{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T06:13:44Z","timestamp":1772172824190,"version":"3.50.1"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1008217","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2021,2,2]],"date-time":"2021-02-02T00:00:00Z","timestamp":1612224000000}}],"reference-count":37,"publisher":"Public Library of Science (PLoS)","issue":"1","license":[{"start":{"date-parts":[[2021,1,21]],"date-time":"2021-01-21T00:00:00Z","timestamp":1611187200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"crossref","award":["18H03621"],"award-info":[{"award-number":["18H03621"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Ministry of Education","award":["NRF-2020R1I1A2071670"],"award-info":[{"award-number":["NRF-2020R1I1A2071670"]}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>\n                    Repeated interaction promotes cooperation among rational individuals under the shadow of future, but it is hard to maintain cooperation when a large number of error-prone individuals are involved. One way to construct a cooperative Nash equilibrium is to find a \u2018friendly-rivalry\u2019 strategy, which aims at full cooperation but never allows the co-players to be better off. Recently it has been shown that for the iterated Prisoner\u2019s Dilemma in the presence of error, a friendly rival can be designed with the following five rules: Cooperate if everyone did, accept punishment for your own mistake, punish defection, recover cooperation if you find a chance, and defect in all the other circumstances. In this work, we construct such a friendly-rivalry strategy for the iterated\n                    <jats:italic>n<\/jats:italic>\n                    -person public-goods game by generalizing those five rules. The resulting strategy makes a decision with referring to the previous\n                    <jats:italic>m<\/jats:italic>\n                    = 2\n                    <jats:italic>n<\/jats:italic>\n                    \u2212 1 rounds. A friendly-rivalry strategy for\n                    <jats:italic>n<\/jats:italic>\n                    = 2 inherently has evolutionary robustness in the sense that no mutant strategy has higher fixation probability in this population than that of a neutral mutant. Our evolutionary simulation indeed shows excellent performance of the proposed strategy in a broad range of environmental conditions when\n                    <jats:italic>n<\/jats:italic>\n                    = 2 and 3.\n                  <\/jats:p>","DOI":"10.1371\/journal.pcbi.1008217","type":"journal-article","created":{"date-parts":[[2021,1,21]],"date-time":"2021-01-21T13:29:51Z","timestamp":1611235791000},"page":"e1008217","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":7,"title":["Friendly-rivalry solution to the iterated n-person public-goods game"],"prefix":"10.1371","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5872-420X","authenticated-orcid":true,"given":"Yohsuke","family":"Murase","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4143-1187","authenticated-orcid":true,"given":"Seung Ki","family":"Baek","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2021,1,21]]},"reference":[{"key":"pcbi.1008217.ref001","volume-title":"Supercooperators","author":"MA Nowak","year":"2011"},{"issue":"5805","key":"pcbi.1008217.ref002","doi-asserted-by":"crossref","first-page":"1560","DOI":"10.1126\/science.1133755","article-title":"Five rules for the evolution of cooperation","volume":"314","author":"MA Nowak","year":"2006","journal-title":"Science"},{"key":"pcbi.1008217.ref003","doi-asserted-by":"crossref","DOI":"10.1515\/9781400832255","volume-title":"The Calculus of Selfishness","author":"K Sigmund","year":"2010"},{"key":"pcbi.1008217.ref004","volume-title":"Game Theory","author":"D Fudenberg","year":"1991"},{"issue":"4","key":"pcbi.1008217.ref005","doi-asserted-by":"crossref","first-page":"611","DOI":"10.1177\/0022002785029004004","article-title":"The optimal level of generosity in a selfish, uncertain environment","volume":"29","author":"P Molander","year":"1985","journal-title":"J Conflict Resolut"},{"issue":"3","key":"pcbi.1008217.ref006","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1016\/S0022-5193(88)80219-4","article-title":"The evolution of reciprocity in sizable groups","volume":"132","author":"R Boyd","year":"1988","journal-title":"J Theor Biol"},{"issue":"1","key":"pcbi.1008217.ref007","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1177\/1470594X06060617","article-title":"Behavioral