind":"pith_short_16","alias_value":"5DTTKGH2N6ECXNOC","created_at":"2026-05-20T00:05:30.562664+00:00"},{"alias_kind":"pith_short_8","alias_value":"5DTTKGH2","created_at":"2026-05-20T00:05:30.562664+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/5DTTKGH2N6ECXNOCMFXYVXN5HM","json":"https://pith.science/pith/5DTTKGH2N6ECXNOCMFXYVXN5HM.json","graph_json":"https://pith.science/api/pith-number/5DTTKGH2N6ECXNOCMFXYVXN5HM/graph.json","events_json":"https://pith.science/api/pith-number/5DTTKGH2N6ECXNOCMFXYVXN5HM/events.json","paper":"https://pith.science/paper/5DTTKGH2"},"agent_actions":{"view_html":"https://pith.science/pith/5DTTKGH2N6ECXNOCMFXYVXN5HM","download_json":"https://pith.science/pith/5DTTKGH2N6ECXNOCMFXYVXN5HM.json","view_paper":"https://pith.science/paper/5DTTKGH2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.09415&json=true","fetch_graph":"https://pith.science/api/pith-number/5DTTKGH2N6ECXNOCMFXYVXN5HM/graph.json","fetch_events":"https://pith.science/api/pith-number/5DTTKGH2N6ECXNOCMFXYVXN5HM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5DTTKGH2N6ECXNOCMFXYVXN5HM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5DTTKGH2N6ECXNOCMFXYVXN5HM/action/storage_attestation","attest_author":"https://pith.science/pith/5DTTKGH2N6ECXNOCMFXYVXN5HM/action/author_attestation","sign_citation":"https://pith.science/pith/5DTTKGH2N6ECXNOCMFXYVXN5HM/action/citation_signature","submit_replication":"https://pith.science/pith/5DTTKGH2N6ECXNOCMFXYVXN5HM/action/replication_record"}},"created_at":"2026-05-20T00:05:30.562664+00:00","updated_at":"2026-05-20T00:05:30.562664+00:00"}