{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T09:42:32Z","timestamp":1773481352867,"version":"3.50.1"},"reference-count":17,"publisher":"Proceedings of the National Academy of Sciences","issue":"28","content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2013,7,9]]},"abstract":"\n Consider the revenue-maximizing problem in which a single seller wants to sell\n k<\/jats:italic>\n different items to a single buyer, who has independently distributed values for the items with additive valuation. The\n \n \n <\/jats:inline-formula>\n case was completely resolved by Myerson\u2019s classical work in 1981, whereas for larger\n k<\/jats:italic>\n the problem has been the subject of much research efforts ever since. Recently, Hart and Nisan analyzed two simple mechanisms: selling the items separately, or selling them as a single bundle. They showed that selling separately guarantees at least a\n \n \n <\/jats:inline-formula>\n fraction of the optimal revenue; and for identically distributed items, bundling yields at least a\n \n \n <\/jats:inline-formula>\n fraction of the optimal revenue. In this paper, we prove that selling separately guarantees at least\n \n \n <\/jats:inline-formula>\n fraction of the optimal revenue, whereas for identically distributed items, bundling yields at least a constant fraction of the optimal revenue. These bounds are tight (up to a constant factor), settling the open questions raised by Hart and Nisan. The results are valid for arbitrary probability distributions without restrictions. Our results also have implications on other interesting issues, such as monotonicity and randomization of selling mechanisms.\n <\/jats:p>","DOI":"10.1073\/pnas.1309533110","type":"journal-article","created":{"date-parts":[[2013,6,25]],"date-time":"2013-06-25T04:20:05Z","timestamp":1372134005000},"page":"11232-11237","update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":85,"title":["On revenue maximization for selling multiple independently distributed items"],"prefix":"10.1073","volume":"110","author":[{"given":"Xinye","family":"Li","sequence":"first","affiliation":[{"name":"Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China"}]},{"given":"Andrew Chi-Chih","family":"Yao","sequence":"additional","affiliation":[{"name":"Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China"}]}],"member":"341","published-online":{"date-parts":[[2013,6,24]]},"reference":[{"key":"e_1_3_3_1_2","doi-asserted-by":"publisher","DOI":"10.1287\/moor.6.1.58"},{"key":"e_1_3_3_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0531(88)90135-4"},{"key":"e_1_3_3_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jet.2005.08.007"},{"key":"e_1_3_3_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jet.2006.12.007"},{"key":"e_1_3_3_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jet.2006.02.001"},{"key":"e_1_3_3_6_2","doi-asserted-by":"crossref","unstructured":"Lev O (2011) A two-dimensional problem of revenue maximization. J Math Econ 47(6):718-727.","DOI":"10.1016\/j.jmateco.2011.08.007"},{"key":"e_1_3_3_7_2","unstructured":"Hart S Reny P (2012) Maximizing revenue with multiple goods: Nonmonotonicity and other observations. Discussion paper series DP-630 (The Center for the Study of Rationality Hebrew University Jerusalem)."},{"key":"e_1_3_3_8_2","doi-asserted-by":"crossref","unstructured":"Hart S Nisan N (2013) The Menu-size complexity of auctions. Proceedings of the 14th ACM Conference on Electronic Commerce (Philadelphia) pp 565\u2013566.","DOI":"10.1145\/2482540.2482544"},{"key":"e_1_3_3_9_2","doi-asserted-by":"crossref","unstructured":"Briest P Chawla S Hartline J-D Kleinberg R-D Weinberg S-M (2010) Pricing randomized allocations. Proceedings of the 21st ACM-SIAM Symposium on Discrete Algorithms (SODA) (Austin TX) pp 585\u2013597.","DOI":"10.1137\/1.9781611973075.49"},{"key":"e_1_3_3_10_2","doi-asserted-by":"crossref","unstructured":"Cai Y Daskalakis C Weinberg S-M (2012) An algorithmic characterization of multi-dimensional mechanisms. Proceedings of the 44th Annual ACM Symposium on Theory of Computing (STOC) (New York) pp 459\u2013478.","DOI":"10.1145\/2213977.2214021"},{"key":"e_1_3_3_11_2","doi-asserted-by":"crossref","unstructured":"Cai Y Daskalakis C Weinberg S-M (2012) Optimal multi-dimensional mechanism design: Reducing revenue to welfare maximization. Proceedings of the 53rd Annual IEEE Symposium on Foundations of Computer Science (FOCS) (New Brunswick NJ) pp 130\u2013139.","DOI":"10.1109\/FOCS.2012.88"},{"key":"e_1_3_3_12_2","doi-asserted-by":"crossref","unstructured":"Cai Y Daskalakis C Weinberg S-M (2013) Reducing revenue to welfare maximization: Approximation algorithms and other generalizations. Proceedings of the 24th ACM-SIAM Symposium on Discrete Algorithms (SODA) (New Orleans) pp 578\u2013595.","DOI":"10.1137\/1.9781611973105.42"},{"key":"e_1_3_3_13_2","doi-asserted-by":"crossref","unstructured":"Chawla S Hartline J-D Kleinberg R-D (2007) Algorithmic pricing via virtual valuations. Proceedings of the 8th ACM Conference on Electric Commerce (EC) (San Diego) pp 243\u2013251.","DOI":"10.1145\/1250910.1250946"},{"key":"e_1_3_3_14_2","doi-asserted-by":"crossref","unstructured":"Chawla S Hartline J-D Malec D-L Sivan B (2010) Multi-parameter mechanism design and sequential posted pricing. Proceedings of the 42th Annual ACM Symposium on Theory of Computing (STOC) (Cambridge MA) pp 311\u2013320.","DOI":"10.1145\/1806689.1806733"},{"key":"e_1_3_3_15_2","doi-asserted-by":"crossref","unstructured":"Cai Y Huang Z (2013) Simple and nearly optimal multi-item auctions. Proceedings of the 24th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) (New Orleans) pp 564\u2013577.","DOI":"10.1137\/1.9781611973105.41"},{"key":"e_1_3_3_16_2","doi-asserted-by":"crossref","unstructured":"Hart S Nisan N (2012) Approximate revenue maximization with multiple items. Proceedings of the 13th ACM Conference on Electronic Commerce (Valencia Spain) pp 656.","DOI":"10.1145\/2229012.2229061"},{"key":"e_1_3_3_17_2","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177704147"}],"container-title":["Proceedings of the National Academy of Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pnas.org\/doi\/pdf\/10.1073\/pnas.1309533110","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,15]],"date-time":"2022-04-15T23:50:42Z","timestamp":1650066642000},"score":1,"resource":{"primary":{"URL":"https:\/\/pnas.org\/doi\/full\/10.1073\/pnas.1309533110"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,6,24]]},"references-count":17,"journal-issue":{"issue":"28","published-print":{"date-parts":[[2013,7,9]]}},"alternative-id":["10.1073\/pnas.1309533110"],"URL":"https:\/\/doi.org\/10.1073\/pnas.1309533110","relation":{},"ISSN":["0027-8424","1091-6490"],"issn-type":[{"value":"0027-8424","type":"print"},{"value":"1091-6490","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,6,24]]},"assertion":[{"value":"2013-06-24","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}