ethics meets natural justice","volume":"5","author":"H Gintis","year":"2006","journal-title":"Politics Philos Econ"},{"issue":"26","key":"pcbi.1008217.ref008","doi-asserted-by":"crossref","first-page":"10409","DOI":"10.1073\/pnas.1206569109","article-title":"Iterated Prisoner\u2019s Dilemma contains strategies that dominate any evolutionary opponent","volume":"109","author":"WH Press","year":"2012","journal-title":"Proc Natl Acad Sci USA"},{"issue":"17","key":"pcbi.1008217.ref009","doi-asserted-by":"crossref","first-page":"6913","DOI":"10.1073\/pnas.1214834110","article-title":"Evolution of extortion in Iterated Prisoner\u2019s Dilemma games","volume":"110","author":"C Hilbe","year":"2013","journal-title":"Proc Natl Acad Sci USA"},{"issue":"11","key":"pcbi.1008217.ref010","doi-asserted-by":"crossref","first-page":"e77886","DOI":"10.1371\/journal.pone.0077886","article-title":"Adaptive dynamics of extortion and compliance","volume":"8","author":"C Hilbe","year":"2013","journal-title":"PloS one"},{"issue":"38","key":"pcbi.1008217.ref011","doi-asserted-by":"crossref","first-page":"15348","DOI":"10.1073\/pnas.1306246110","article-title":"From extortion to generosity, evolution in the Iterated Prisoner\u2019s Dilemma","volume":"110","author":"AJ Stewart","year":"2013","journal-title":"Proc Natl Acad Sci USA"},{"issue":"1","key":"pcbi.1008217.ref012","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/ncomms3193","article-title":"Evolutionary instability of zero-determinant strategies demonstrates that winning is not everything","volume":"4","author":"C Adami","year":"2013","journal-title":"Nat Commun"},{"key":"pcbi.1008217.ref013","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.geb.2015.05.005","article-title":"Partners or rivals? Strategies for the iterated prisoner\u2019s dilemma","volume":"92","author":"C Hilbe","year":"2015","journal-title":"Games Econ Behav"},{"issue":"7","key":"pcbi.1008217.ref014","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1038\/s41562-018-0320-9","article-title":"Partners and rivals in direct reciprocity","volume":"2","author":"C Hilbe","year":"2018","journal-title":"Nat Hum Behav"},{"issue":"3","key":"pcbi.1008217.ref015","doi-asserted-by":"crossref","first-page":"175","DOI":"10.3390\/g6030175","article-title":"What you gotta know to play good in the iterated Prisoner\u2019s Dilemma","volume":"6","author":"E Akin","year":"2015","journal-title":"Games"},{"key":"pcbi.1008217.ref016","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1515\/9783110461510-004","volume-title":"Ergodic Theory, Advances in Dynamical Systems","author":"E Akin","year":"2016"},{"issue":"1","key":"pcbi.1008217.ref017","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.geb.2012.05.002","article-title":"Unbeatable imitation","volume":"76","author":"P Duersch","year":"2012","journal-title":"Games Econ Behav"},{"key":"pcbi.1008217.ref018","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jtbi.2016.09.017","article-title":"Combination with anti-tit-for-tat remedies problems of tit-for-tat","volume":"412","author":"SD Yi","year":"2017","journal-title":"J Theor Biol"},{"key":"pcbi.1008217.ref019","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.jtbi.2018.04.027","article-title":"Seven rules to avoid the tragedy of the commons","volume":"449","author":"Y Murase","year":"2018","journal-title":"J Theor Biol"},{"issue":"49","key":"pcbi.1008217.ref020","doi-asserted-by":"crossref","first-page":"17558","DOI":"10.1073\/pnas.1408618111","article-title":"Collapse of cooperation in evolving games","volume":"111","author":"AJ Stewart","year":"2014","journal-title":"Proc Natl Acad Sci USA"},{"key":"pcbi.1008217.ref021","doi-asserted-by":"crossref","first-page":"16904","DOI":"10.1038\/s41598-020-73855-x","article-title":"Five rules for friendly rivalry in direct reciprocity","volume":"10","author":"Y Murase","year":"2020","journal-title":"Sci Rep"},{"key":"pcbi.1008217.ref022","doi-asserted-by":"crossref","first-page":"26889","DOI":"10.1038\/srep26889","article-title":"Small groups and long memories promote cooperation","volume":"6","author":"AJ Stewart","year":"2016","journal-title":"Sci Rep"},{"issue":"1","key":"pcbi.1008217.ref023","doi-asserted-by":"crossref","first-page":"011125","DOI":"10.1103\/PhysRevE.78.011125","article-title":"Intelligent Tit-for-Tat in the iterated prisoner\u2019s dilemma game","volume":"78","author":"SK Baek","year":"2008","journal-title":"Phys Rev