{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T11:18:25Z","timestamp":1782299905064,"version":"3.54.5"},"reference-count":37,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2020,7,6]],"date-time":"2020-07-06T00:00:00Z","timestamp":1593993600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003329","name":"Ministerio de Econom\u00eda y Competitividad","doi-asserted-by":"publisher","award":["PGC2018-094754-B- C21"],"award-info":[{"award-number":["PGC2018-094754-B- C21"]}],"id":[{"id":"10.13039\/501100003329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003329","name":"Ministerio de Econom\u00eda y Competitividad","doi-asserted-by":"publisher","award":["FIS2015-71929-REDT"],"award-info":[{"award-number":["FIS2015-71929-REDT"]}],"id":[{"id":"10.13039\/501100003329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002809","name":"Generalitat de Catalunya","doi-asserted-by":"publisher","award":["2017SGR-896"],"award-info":[{"award-number":["2017SGR-896"]}],"id":[{"id":"10.13039\/501100002809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007512","name":"Universitat Rovira i Virgili","doi-asserted-by":"publisher","award":["2019PFR-URV-B2-41"],"award-info":[{"award-number":["2019PFR-URV-B2-41"]}],"id":[{"id":"10.13039\/501100007512","id-type":"DOI","asserted-by":"publisher"}]},{"name":"ICREA Academia and the James S. McDonnell Foundation","award":["220020325"],"award-info":[{"award-number":["220020325"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Many real systems are strongly characterized by collective cooperative phenomena whose existence and properties still need a satisfactory explanation. Coherently with their collective nature, they call for new and more accurate descriptions going beyond pairwise models, such as graphs, in which all the interactions are considered as involving only two individuals at a time. Hypergraphs respond to this need, providing a mathematical representation of a system allowing from pairs to larger groups. In this work, through the use of different hypergraphs, we study how group interactions influence the evolution of cooperation in a structured population, by analyzing the evolutionary dynamics of the public goods game. Here we show that, likewise to network reciprocity, group interactions also promote cooperation. More importantly, by means of an invasion analysis in which the conditions for a strategy to survive are studied, we show how, in heterogeneously-structured populations, reciprocity among players is expected to grow with the increasing of the order of the interactions. This is due to the heterogeneity of connections and, particularly, to the presence of individuals standing out as hubs in the population. Our analysis represents a first step towards the study of evolutionary dynamics through higher-order interactions, and gives insights into why cooperation in heterogeneous higher-order structures is enhanced. Lastly, it also gives clues about the co-existence of cooperative and non-cooperative behaviors related to the structural properties of the interaction patterns.<\/jats:p>","DOI":"10.3390\/e22070744","type":"journal-article","created":{"date-parts":[[2020,7,6]],"date-time":"2020-07-06T11:07:42Z","timestamp":1594033662000},"page":"744","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":53,"title":["Evolution of Cooperation in the Presence of Higher-Order Interactions: From Networks to Hypergraphs"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6333-4847","authenticated-orcid":false,"given":"Giulio","family":"Burgio","sequence":"first","affiliation":[{"name":"Departament d\u2019Enginyeria Inform\u00e0tica i Matem\u00e0tiques, Universitat Rovira i Virgili, Av. Pa\u00efsos Catalans 26, 43007 Tarragona, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7563-9269","authenticated-orcid":false,"given":"Joan T.","family":"Matamalas","sequence":"additional","affiliation":[{"name":"Harvard Medical School &amp; Brigham and Women\u2019s Hospital, 75 Francis St, Boston, MA 02115, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1820-0062","authenticated-orcid":false,"given":"Sergio","family":"G\u00f3mez","sequence":"additional","affiliation":[{"name":"Departament d\u2019Enginyeria Inform\u00e0tica i Matem\u00e0tiques, Universitat Rovira i Virgili, Av. 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