{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T13:41:37Z","timestamp":1772286097024,"version":"3.50.1"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2002,4,25]],"date-time":"2002-04-25T00:00:00Z","timestamp":1019692800000},"content-version":"unspecified","delay-in-days":55,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2002,3]]},"abstract":"<jats:p>We consider a stochastic process based on the iterated prisoner's dilemma game. During \nthe game, each of <jats:italic>n<\/jats:italic> players has a state, either <jats:italic>cooperate<\/jats:italic> or <jats:italic>defect<\/jats:italic>. The players are connected \nby an \u2018interaction graph\u2019. During each step of the process, an edge of the graph is chosen \nuniformly at random and the states of the players connected by the edge are modified \naccording to the <jats:italic>Pavlov<\/jats:italic> strategy. The process converges to a unique absorbing state in \nwhich all players cooperate. We prove two conjectures of Kittock: the convergence rate is \nexponential in <jats:italic>n<\/jats:italic> when the interaction graph is a complete graph, and it is polynomial in <jats:italic>n<\/jats:italic> \nwhen the interaction graph is a cycle. In fact, we show that the rate is <jats:italic>O<\/jats:italic>(<jats:italic>n<\/jats:italic> log <jats:italic>n<\/jats:italic>) in the \nlatter case.<\/jats:p>","DOI":"10.1017\/s096354830100503x","type":"journal-article","created":{"date-parts":[[2003,10,15]],"date-time":"2003-10-15T15:59:58Z","timestamp":1066233598000},"page":"135-147","source":"Crossref","is-referenced-by-count":13,"title":["Convergence of the Iterated Prisoner's Dilemma Game"],"prefix":"10.1017","volume":"11","author":[{"given":"MARTIN","family":"DYER","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"LESLIE ANN","family":"GOLDBERG","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"CATHERINE","family":"GREENHILL","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"GABRIEL","family":"ISTRATE","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MARK","family":"JERRUM","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2002,4,25]]},"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S096354830100503X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,3]],"date-time":"2019-04-03T19:53:53Z","timestamp":1554321233000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S096354830100503X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,3]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2002,3]]}},"alternative-id":["S096354830100503X"],"URL":"https:\/\/doi.org\/10.1017\/s096354830100503x","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,3]]}}}