{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T20:30:16Z","timestamp":1774125016409,"version":"3.50.1"},"reference-count":18,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2016,2,12]],"date-time":"2016-02-12T00:00:00Z","timestamp":1455235200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"NSA Young Investigators Grant"},{"name":"USA-Israel BSF Grant"},{"name":"National Science Foundation","award":["DMS-1041500 and DMS-1201380"],"award-info":[{"award-number":["DMS-1041500 and DMS-1201380"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Algorithms"],"published-print":{"date-parts":[[2016,2,12]]},"abstract":"<jats:p>\n                    The Internet has emerged as perhaps the most important network in modern computing, but rather miraculously, it was created through the individual actions of a multitude of agents rather than by a central planning authority. This motivates the game-theoretic study of network formation, and our article considers one of the most well-studied models, originally proposed by Fabrikant et al. In the model, each of\n                    <jats:italic toggle=\"yes\">n<\/jats:italic>\n                    agents corresponds to a vertex, which can create edges to other vertices at a cost of \u03b1 each, for some parameter \u03b1. Every edge can be freely used by every vertex, regardless of who paid the creation cost. To reflect the desire to be close to other vertices, each agent\u2019s cost function is further augmented by the sum total of all (graph-theoretic) distances to all other vertices.\n                  <\/jats:p>\n                  <jats:p>\n                    Previous research proved that for many regimes of the (\u03b1,\n                    <jats:italic toggle=\"yes\">n<\/jats:italic>\n                    ) parameter space, the total social cost (sum of all agents\u2019 costs) of every Nash equilibrium is bounded by at most a constant multiple of the optimal social cost. In algorithmic game-theoretic nomenclature, this approximation ratio is called the price of anarchy. In our article, we significantly sharpen some of those results, proving that for all constant nonintegral \u03b1 &gt; 2, the price of anarchy is in fact 1 +\n                    <jats:italic toggle=\"yes\">o<\/jats:italic>\n                    (1); that is, not only is it bounded by a constant, but also it tends to 1 as\n                    <jats:italic toggle=\"yes\">n<\/jats:italic>\n                    \u2192 \u221e. For constant integral \u03b1 \u2a7e 2, we show that the price of anarchy is bounded away from 1. We provide quantitative estimates on the rates of convergence for both results.\n                  <\/jats:p>","DOI":"10.1145\/2729978","type":"journal-article","created":{"date-parts":[[2016,2,22]],"date-time":"2016-02-22T08:07:16Z","timestamp":1456128436000},"page":"1-10","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Anarchy Is Free in Network Creation"],"prefix":"10.1145","volume":"12","author":[{"given":"Ronald","family":"Graham","sequence":"first","affiliation":[{"name":"University of California, San Diego, La Jolla, CA"}]},{"given":"Linus","family":"Hamilton","sequence":"additional","affiliation":[{"name":"Carnegie Mellon University, Pittsburgh, PA"}]},{"given":"Ariel","family":"Levavi","sequence":"additional","affiliation":[{"name":"University of California, San Diego, La Jolla, CA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0777-0644","authenticated-orcid":false,"given":"Po-Shen","family":"Loh","sequence":"additional","affiliation":[{"name":"Carnegie Mellon University, Pittsburgh, PA"}]}],"member":"320","published-online":{"date-parts":[[2016,2,12]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.5555\/1347082.1347115"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.5555\/1109557.1109568"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/1810479.1810502"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.5555\/1283383.1283404"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2004.68"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/780542.780617"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073814.1073833"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.5555\/545381.545436"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/2151171.2151176"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/872035.872088"},{"key":"e_1_2_1_11_1","volume-title":"A survey of network formation models: Stability and efficiency","author":"Jackson Matthew O.","unstructured":"Matthew O. Jackson. 2005. A survey of network formation models: Stability and efficiency. In Group Formation in Economics; Networks, Clubs, and Coalitions, Gabrielle Demange and Myrna Wooders (Eds.). Cambridge University Press, 11--57."},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.5555\/1764891.1764944"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-03536-9_10"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00224-013-9459-y"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/380752.380883"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/509907.509971"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.5555\/1076293"},{"key":"e_1_2_1_18_1","volume-title":"Algorithmic Game Theory, Noam Nisan, Tim Roughgarden, \u00c9va Tardos, and Vijay V","author":"Tardos \u00c9va","unstructured":"\u00c9va Tardos and Tom Wexler. 2007. Network formation games and the potential function method. In Algorithmic Game Theory, Noam Nisan, Tim Roughgarden, \u00c9va Tardos, and Vijay V. Vazirani (Eds.). Cambridge University Press, 487--516."}],"container-title":["ACM Transactions on Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2729978","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2729978","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2729978","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T09:47:14Z","timestamp":1763459234000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2729978"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,2,12]]},"references-count":18,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2016,2,12]]}},"alternative-id":["10.1145\/2729978"],"URL":"https:\/\/doi.org\/10.1145\/2729978","relation":{},"ISSN":["1549-6325","1549-6333"],"issn-type":[{"value":"1549-6325","type":"print"},{"value":"1549-6333","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,2,12]]},"assertion":[{"value":"2013-11-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2015-01-01","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2016-02-12","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}