{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,23]],"date-time":"2025-10-23T05:32:03Z","timestamp":1761197523208,"version":"3.41.0"},"reference-count":19,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2017,11,30]],"date-time":"2017-11-30T00:00:00Z","timestamp":1512000000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-1217989 and CCF-1527568"],"award-info":[{"award-number":["CCF-1217989 and CCF-1527568"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Science Foundation Graduate Research Fellowship Program","award":["DGE-1342536"],"award-info":[{"award-number":["DGE-1342536"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Econ. Comput."],"published-print":{"date-parts":[[2017,11,30]]},"abstract":"<jats:p>\n            Two classes of distributions that are widely used in the analysis of Bayesian auctions are the monotone hazard rate (MHR) and regular distributions. They can both be characterized in terms of the rate of change of the associated virtual value functions: for MHR distributions, the condition is that for values\n            <jats:italic>v<\/jats:italic>\n            &lt;\n            <jats:italic>v<\/jats:italic>\n            <jats:sup>\u2032<\/jats:sup>\n            , \u03d5 (\n            <jats:italic>v<\/jats:italic>\n            <jats:sup>\u2032<\/jats:sup>\n            ) - \u03d5 (\n            <jats:italic>v<\/jats:italic>\n            ) \u2265\n            <jats:italic>v<\/jats:italic>\n            <jats:sup>\u2032<\/jats:sup>\n            -\n            <jats:italic>v<\/jats:italic>\n            , and for regular distributions, \u03d5 (\n            <jats:italic>v<\/jats:italic>\n            <jats:sup>\u2032<\/jats:sup>\n            ) - \u03d5 (\n            <jats:italic>v<\/jats:italic>\n            ) \u2265 0. Cole and Roughgarden introduced the interpolating class of \u03b1-strongly regular distributions (\u03b1-SR distributions for short), for which \u03d5 (\n            <jats:italic>v<\/jats:italic>\n            <jats:sup>\u2032<\/jats:sup>\n            ) - \u03d5 (\n            <jats:italic>v<\/jats:italic>\n            ) \u2265 \u03b1 (\n            <jats:italic>v<\/jats:italic>\n            <jats:sup>\u2032<\/jats:sup>\n            -\n            <jats:italic>v<\/jats:italic>\n            ), for 0 \u2264 \u03b1 \u2264 1.\n          <\/jats:p>\n          <jats:p>In this article, we investigate five distinct auction settings for which good expected revenue bounds are known when the bidders\u2019 valuations are given by MHR distributions. In every case, we show that these bounds degrade gracefully when extended to \u03b1-SR distributions. For four of these settings, the auction mechanism requires knowledge of these distributions (in the remaining setting, the distributions are needed only to ensure good bounds on the expected revenue). In these cases, we also investigate what happens when the distributions are known only approximately via samples, specifically how to modify the mechanisms so that they remain effective and how the expected revenue depends on the number of samples.<\/jats:p>","DOI":"10.1145\/3157083","type":"journal-article","created":{"date-parts":[[2017,12,22]],"date-time":"2017-12-22T17:17:37Z","timestamp":1513963057000},"page":"1-29","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Applications of \u03b1-Strongly Regular Distributions to Bayesian Auctions"],"prefix":"10.1145","volume":"5","author":[{"given":"Richard","family":"Cole","sequence":"first","affiliation":[{"name":"Courant Institute"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shravas","family":"Rao","sequence":"additional","affiliation":[{"name":"Courant Institute"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2017,12,22]]},"reference":[{"doi-asserted-by":"publisher","key":"e_1_2_1_1_1","DOI":"10.1145\/1566374.1566408"},{"doi-asserted-by":"publisher","key":"e_1_2_1_2_1","DOI":"10.1016\/S0022-0531(03)00089-9"},{"volume-title":"Proceedings of the 24th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA\u201913)","author":"Azar Pablo","key":"e_1_2_1_3_1"},{"doi-asserted-by":"publisher","key":"e_1_2_1_4_1","DOI":"10.4086\/toc.2012.v008a020"},{"doi-asserted-by":"publisher","key":"e_1_2_1_5_1","DOI":"10.2307\/2938238"},{"doi-asserted-by":"publisher","key":"e_1_2_1_6_1","DOI":"10.2307\/2938239"},{"doi-asserted-by":"publisher","key":"e_1_2_1_7_1","DOI":"10.1145\/1993574.1993613"},{"doi-asserted-by":"publisher","key":"e_1_2_1_8_1","DOI":"10.1007\/978-3-319-13129-0_4"},{"doi-asserted-by":"publisher","key":"e_1_2_1_9_1","DOI":"10.1145\/2591796.2591867"},{"doi-asserted-by":"publisher","key":"e_1_2_1_10_1","DOI":"10.1007\/978-3-642-25510-6_10"},{"doi-asserted-by":"publisher","key":"e_1_2_1_11_1","DOI":"10.1016\/j.geb.2014.03.011"},{"doi-asserted-by":"publisher","key":"e_1_2_1_12_1","DOI":"10.1007\/s00199-012-0705-3"},{"doi-asserted-by":"publisher","key":"e_1_2_1_13_1","DOI":"10.1145\/1367497.1367524"},{"doi-asserted-by":"crossref","unstructured":"J. D. Hartline. 2014. Mechanism Design and Approximation. Book draft.  J. D. Hartline. 2014. Mechanism Design and Approximation. Book draft.","key":"e_1_2_1_14_1","DOI":"10.1561\/9781601986719"},{"doi-asserted-by":"crossref","unstructured":"J. D. Hartline and A. Karlin. 2007. Profit maximization in mechanism design. In Algorithmic Game Theory N. Nisan T. Roughgarden \u00c9. Tardos and V. V. Vazirani (Eds.). Cambridge University Press 331--362.  J. D. Hartline and A. Karlin. 2007. Profit maximization in mechanism design. In Algorithmic Game Theory N. Nisan T. Roughgarden \u00c9. Tardos and V. V. Vazirani (Eds.). Cambridge University Press 331--362.","key":"e_1_2_1_15_1","DOI":"10.1017\/CBO9780511800481.015"},{"doi-asserted-by":"publisher","key":"e_1_2_1_16_1","DOI":"10.1145\/1598780.1598785"},{"doi-asserted-by":"publisher","key":"e_1_2_1_17_1","DOI":"10.1145\/2492002.2482584"},{"doi-asserted-by":"publisher","key":"e_1_2_1_18_1","DOI":"10.1287\/moor.6.1.58"},{"key":"e_1_2_1_19_1","first-page":"2015","article-title":"The Quantitative View of MYerson Regularity. Discussion Papers","author":"Schweizer Nikolaus","year":"2015","journal-title":"Research Unit: Economics of Change SP"}],"container-title":["ACM Transactions on Economics and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3157083","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3157083","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3157083","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T02:11:29Z","timestamp":1750212689000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3157083"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,11,30]]},"references-count":19,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2017,11,30]]}},"alternative-id":["10.1145\/3157083"],"URL":"https:\/\/doi.org\/10.1145\/3157083","relation":{},"ISSN":["2167-8375","2167-8383"],"issn-type":[{"type":"print","value":"2167-8375"},{"type":"electronic","value":"2167-8383"}],"subject":[],"published":{"date-parts":[[2017,11,30]]},"assertion":[{"value":"2016-07-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2017-07-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2017-12-22","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}