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Comput."],"published-print":{"date-parts":[[2016,2,3]]},"abstract":"<jats:p>\n            We study the price of anarchy (PoA) of simultaneous first-price auctions (FPAs) for buyers with submodular and subadditive valuations. The current best upper bounds for the Bayesian price of anarchy (BPoA) of these auctions are\n            <jats:italic>e<\/jats:italic>\n            \/(\n            <jats:italic>e<\/jats:italic>\n            \u2212 1) [Syrgkanis and Tardos 2013] and 2 [Feldman et al. 2013], respectively. We provide matching lower bounds for both cases\n            <jats:italic>even<\/jats:italic>\n            for the case of full information and for mixed Nash equilibria via an explicit construction. We present an alternative proof of the upper bound of\n            <jats:italic>e<\/jats:italic>\n            \/(\n            <jats:italic>e<\/jats:italic>\n            \u2212 1) for FPAs with fractionally subadditive valuations that reveals the worst-case price distribution, which is used as a building block for the matching lower bound construction.\n          <\/jats:p>\n          <jats:p>We generalize our results to a general class of item bidding auctions that we call bid-dependent auctions (including FPAs and all-pay auctions) where the winner is always the highest bidder and each bidder\u2019s payment depends only on his own bid.<\/jats:p>\n          <jats:p>\n            Finally, we apply our techniques to discriminatory price multiunit auctions. We complement the results of de Keijzer et al. [2013] for the case of subadditive valuations by providing a matching lower bound of 2. For the case of submodular valuations, we provide a lower bound of 1.109. For the same class of valuations, we were able to reproduce the upper bound of\n            <jats:italic>e<\/jats:italic>\n            \/(\n            <jats:italic>e<\/jats:italic>\n            \u2212 1) using our nonsmooth approach.\n          <\/jats:p>","DOI":"10.1145\/2847520","type":"journal-article","created":{"date-parts":[[2016,1,14]],"date-time":"2016-01-14T02:18:38Z","timestamp":1452737918000},"page":"1-33","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":17,"title":["Tight Bounds for the Price of Anarchy of Simultaneous First-Price Auctions"],"prefix":"10.1145","volume":"4","author":[{"given":"George","family":"Christodoulou","sequence":"first","affiliation":[{"name":"University of Liverpool, Liverpool, United Kingdom"}]},{"given":"Annam\u00e1ria","family":"Kov\u00e1cs","sequence":"additional","affiliation":[{"name":"Goethe University"}]},{"given":"Alkmini","family":"Sgouritsa","sequence":"additional","affiliation":[{"name":"University of Liverpool, Liverpool, United Kingdom"}]},{"given":"Bo","family":"Tang","sequence":"additional","affiliation":[{"name":"University of Liverpool, Liverpool, United Kingdom"}]}],"member":"320","published-online":{"date-parts":[[2016,1,13]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01211819"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.5555\/2133036.2133091"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-35311-6_25"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1006\/game.1998.0659"},{"key":"e_1_2_1_5_1","doi-asserted-by":"crossref","unstructured":"Michal Bresky. 2008. Pure Equilibrium Strategies in Multi-Unit Auctions with Private Value Bidders. CERGE-EI Working Papers wp376. The Center for Economic Research and Graduate Education Economic Institute Prague. http:\/\/ideas.repec.org\/p\/cer\/papers\/wp376.html.  Michal Bresky. 2008. Pure Equilibrium Strategies in Multi-Unit Auctions with Private Value Bidders. CERGE-EI Working Papers wp376. The Center for Economic Research and Graduate Education Economic Institute Prague. http:\/\/ideas.repec.org\/p\/cer\/papers\/wp376.html.","DOI":"10.2139\/ssrn.1483179"},{"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\/2492002.2483188"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/1806689.1806733"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-70575-8_67"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/2847520"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01726210"},{"volume-title":"Algorithms\u2014ESA","year":"2013","author":"de Keijzer Bart","key":"e_1_2_1_12_1"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1257\/aer.97.1.242"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/1132516.1132523"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.4086\/toc.2010.v006a011"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/2488608.2488634"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/2229012.2229055"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.2307\/1914085"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/1566374.1566407"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/1993574.1993619"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.5555\/1764891.1764944"},{"key":"e_1_2_1_22_1","unstructured":"Vijay Krishna. 2002. Auction Theory. Academic Press.  Vijay Krishna. 2002. Auction Theory. 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