{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:44AJJML7D5RGAGKXO2BVPBGT2A","short_pith_number":"pith:44AJJML7","schema_version":"1.0","canonical_sha256":"e70094b17f1f6260195776835784d3d026b20a4af9ab5076993e4373352205ee","source":{"kind":"arxiv","id":"1708.08907","version":4},"attestation_state":"computed","paper":{"title":"Bounding the Menu-Size of Approximately Optimal Auctions via Optimal-Transport Duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Yannai A. Gonczarowski","submitted_at":"2017-08-29T17:48:59Z","abstract_excerpt":"The question of the minimum menu-size for approximate (i.e., up-to-$\\varepsilon$) Bayesian revenue maximization when selling two goods to an additive risk-neutral quasilinear buyer was introduced by Hart and Nisan (2013), who give an upper bound of $O(\\frac{1}{\\varepsilon^4})$ for this problem. Using the optimal-transport duality framework of Daskalakis et al. (2013, 2015), we derive the first lower bound for this problem - of $\\Omega(\\frac{1}{\\sqrt[4]{\\varepsilon}})$, even when the values for the two goods are drawn i.i.d. from \"nice\" distributions, establishing how to reason about approximat"},"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":"1708.08907","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2017-08-29T17:48:59Z","cross_cats_sorted":[],"title_canon_sha256":"133885c2fcad7781dfa8cec6af80078b54053198b47afbcf2552bdcc57366818","abstract_canon_sha256":"9e4014fbabd41e25e93ce68a79c04354b69b1b0f590992d92ad31f74767126a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:00.375644Z","signature_b64":"ffwgEJ30smIMyVpjLd5QPMegSSanudN8mTxsHJwDRaahNjBLBCsfeMlzR8JSxCXzk8h48/G/yunNslfkCakwAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e70094b17f1f6260195776835784d3d026b20a4af9ab5076993e4373352205ee","last_reissued_at":"2026-05-18T00:11:00.374846Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:00.374846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounding the Menu-Size of Approximately Optimal Auctions via Optimal-Transport Duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Yannai A. Gonczarowski","submitted_at":"2017-08-29T17:48:59Z","abstract_excerpt":"The question of the minimum menu-size for approximate (i.e., up-to-$\\varepsilon$) Bayesian revenue maximization when selling two goods to an additive risk-neutral quasilinear buyer was introduced by Hart and Nisan (2013), who give an upper bound of $O(\\frac{1}{\\varepsilon^4})$ for this problem. Using the optimal-transport duality framework of Daskalakis et al. (2013, 2015), we derive the first lower bound for this problem - of $\\Omega(\\frac{1}{\\sqrt[4]{\\varepsilon}})$, even when the values for the two goods are drawn i.i.d. from \"nice\" distributions, establishing how to reason about approximat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.08907","kind":"arxiv","version":4},"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":"1708.08907","created_at":"2026-05-18T00:11:00.374984+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.08907v4","created_at":"2026-05-18T00:11:00.374984+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.08907","created_at":"2026-05-18T00:11:00.374984+00:00"},{"alias_kind":"pith_short_12","alias_value":"44AJJML7D5RG","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_16","alias_value":"44AJJML7D5RGAGKX","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_8","alias_value":"44AJJML7","created_at":"2026-05-18T12:30:58.224056+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/44AJJML7D5RGAGKXO2BVPBGT2A","json":"https://pith.science/pith/44AJJML7D5RGAGKXO2BVPBGT2A.json","graph_json":"https://pith.science/api/pith-number/44AJJML7D5RGAGKXO2BVPBGT2A/graph.json","events_json":"https://pith.science/api/pith-number/44AJJML7D5RGAGKXO2BVPBGT2A/events.json","paper":"https://pith.science/paper/44AJJML7"},"agent_actions":{"view_html":"https://pith.science/pith/44AJJML7D5RGAGKXO2BVPBGT2A","download_json":"https://pith.science/pith/44AJJML7D5RGAGKXO2BVPBGT2A.json","view_paper":"https://pith.science/paper/44AJJML7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.08907&json=true","fetch_graph":"https://pith.science/api/pith-number/44AJJML7D5RGAGKXO2BVPBGT2A/graph.json","fetch_events":"https://pith.science/api/pith-number/44AJJML7D5RGAGKXO2BVPBGT2A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/44AJJML7D5RGAGKXO2BVPBGT2A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/44AJJML7D5RGAGKXO2BVPBGT2A/action/storage_attestation","attest_author":"https://pith.science/pith/44AJJML7D5RGAGKXO2BVPBGT2A/action/author_attestation","sign_citation":"https://pith.science/pith/44AJJML7D5RGAGKXO2BVPBGT2A/action/citation_signature","submit_replication":"https://pith.science/pith/44AJJML7D5RGAGKXO2BVPBGT2A/action/replication_record"}},"created_at":"2026-05-18T00:11:00.374984+00:00","updated_at":"2026-05-18T00:11:00.374984+00:00"}