{"doi":"10.1073/pnas.2315558121","oa_version":"Published Version","department":[{"_id":"KrCh"}],"project":[{"grant_number":"863818","call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E"},{"grant_number":"754411","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2024-03-12T13:29:25Z","type":"journal_article","file_date_updated":"2024-03-12T13:12:22Z","acknowledgement":"This work was supported by the European Research Council CoG 863818 (ForM-SMArt) (to K.C.) and the European Research Council Starting Grant 850529: E-DIRECT (to C.H.), the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement #754411 and the French Agence Nationale de la Recherche (under the Investissement d’Avenir Programme, ANR-17-EURE-0010) (to M.K.).","ec_funded":1,"_id":"15083","file":[{"file_size":2203220,"creator":"dernst","access_level":"open_access","date_updated":"2024-03-12T13:12:22Z","success":1,"date_created":"2024-03-12T13:12:22Z","checksum":"068520e3efd4d008bb9177e8aedb7d22","file_name":"2024_PNAS_Huebner.pdf","file_id":"15109","relation":"main_file","content_type":"application/pdf"}],"status":"public","article_type":"original","publisher":"Proceedings of the National Academy of Sciences","license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","external_id":{"pmid":["38408249"]},"date_created":"2024-03-05T09:18:49Z","month":"03","publication_status":"published","issue":"10","publication":"Proceedings of the National Academy of Sciences","has_accepted_license":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","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"},"article_number":"e2315558121","article_processing_charge":"Yes (in subscription journal)","intvolume":"       121","citation":{"ieee":"V. Hübner, M. Staab, C. Hilbe, K. Chatterjee, and M. Kleshnina, “Efficiency and resilience of cooperation in asymmetric social dilemmas,” <i>Proceedings of the National Academy of Sciences</i>, vol. 121, no. 10. Proceedings of the National Academy of Sciences, 2024.","short":"V. Hübner, M. Staab, C. Hilbe, K. Chatterjee, M. Kleshnina, Proceedings of the National Academy of Sciences 121 (2024).","chicago":"Hübner, Valentin, Manuel Staab, Christian Hilbe, Krishnendu Chatterjee, and Maria Kleshnina. “Efficiency and Resilience of Cooperation in Asymmetric Social Dilemmas.” <i>Proceedings of the National Academy of Sciences</i>. Proceedings of the National Academy of Sciences, 2024. <a href=\"https://doi.org/10.1073/pnas.2315558121\">https://doi.org/10.1073/pnas.2315558121</a>.","ama":"Hübner V, Staab M, Hilbe C, Chatterjee K, Kleshnina M. Efficiency and resilience of cooperation in asymmetric social dilemmas. <i>Proceedings of the National Academy of Sciences</i>. 2024;121(10). doi:<a href=\"https://doi.org/10.1073/pnas.2315558121\">10.1073/pnas.2315558121</a>","apa":"Hübner, V., Staab, M., Hilbe, C., Chatterjee, K., &#38; Kleshnina, M. (2024). Efficiency and resilience of cooperation in asymmetric social dilemmas. <i>Proceedings of the National Academy of Sciences</i>. Proceedings of the National Academy of Sciences. <a href=\"https://doi.org/10.1073/pnas.2315558121\">https://doi.org/10.1073/pnas.2315558121</a>","mla":"Hübner, Valentin, et al. “Efficiency and Resilience of Cooperation in Asymmetric Social Dilemmas.” <i>Proceedings of the National Academy of Sciences</i>, vol. 121, no. 10, e2315558121, Proceedings of the National Academy of Sciences, 2024, doi:<a href=\"https://doi.org/10.1073/pnas.2315558121\">10.1073/pnas.2315558121</a>.","ista":"Hübner V, Staab M, Hilbe C, Chatterjee K, Kleshnina M. 2024. Efficiency and resilience of cooperation in asymmetric social dilemmas. Proceedings of the National Academy of Sciences. 121(10), e2315558121."},"related_material":{"record":[{"id":"15108","relation":"research_data","status":"public"}],"link":[{"url":"https://ista.ac.at/en/news/what-math-tells-us-about-social-dilemmas/","relation":"press_release","description":"News on ISTA Website"}]},"title":"Efficiency and resilience of cooperation in asymmetric social dilemmas","ddc":["000"],"publication_identifier":{"eissn":["1091-6490"],"issn":["0027-8424"]},"quality_controlled":"1","date_published":"2024-03-05T00:00:00Z","volume":121,"pmid":1,"abstract":[{"lang":"eng","text":"<jats:p>Direct reciprocity is a powerful mechanism for cooperation in social dilemmas. The very logic of reciprocity, however, seems to require that individuals are symmetric, and that everyone has the same means to influence each others’ payoffs. Yet in many applications, individuals are asymmetric. Herein, we study the effect of asymmetry in linear public good games. Individuals may differ in their endowments (their ability to contribute to a public good) and in their productivities (how effective their contributions are). Given the individuals’ productivities, we ask which allocation of endowments is optimal for cooperation. To this end, we consider two notions of optimality. The first notion focuses on the resilience of cooperation. The respective endowment distribution ensures that full cooperation is feasible even under the most adverse conditions. The second notion focuses on efficiency. The corresponding endowment distribution maximizes group welfare. Using analytical methods, we fully characterize these two endowment distributions. This analysis reveals that both optimality notions favor some endowment inequality: More productive players ought to get higher endowments. Yet the two notions disagree on how unequal endowments are supposed to be. A focus on resilience results in less inequality. With additional simulations, we show that the optimal endowment allocation needs to account for both the resilience and the efficiency of cooperation.</jats:p>"}],"oa":1,"year":"2024","day":"05","language":[{"iso":"eng"}],"author":[{"last_name":"Hübner","first_name":"Valentin","id":"2c8aa207-dc7d-11ea-9b2f-f22972ecd910","full_name":"Hübner, Valentin"},{"last_name":"Staab","first_name":"Manuel","full_name":"Staab, Manuel"},{"last_name":"Hilbe","orcid":"0000-0001-5116-955X","first_name":"Christian","id":"2FDF8F3C-F248-11E8-B48F-1D18A9856A87","full_name":"Hilbe, Christian"},{"first_name":"Krishnendu","last_name":"Chatterjee","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Kleshnina","first_name":"Maria","full_name":"Kleshnina, Maria"}]}