{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T10:16:59Z","timestamp":1768558619985,"version":"3.49.0"},"reference-count":24,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2014,10,28]],"date-time":"2014-10-28T00:00:00Z","timestamp":1414454400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100005492","name":"Stanford University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100005492","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000143","name":"Division of Computing and Communication Foundations","doi-asserted-by":"publisher","award":["CCF-1016885"],"award-info":[{"award-number":["CCF-1016885"]}],"id":[{"id":"10.13039\/100000143","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000143","name":"Division of Computing and Communication Foundations","doi-asserted-by":"publisher","award":["CCF-0448664 and CCF-1016885"],"award-info":[{"award-number":["CCF-0448664 and CCF-1016885"]}],"id":[{"id":"10.13039\/100000143","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000879","name":"Alfred P. Sloan Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000879","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001655","name":"German Academic Exchange Service","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001655","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Econ. Comput."],"published-print":{"date-parts":[[2014,10,28]]},"abstract":"<jats:p>We characterize the Price of Anarchy (POA) in weighted congestion games, as a function of the allowable resource cost functions. Our results provide as thorough an understanding of this quantity as is already known for nonatomic and unweighted congestion games, and take the form of universal (cost function-independent) worst-case examples. One noteworthy by-product of our proofs is the fact that weighted congestion games are \u201ctight,\u201d which implies that the worst-case price of anarchy with respect to pure Nash equilibria, mixed Nash equilibria, correlated equilibria, and coarse correlated equilibria are always equal (under mild conditions on the allowable cost functions). Another is the fact that, like nonatomic but unlike atomic (unweighted) congestion games, weighted congestion games with trivial structure already realize the worst-case POA, at least for polynomial cost functions.<\/jats:p>\n          <jats:p>We also prove a new result about unweighted congestion games: the worst-case price of anarchy in symmetric games is as large as in their more general asymmetric counterparts.<\/jats:p>","DOI":"10.1145\/2629666","type":"journal-article","created":{"date-parts":[[2014,10,28]],"date-time":"2014-10-28T12:40:29Z","timestamp":1414500029000},"page":"1-23","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":44,"title":["Weighted Congestion Games"],"prefix":"10.1145","volume":"2","author":[{"given":"Kshipra","family":"Bhawalkar","sequence":"first","affiliation":[{"name":"Stanford University, CA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martin","family":"Gairing","sequence":"additional","affiliation":[{"name":"University of Liverpool, Liverpool, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tim","family":"Roughgarden","sequence":"additional","affiliation":[{"name":"Stanford University, CA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2014,10,28]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1137\/090748986"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1137\/070680096"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/1060590.1060599"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.4086\/toc.2010.v006a008"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-010-9427-8"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/11561071_8"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/1060590.1060600"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1040.0098"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00224-009-9205-7"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/1383369.1383383"},{"key":"e_1_2_1_11_1","volume-title":"Proceedings of the 3rd International Workshop on Internet and Network Economics (WINE). 381--387","author":"Gairing M.","unstructured":"M. Gairing and F. Schoppmann . 2007. Total latency in singleton congestion games . In Proceedings of the 3rd International Workshop on Internet and Network Economics (WINE). 381--387 . M. Gairing and F. Schoppmann. 2007. Total latency in singleton congestion games. In Proceedings of the 3rd International Workshop on Internet and Network Economics (WINE). 381--387."},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1120.0543"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00224-011-9315-x"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/1132516.1132529"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-4896(03)00076-3"},{"key":"e_1_2_1_16_1","volume-title":"Proceedings of the 16th Annual Symposium on Theoretical Aspects of Computer Science (STACS). 404--413","author":"Koutsoupias E.","unstructured":"E. Koutsoupias and C. H. Papadimitriou . 1999. Worst-case equilibria . In Proceedings of the 16th Annual Symposium on Theoretical Aspects of Computer Science (STACS). 404--413 . E. Koutsoupias and C. H. Papadimitriou. 1999. Worst-case equilibria. In Proceedings of the 16th Annual Symposium on Theoretical Aspects of Computer Science (STACS). 404--413."},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2008.06.045"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-009-9367-3"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01737559"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-0000(03)00044-8"},{"key":"e_1_2_1_21_1","first-page":"1071","article-title":"Potential functions and the inefficiency of equilibria","author":"Roughgarden T.","year":"2006","unstructured":"T. Roughgarden . 2006 . Potential functions and the inefficiency of equilibria . In Proceedings of the ICM , Vol. III. 1071 -- 1094 . T. Roughgarden. 2006. Potential functions and the inefficiency of equilibria. In Proceedings of the ICM, Vol. III. 1071--1094.","journal-title":"Proceedings of the ICM"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/1536414.1536485"},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/2229012.2229078"},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.geb.2003.06.004"}],"container-title":["ACM Transactions on Economics and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2629666","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2629666","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T06:13:30Z","timestamp":1750227210000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2629666"}},"subtitle":["The Price of Anarchy, Universal Worst-Case Examples, and Tightness"],"short-title":[],"issued":{"date-parts":[[2014,10,28]]},"references-count":24,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2014,10,28]]}},"alternative-id":["10.1145\/2629666"],"URL":"https:\/\/doi.org\/10.1145\/2629666","relation":{},"ISSN":["2167-8375","2167-8383"],"issn-type":[{"value":"2167-8375","type":"print"},{"value":"2167-8383","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,10,28]]},"assertion":[{"value":"2012-07-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2014-03-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2014-10-28","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}