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ACM"],"published-print":{"date-parts":[[2016,5,4]]},"abstract":"<jats:p>\n            We study the following simple Bayesian auction setting:\n            <jats:italic>m<\/jats:italic>\n            items are sold to\n            <jats:italic>n<\/jats:italic>\n            selfish bidders in\n            <jats:italic>m<\/jats:italic>\n            independent second-price auctions. Each bidder has a\n            <jats:italic>private<\/jats:italic>\n            valuation function that specifies his or her complex preferences over\n            <jats:italic>all<\/jats:italic>\n            subsets of items. Bidders only have\n            <jats:italic>beliefs<\/jats:italic>\n            about the valuation functions of the other bidders, in the form of probability distributions. The objective is to allocate the items to the bidders in a way that provides a good approximation to the optimal social welfare value. We show that if bidders have submodular or, more generally, fractionally subadditive (aka XOS) valuation functions, every Bayes-Nash equilibrium of the resulting game provides a 2-approximation to the optimal social welfare. Moreover, we show that in the full-information game, a pure Nash always exists and can be found in time that is polynomial in both\n            <jats:italic>m<\/jats:italic>\n            and\n            <jats:italic>n<\/jats:italic>\n            .\n          <\/jats:p>","DOI":"10.1145\/2835172","type":"journal-article","created":{"date-parts":[[2016,4,7]],"date-time":"2016-04-07T22:16:10Z","timestamp":1460067370000},"page":"1-19","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":38,"title":["Bayesian Combinatorial Auctions"],"prefix":"10.1145","volume":"63","author":[{"given":"George","family":"Christodoulou","sequence":"first","affiliation":[{"name":"Computer Science Department, University of Liverpool, Liverpool, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Annam\u00e1ria","family":"Kov\u00e1cs","sequence":"additional","affiliation":[{"name":"Informatics Institute, Goethe University, Frankfurt M., Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael","family":"Schapira","sequence":"additional","affiliation":[{"name":"The School of Computer Science and Engineering, The Hebrew University of Jerusalem, Israel, Jerusalem, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2016,4,7]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2012.05.017"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2004.68"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.5555\/2133036.2133091"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-35311-6_25"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/1064009.1064013"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/1993574.1993588"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/1993574.1993588"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-70575-8_67"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/2847520"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01726210"},{"key":"e_1_2_1_11_1","volume-title":"ESA(Lecture Notes in Computer Science), Hans L","author":"de Keijzer Bart","unstructured":"Bart de Keijzer , Evangelos Markakis , Guido Sch\u00e4fer , and Orestis Telelis . 2013. Inefficiency of standard multi-unit auctions . In ESA(Lecture Notes in Computer Science), Hans L . Bodlaender and Giuseppe F. Italiano (Eds.), Vol. 8125 . Springer , 385--396. Bart de Keijzer, Evangelos Markakis, Guido Sch\u00e4fer, and Orestis Telelis. 2013. Inefficiency of standard multi-unit auctions. In ESA(Lecture Notes in Computer Science), Hans L. Bodlaender and Giuseppe F. Italiano (Eds.), Vol. 8125. Springer, 385--396."},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/1993636.1993656"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/1060590.1060681"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.5555\/1109557.1109675"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/1132516.1132523"},{"key":"e_1_2_1_16_1","unstructured":"Uriel Feige and Jan Vondrak. 2006. The Allocation Problem with Submodular Utility Functions. Manuscript.  Uriel Feige and Jan Vondrak. 2006. The Allocation Problem with Submodular Utility Functions. 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Nash equilibria in competitive societies, with applications to facility location, traffic routing and auctions . In FOCS. IEEE Computer Society . Adrian Vetta. 2002. Nash equilibria in competitive societies, with applications to facility location, traffic routing and auctions. In FOCS. 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