{"OA_place":"publisher","license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","ddc":["000"],"intvolume":"       121","date_published":"2024-12-10T00:00:00Z","date_updated":"2025-01-02T12:17:23Z","publication_identifier":{"eissn":["1091-6490"],"issn":["0027-8424"]},"project":[{"grant_number":"863818","name":"Formal Methods for Stochastic Models: Algorithms and Applications","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","call_identifier":"H2020"}],"type":"journal_article","title":"Density amplifiers of cooperation for spatial games","abstract":[{"lang":"eng","text":"Spatial games provide a simple and elegant mathematical model to study the evolution of cooperation in networks. In spatial games, individuals reside in vertices, adopt simple strategies, and interact with neighbors to receive a payoff. Depending on their own and neighbors’ payoffs, individuals can change their strategy. The payoff is determined by the Prisoners’ Dilemma, a classical matrix game, where players cooperate or defect. While cooperation is the desired behavior, defection provides a higher payoff for a selfish individual. There are many theoretical and empirical studies related to the role of the network in the evolution of cooperation. However, the fundamental question of whether there exist networks that for low initial cooperation rate ensure a high chance of fixation, i.e., cooperation spreads across the whole population, has remained elusive for spatial games with strong selection. In this work, we answer this fundamental question in the affirmative by presenting network structures that ensure high fixation probability for cooperators in the strong selection regime. Besides, our structures have many desirable properties: (a) they ensure the spread of cooperation even for a low initial density of cooperation and high temptation of defection, (b) they have constant degrees, and (c) the number of steps, until cooperation spreads, is at most quadratic in the size of the network."}],"status":"public","language":[{"iso":"eng"}],"OA_type":"hybrid","has_accepted_license":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","publication_status":"published","publication":"Proceedings of the National Academy of Sciences of the United States of America","tmp":{"name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode"},"oa":1,"doi":"10.1073/pnas.2405605121","ec_funded":1,"file":[{"relation":"main_file","date_updated":"2025-01-02T12:14:15Z","checksum":"0115e9090b478e0644308c6dab58605b","access_level":"open_access","file_name":"2024_PNAS_Svoboda.pdf","date_created":"2025-01-02T12:14:15Z","creator":"dernst","content_type":"application/pdf","file_size":2491151,"file_id":"18721","success":1}],"acknowledgement":"J.S. and K.C. were supported by the European Research Council CoG 863818 (ForM-SMArt) and Austrian Science Fund 10.55776/COE12.","quality_controlled":"1","year":"2024","APC_amount":"2750 USD","_id":"18703","citation":{"ista":"Svoboda J, Chatterjee K. 2024. Density amplifiers of cooperation for spatial games. Proceedings of the National Academy of Sciences of the United States of America. 121(50), e2405605121.","ama":"Svoboda J, Chatterjee K. Density amplifiers of cooperation for spatial games. <i>Proceedings of the National Academy of Sciences of the United States of America</i>. 2024;121(50). doi:<a href=\"https://doi.org/10.1073/pnas.2405605121\">10.1073/pnas.2405605121</a>","mla":"Svoboda, Jakub, and Krishnendu Chatterjee. “Density Amplifiers of Cooperation for Spatial Games.” <i>Proceedings of the National Academy of Sciences of the United States of America</i>, vol. 121, no. 50, e2405605121, National Academy of Sciences, 2024, doi:<a href=\"https://doi.org/10.1073/pnas.2405605121\">10.1073/pnas.2405605121</a>.","chicago":"Svoboda, Jakub, and Krishnendu Chatterjee. “Density Amplifiers of Cooperation for Spatial Games.” <i>Proceedings of the National Academy of Sciences of the United States of America</i>. National Academy of Sciences, 2024. <a href=\"https://doi.org/10.1073/pnas.2405605121\">https://doi.org/10.1073/pnas.2405605121</a>.","ieee":"J. Svoboda and K. Chatterjee, “Density amplifiers of cooperation for spatial games,” <i>Proceedings of the National Academy of Sciences of the United States of America</i>, vol. 121, no. 50. National Academy of Sciences, 2024.","short":"J. Svoboda, K. Chatterjee, Proceedings of the National Academy of Sciences of the United States of America 121 (2024).","apa":"Svoboda, J., &#38; Chatterjee, K. (2024). Density amplifiers of cooperation for spatial games. <i>Proceedings of the National Academy of Sciences of the United States of America</i>. National Academy of Sciences. <a href=\"https://doi.org/10.1073/pnas.2405605121\">https://doi.org/10.1073/pnas.2405605121</a>"},"date_created":"2024-12-22T23:01:47Z","department":[{"_id":"KrCh"}],"scopus_import":"1","day":"10","month":"12","issue":"50","publisher":"National Academy of Sciences","oa_version":"Published Version","author":[{"full_name":"Svoboda, Jakub","last_name":"Svoboda","orcid":"0000-0002-1419-3267","id":"130759D2-D7DD-11E9-87D2-DE0DE6697425","first_name":"Jakub"},{"first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","orcid":"0000-0002-4561-241X"}],"article_processing_charge":"Yes","file_date_updated":"2025-01-02T12:14:15Z","article_type":"original","article_number":"e2405605121","external_id":{"pmid":["39642209"]},"pmid":1,"volume":121}