E"},{"issue":"1","key":"pcbi.1008217.ref024","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/0040-5809(90)90005-G","article-title":"Stochastic strategies in the prisoner\u2019s dilemma","volume":"38","author":"M Nowak","year":"1990","journal-title":"Theor Popul Biol"},{"issue":"7","key":"pcbi.1008217.ref025","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1007\/BF00184645","article-title":"Automata, repeated games and noise","volume":"33","author":"MA Nowak","year":"1995","journal-title":"J Math Biol"},{"key":"pcbi.1008217.ref026","doi-asserted-by":"crossref","first-page":"13370","DOI":"10.1038\/s41598-020-70281-x","article-title":"Automata representation of successful strategies for social dilemmas","volume":"10","author":"Y Murase","year":"2020","journal-title":"Sci Rep"},{"issue":"31","key":"pcbi.1008217.ref027","doi-asserted-by":"crossref","first-page":"10797","DOI":"10.1073\/pnas.0502589102","article-title":"Evolutionary cycles of cooperation and defection","volume":"102","author":"LA Imhof","year":"2005","journal-title":"Proc Natl Acad Sci USA"},{"issue":"3","key":"pcbi.1008217.ref028","doi-asserted-by":"crossref","first-page":"574","DOI":"10.1016\/j.jtbi.2007.03.027","article-title":"Tit-for-tat or win-stay, lose-shift?","volume":"247","author":"LA Imhof","year":"2007","journal-title":"J Theor Biol"},{"issue":"1680","key":"pcbi.1008217.ref029","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1098\/rspb.2009.1171","article-title":"Stochastic evolutionary dynamics of direct reciprocity","volume":"277","author":"LA Imhof","year":"2010","journal-title":"Proc R Roc B"},{"issue":"18","key":"pcbi.1008217.ref030","doi-asserted-by":"crossref","first-page":"4715","DOI":"10.1073\/pnas.1621239114","article-title":"Memory-n strategies of direct reciprocity","volume":"114","author":"C Hilbe","year":"2017","journal-title":"Proc Natl Acad Sci USA"},{"key":"pcbi.1008217.ref031","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1016\/j.jtbi.2014.04.025","article-title":"Optional games on cycles and complete graphs","volume":"356","author":"HC Jeong","year":"2014","journal-title":"J Theor Biol"},{"key":"pcbi.1008217.ref032","doi-asserted-by":"crossref","first-page":"25676","DOI":"10.1038\/srep25676","article-title":"Comparing reactive and memory-one strategies of direct reciprocity","volume":"6","author":"SK Baek","year":"2016","journal-title":"Sci Rep"},{"key":"pcbi.1008217.ref033","first-page":"012001","article-title":"An open-source job management framework for parameter-space exploration: OACIS","volume":"921","author":"Y Murase","year":"2017","journal-title":"J Phys: Conf Ser"},{"issue":"8-9","key":"pcbi.1008217.ref034","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/j.ipl.2010.02.001","article-title":"The Floyd\u2013Warshall algorithm on graphs with negative cycles","volume":"110","author":"S Hougardy","year":"2010","journal-title":"Inf Process Lett"},{"issue":"1381","key":"pcbi.1008217.ref035","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1098\/rspb.1997.0073","article-title":"Effects of increasing the number of players and memory size in the iterated Prisoner\u2019s Dilemma: a numerical approach","volume":"264","author":"C Hauert","year":"1997","journal-title":"Proc R Soc B"},{"key":"pcbi.1008217.ref036","first-page":"337","volume-title":"The Economy as an Evolving Complex System II","author":"K Lindgren","year":"1997"},{"issue":"1","key":"pcbi.1008217.ref037","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/srep07843","article-title":"Reputation drives cooperative behaviour and network formation in human groups","volume":"5","author":"JA Cuesta","year":"2015","journal-title":"Sci Rep"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1008217","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2021,2,2]],"date-time":"2021-02-02T00:00:00Z","timestamp":1612224000000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1008217","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,12]],"date-time":"2022-12-12T13:28:21Z","timestamp":1670851701000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1008217"}},"subtitle":[],"editor":[{"given":"Yamir","family":"Moreno","sequence":"first","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2021,1,21]]},"references-count":37,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1,21]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1008217","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/2020.08.05.237552","asserted-by":"object"}]},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,21]]}}}