{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,3]],"date-time":"2025-12-03T17:15:08Z","timestamp":1764782108298,"version":"3.45.0"},"reference-count":35,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2017,10,12]],"date-time":"2017-10-12T00:00:00Z","timestamp":1507766400000},"content-version":"vor","delay-in-days":365,"URL":"http:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","award":["CCF-1101389"],"award-info":[{"award-number":["CCF-1101389"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"name":"NSF CAREER grant"},{"name":"Google Research grant"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Econ. Comput."],"published-print":{"date-parts":[[2017,5,31]]},"abstract":"<jats:p>\n                    In this article, we study infinitely repeated games in settings of imperfect monitoring. We first prove a family of theorems showing that when the signals observed by the players satisfy a condition known as (\u03f5, \u03b3)-differential privacy, the folk theorem has little bite: for values of \u03f5 and \u03b3 sufficiently small, for a fixed discount factor, any equilibrium of the repeated game involves players playing approximate equilibria of the stage game in every period. Next we argue that in large games (\n                    <jats:italic toggle=\"yes\">n<\/jats:italic>\n                    player games in which unilateral deviations by single players have only a small impact on the utility of other players), many monitoring settings naturally lead to signals that satisfy (\u03f5, \u03b3)-differential privacy for \u03f5 and \u03b3 tending to zero as the number of players\n                    <jats:italic toggle=\"yes\">n<\/jats:italic>\n                    grows large. We conclude that in such settings, the set of equilibria of the repeated game collapses to the set of equilibria of the stage game.\n                  <\/jats:p>\n                  <jats:p>Our results nest and generalize previous results of Green [1980] and Sabourian [1990], suggesting that differential privacy is a natural measure of the \u201clargeness\u201d of a game. Further, techniques from the literature on differential privacy allow us to prove quantitative bounds, where the existing literature focuses on limiting results.<\/jats:p>","DOI":"10.1145\/2976734","type":"journal-article","created":{"date-parts":[[2016,10,12]],"date-time":"2016-10-12T14:33:55Z","timestamp":1476282835000},"page":"1-20","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":7,"title":["An Antifolk Theorem for Large Repeated Games"],"prefix":"10.1145","volume":"5","author":[{"given":"Mallesh M.","family":"Pai","sequence":"first","affiliation":[{"name":"University of Pennsylvania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aaron","family":"Roth","sequence":"additional","affiliation":[{"name":"University of Pennsylvania, Philadelphia PA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jonathan","family":"Ullman","sequence":"additional","affiliation":[{"name":"Columbia University, Boston, MA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2016,10,12]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.2307\/1913097"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1006\/game.2000.0826"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1257\/aer.20141469"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.geb.2009.04.016"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/2492002.2482549"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/11761679_29"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/11681878_14"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2010.12"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1006\/game.1997.0595"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.2307\/2951505"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/2482540.2482585"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.geb.2013.06.013"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/1386790.1386833"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0531(80)90038-1"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.2307\/1911462"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/2554797.2554847"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/2213977.2214088"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00153"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/2554797.2554834"},{"key":"e_1_2_1_20_1","first-page":"1160","article-title":"When are agents negligible","volume":"85","author":"Levine D. 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