{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T01:35:37Z","timestamp":1769823337956,"version":"3.49.0"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1010987","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2023,7,12]],"date-time":"2023-07-12T00:00:00Z","timestamp":1689120000000}}],"reference-count":57,"publisher":"Public Library of Science (PLoS)","issue":"6","license":[{"start":{"date-parts":[[2023,6,29]],"date-time":"2023-06-29T00:00:00Z","timestamp":1687996800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100019180","name":"HORIZON EUROPE European Research Council","doi-asserted-by":"publisher","award":["850529"],"award-info":[{"award-number":["850529"]}],"id":[{"id":"10.13039\/100019180","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Human interactions can take the form of social dilemmas: collectively, people fare best if all cooperate but each individual is tempted to free ride. Social dilemmas can be resolved when individuals interact repeatedly. Repetition allows them to adopt reciprocal strategies which incentivize cooperation. The most basic model for direct reciprocity is the repeated donation game, a variant of the prisoner\u2019s dilemma. Two players interact over many rounds; in each round they decide whether to cooperate or to defect. Strategies take into account the history of the play. Memory-one strategies depend only on the previous round. Even though they are among the most elementary strategies of direct reciprocity, their evolutionary dynamics has been difficult to study analytically. As a result, much previous work has relied on simulations. Here, we derive and analyze their adaptive dynamics. We show that the four-dimensional space of memory-one strategies has an invariant three-dimensional subspace, generated by the memory-one counting strategies. Counting strategies record how many players cooperated in the previous round, without considering who cooperated. We give a partial characterization of adaptive dynamics for memory-one strategies and a full characterization for memory-one counting strategies.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1010987","type":"journal-article","created":{"date-parts":[[2023,6,29]],"date-time":"2023-06-29T18:24:30Z","timestamp":1688063070000},"page":"e1010987","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":8,"title":["Adaptive dynamics of memory-one strategies in the repeated donation game"],"prefix":"10.1371","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-6551-5996","authenticated-orcid":true,"given":"Philip","family":"LaPorte","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5116-955X","authenticated-orcid":true,"given":"Christian","family":"Hilbe","sequence":"additional","affiliation":[]},{"given":"Martin A.","family":"Nowak","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2023,6,29]]},"reference":[{"key":"pcbi.1010987.ref001","doi-asserted-by":"crossref","DOI":"10.1515\/9781400832255","volume-title":"The Calculus of Selfishness","author":"K Sigmund","year":"2010"},{"key":"pcbi.1010987.ref002","doi-asserted-by":"crossref","DOI":"10.2307\/j.ctvjghw98","volume-title":"Evolutionary dynamics","author":"MA Nowak","year":"2006"},{"key":"pcbi.1010987.ref003","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.1010987.ref004","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1086\/406755","article-title":"The evolution of reciprocal altruism","volume":"46","author":"RL Trivers","year":"1971","journal-title":"The Quarterly Review of Biology"},{"key":"pcbi.1010987.ref005","doi-asserted-by":"crossref","first-page":"1390","DOI":"10.1126\/science.7466396","article-title":"The evolution of cooperation","volume":"211","author":"R Axelrod","year":"1981","journal-title":"Science"},{"key":"pcbi.1010987.ref006","doi-asserted-by":"crossref","first-page":"102","DOI":"10.3389\/frobt.2018.00102","article-title":"No strategy can win in the repeated prisoner\u2019s dilemma: Linking game theory and computer simulations","volume":"5","author":"J Garc\u00eda","year":"2018","journal-title":"Frontiers in Robotics and AI"},{"issue":"7","key":"pcbi.1010987.ref007","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":"Nature Human Behaviour"},{"key":"pcbi.1010987.ref008","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1057\/s41599-021-00718-9","article-title":"A bibliometric study of research topics, collaboration and centrality in the field of the Iterated Prisoner\u2019s Dilemma","volume":"8","author":"NE Glynatsi","year":"2021","journal-title":"Humanities and Social Sciences Communications"},{"key":"pcbi.1010987.ref009","doi-asserted-by":"crossref","unstructured":"Rapoport A. 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