{"DOAJ_listed":"1","language":[{"iso":"eng"}],"volume":4,"date_updated":"2025-07-10T11:59:47Z","status":"public","OA_place":"publisher","article_type":"original","tmp":{"name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","image":"/images/cc_by_nc.png","legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode","short":"CC BY-NC (4.0)"},"_id":"19843","project":[{"call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","grant_number":"863818"}],"department":[{"_id":"KrCh"}],"abstract":[{"text":"Social dilemmas are collective-action problems where individual interests are at odds with group interests. Such dilemmas occur frequently at all scales of human interactions. When dealing with collective-action problems, people often act reciprocally. They adjust their behavior to match the previous behavior of the recipient. The literature distinguishes two kinds of reciprocity. According to direct reciprocity, individuals react to their immediate experiences with the recipient. They are more likely to cooperate if the recipient previously cooperated with them. According to indirect reciprocity, individuals react to the recipient’s general behavior, irrespectively of whether or not they benefited directly. In practice, the two kinds of reciprocity are often intertwined; people typically base their decisions on both direct experiences and indirect observations. Yet only recently have researchers begun to explore how the two kinds of reciprocity interact. So far, this research only addresses a single type of social dilemma, the donation game, where the effects of individual behaviors are independent. Instead, here we allow for all pairwise social dilemmas. By applying novel techniques to generalize the theory of zero-determinant strategies, we establish an important proof of principle: In all social dilemmas, socially optimal outcomes can be sustained as an equilibrium, using either direct or indirect reciprocity, or arbitrary mixtures thereof. These results neither require games to be repeated infinitely often, nor that individual opinions are synchronized. In this way, we considerably generalize the scope of models of reciprocity, and we build further bridges between the literatures on direct and indirect reciprocity.","lang":"eng"}],"oa":1,"quality_controlled":"1","related_material":{"record":[{"id":"19903","relation":"dissertation_contains","status":"public"}]},"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.).","ec_funded":1,"has_accepted_license":"1","type":"journal_article","oa_version":"Published Version","author":[{"full_name":"Hübner, Valentin","id":"2c8aa207-dc7d-11ea-9b2f-f22972ecd910","first_name":"Valentin","last_name":"Hübner"},{"last_name":"Schmid","first_name":"Laura","orcid":"0000-0002-6978-7329","full_name":"Schmid, Laura","id":"38B437DE-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5116-955X","full_name":"Hilbe, Christian","id":"2FDF8F3C-F248-11E8-B48F-1D18A9856A87","last_name":"Hilbe","first_name":"Christian"},{"full_name":"Chatterjee, Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X","first_name":"Krishnendu","last_name":"Chatterjee"}],"file_date_updated":"2025-06-23T08:09:50Z","publisher":"Oxford University Press","publication_identifier":{"eissn":["2752-6542"]},"title":"Stable strategies of direct and indirect reciprocity across all social dilemmas","day":"01","citation":{"short":"V. Hübner, L. Schmid, C. Hilbe, K. Chatterjee, PNAS Nexus 4 (2025).","mla":"Hübner, Valentin, et al. “Stable Strategies of Direct and Indirect Reciprocity across All Social Dilemmas.” <i>PNAS Nexus</i>, vol. 4, no. 5, pgaf154, Oxford University Press, 2025, doi:<a href=\"https://doi.org/10.1093/pnasnexus/pgaf154\">10.1093/pnasnexus/pgaf154</a>.","apa":"Hübner, V., Schmid, L., Hilbe, C., &#38; Chatterjee, K. (2025). Stable strategies of direct and indirect reciprocity across all social dilemmas. <i>PNAS Nexus</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/pnasnexus/pgaf154\">https://doi.org/10.1093/pnasnexus/pgaf154</a>","ista":"Hübner V, Schmid L, Hilbe C, Chatterjee K. 2025. Stable strategies of direct and indirect reciprocity across all social dilemmas. PNAS Nexus. 4(5), pgaf154.","ieee":"V. Hübner, L. Schmid, C. Hilbe, and K. Chatterjee, “Stable strategies of direct and indirect reciprocity across all social dilemmas,” <i>PNAS Nexus</i>, vol. 4, no. 5. Oxford University Press, 2025.","ama":"Hübner V, Schmid L, Hilbe C, Chatterjee K. Stable strategies of direct and indirect reciprocity across all social dilemmas. <i>PNAS Nexus</i>. 2025;4(5). doi:<a href=\"https://doi.org/10.1093/pnasnexus/pgaf154\">10.1093/pnasnexus/pgaf154</a>","chicago":"Hübner, Valentin, Laura Schmid, Christian Hilbe, and Krishnendu Chatterjee. “Stable Strategies of Direct and Indirect Reciprocity across All Social Dilemmas.” <i>PNAS Nexus</i>. Oxford University Press, 2025. <a href=\"https://doi.org/10.1093/pnasnexus/pgaf154\">https://doi.org/10.1093/pnasnexus/pgaf154</a>."},"publication":"PNAS Nexus","corr_author":"1","ddc":["000"],"publication_status":"published","date_published":"2025-05-01T00:00:00Z","pmid":1,"article_number":"pgaf154","OA_type":"gold","year":"2025","date_created":"2025-06-15T22:01:30Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"5","month":"05","article_processing_charge":"Yes","doi":"10.1093/pnasnexus/pgaf154","file":[{"access_level":"open_access","creator":"dernst","relation":"main_file","file_name":"2025_PNASNexus_Huebner.pdf","date_created":"2025-06-23T08:09:50Z","file_id":"19867","success":1,"checksum":"efd6648db3fc3ea0cdd7155d667e5f11","date_updated":"2025-06-23T08:09:50Z","content_type":"application/pdf","file_size":2551195}],"license":"https://creativecommons.org/licenses/by-nc/4.0/","external_id":{"pmid":["40417077"]},"scopus_import":"1","intvolume":"         4"}