{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:JPCGI2B4F2IOWHWTTUJJ2OSG43","short_pith_number":"pith:JPCGI2B4","schema_version":"1.0","canonical_sha256":"4bc464683c2e90eb1ed39d129d3a46e6cd80dd91159e7308ad175ba17b593246","source":{"kind":"arxiv","id":"1004.1449","version":2},"attestation_state":"computed","paper":{"title":"Multi-Unit Auctions: Beyond Roberts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Noam Nisan, Shahar Dobzinski","submitted_at":"2010-04-09T02:22:26Z","abstract_excerpt":"We exhibit incentive compatible multi-unit auctions that are not affine maximizers (i.e., are not of the VCG family) and yet approximate the social welfare to within a factor of $1+\\epsilon$. For the case of two-item two-bidder auctions we show that these auctions, termed Triage auctions, are the only scalable ones that give an approximation factor better than 2. \"Scalable\" means that the allocation does not depend on the units in which the valuations are measured. We deduce from this that any scalable computationally-efficient incentive-compatible auction for $m$ items and $n \\ge 2$ bidders c"},"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":"1004.1449","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2010-04-09T02:22:26Z","cross_cats_sorted":[],"title_canon_sha256":"787c62adb92748593bff722a6f473af2204b76e06904bfed1c2b18f0fde0be43","abstract_canon_sha256":"aed7c26c52dd2475fc662b019527f9087376e8dadcd68a6dd2ed6939d664f0a3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:16.892124Z","signature_b64":"mozxQ/pKT7E3lG/4Ng62uIbgCM16+UKjaUo4J9sEk6Plh3eiAT+SV3DkHeuk+ORq8doJva39WWowTISnkrHmAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4bc464683c2e90eb1ed39d129d3a46e6cd80dd91159e7308ad175ba17b593246","last_reissued_at":"2026-05-18T02:24:16.891482Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:16.891482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multi-Unit Auctions: Beyond Roberts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Noam Nisan, Shahar Dobzinski","submitted_at":"2010-04-09T02:22:26Z","abstract_excerpt":"We exhibit incentive compatible multi-unit auctions that are not affine maximizers (i.e., are not of the VCG family) and yet approximate the social welfare to within a factor of $1+\\epsilon$. For the case of two-item two-bidder auctions we show that these auctions, termed Triage auctions, are the only scalable ones that give an approximation factor better than 2. \"Scalable\" means that the allocation does not depend on the units in which the valuations are measured. We deduce from this that any scalable computationally-efficient incentive-compatible auction for $m$ items and $n \\ge 2$ bidders c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1449","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":""},"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":"1004.1449","created_at":"2026-05-18T02:24:16.891585+00:00"},{"alias_kind":"arxiv_version","alias_value":"1004.1449v2","created_at":"2026-05-18T02:24:16.891585+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.1449","created_at":"2026-05-18T02:24:16.891585+00:00"},{"alias_kind":"pith_short_12","alias_value":"JPCGI2B4F2IO","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"JPCGI2B4F2IOWHWT","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"JPCGI2B4","created_at":"2026-05-18T12:26:09.077623+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/JPCGI2B4F2IOWHWTTUJJ2OSG43","json":"https://pith.science/pith/JPCGI2B4F2IOWHWTTUJJ2OSG43.json","graph_json":"https://pith.science/api/pith-number/JPCGI2B4F2IOWHWTTUJJ2OSG43/graph.json","events_json":"https://pith.science/api/pith-number/JPCGI2B4F2IOWHWTTUJJ2OSG43/events.json","paper":"https://pith.science/paper/JPCGI2B4"},"agent_actions":{"view_html":"https://pith.science/pith/JPCGI2B4F2IOWHWTTUJJ2OSG43","download_json":"https://pith.science/pith/JPCGI2B4F2IOWHWTTUJJ2OSG43.json","view_paper":"https://pith.science/paper/JPCGI2B4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1004.1449&json=true","fetch_graph":"https://pith.science/api/pith-number/JPCGI2B4F2IOWHWTTUJJ2OSG43/graph.json","fetch_events":"https://pith.science/api/pith-number/JPCGI2B4F2IOWHWTTUJJ2OSG43/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JPCGI2B4F2IOWHWTTUJJ2OSG43/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JPCGI2B4F2IOWHWTTUJJ2OSG43/action/storage_attestation","attest_author":"https://pith.science/pith/JPCGI2B4F2IOWHWTTUJJ2OSG43/action/author_attestation","sign_citation":"https://pith.science/pith/JPCGI2B4F2IOWHWTTUJJ2OSG43/action/citation_signature","submit_replication":"https://pith.science/pith/JPCGI2B4F2IOWHWTTUJJ2OSG43/action/replication_record"}},"created_at":"2026-05-18T02:24:16.891585+00:00","updated_at":"2026-05-18T02:24:16.891585+00:00"}