[{"ec_funded":1,"license":"https://creativecommons.org/licenses/by/4.0/","abstract":[{"lang":"eng","text":"The public goods game is among the most studied metaphors of cooperation in groups. In this game, individuals can use their endowments to make contributions towards a good that benefits everyone. Each individual, however, is tempted to free-ride on the contributions of others. Herein, we study repeated public goods games among asymmetric players. Previous work has explored to which extent asymmetry allows for full cooperation, such that players contribute their full endowment each round. However, by design that work focusses on equilibria where individuals make the same contribution each round. Instead, here we consider players whose contributions along the equilibrium path can change from one round to the next. We do so for three different models – one without any budget constraints, one with endowment constraints, and one in which individuals can save their current endowment to be used in subsequent rounds. In each case, we explore two key quantities: the welfare and the resource efficiency that can be achieved in equilibrium. Welfare corresponds to the sum of all players’ payoffs. Resource efficiency relates this welfare to the total contributions made by the players. Compared to constant contribution sequences, we find that time-dependent contributions can improve resource efficiency across all three models. Moreover, they can improve the players’ welfare in the model with savings."}],"file_date_updated":"2025-12-30T08:01:35Z","language":[{"iso":"eng"}],"oa":1,"OA_type":"hybrid","scopus_import":"1","_id":"19074","related_material":{"record":[{"status":"public","id":"19903","relation":"dissertation_contains"}]},"citation":{"ieee":"V. Hübner, C. Hilbe, M. Staab, M. Kleshnina, and K. Chatterjee, “Time-dependent strategies in repeated asymmetric public goods games,” Dynamic Games and Applications, vol. 15. Springer Nature, pp. 1617–1645, 2025.","mla":"Hübner, Valentin, et al. “Time-Dependent Strategies in Repeated Asymmetric Public Goods Games.” Dynamic Games and Applications, vol. 15, Springer Nature, 2025, pp. 1617–45, doi:10.1007/s13235-025-00627-5.","short":"V. Hübner, C. Hilbe, M. Staab, M. Kleshnina, K. Chatterjee, Dynamic Games and Applications 15 (2025) 1617–1645.","chicago":"Hübner, Valentin, Christian Hilbe, Manuel Staab, Maria Kleshnina, and Krishnendu Chatterjee. “Time-Dependent Strategies in Repeated Asymmetric Public Goods Games.” Dynamic Games and Applications. Springer Nature, 2025. https://doi.org/10.1007/s13235-025-00627-5.","ista":"Hübner V, Hilbe C, Staab M, Kleshnina M, Chatterjee K. 2025. Time-dependent strategies in repeated asymmetric public goods games. Dynamic Games and Applications. 15, 1617–1645.","ama":"Hübner V, Hilbe C, Staab M, Kleshnina M, Chatterjee K. Time-dependent strategies in repeated asymmetric public goods games. Dynamic Games and Applications. 2025;15:1617-1645. doi:10.1007/s13235-025-00627-5","apa":"Hübner, V., Hilbe, C., Staab, M., Kleshnina, M., & Chatterjee, K. (2025). Time-dependent strategies in repeated asymmetric public goods games. Dynamic Games and Applications. Springer Nature. https://doi.org/10.1007/s13235-025-00627-5"},"quality_controlled":"1","date_updated":"2026-04-07T12:30:56Z","department":[{"_id":"KrCh"}],"doi":"10.1007/s13235-025-00627-5","file":[{"date_updated":"2025-12-30T08:01:35Z","file_name":"2025_DynGamesAppl_Huebner.pdf","checksum":"de0a412cbb7d98bf5e6a551c26acbefa","access_level":"open_access","success":1,"content_type":"application/pdf","date_created":"2025-12-30T08:01:35Z","file_size":1126178,"creator":"dernst","file_id":"20888","relation":"main_file"}],"date_created":"2025-02-23T23:01:57Z","publication_status":"published","type":"journal_article","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"day":"01","isi":1,"PlanS_conform":"1","project":[{"name":"Formal Methods for Stochastic Models: Algorithms and Applications","grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","call_identifier":"H2020"},{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"article_type":"original","publisher":"Springer Nature","publication":"Dynamic Games and Applications","OA_place":"publisher","has_accepted_license":"1","status":"public","corr_author":"1","month":"11","intvolume":" 15","publication_identifier":{"eissn":["2153-0793"],"issn":["2153-0785"]},"ddc":["000"],"external_id":{"isi":["001415587800001"]},"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 programme 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), and ARC SRIEAS Grant SR200100005 Securing Antarctica’s Environmental Future (to M.K.). Open access funding provided by Institute of Science and Technology (IST Austria).","author":[{"orcid":"0009-0001-5009-4987","id":"2c8aa207-dc7d-11ea-9b2f-f22972ecd910","last_name":"Hübner","full_name":"Hübner, Valentin","first_name":"Valentin"},{"last_name":"Hilbe","first_name":"Christian","full_name":"Hilbe, Christian","orcid":"0000-0001-5116-955X","id":"2FDF8F3C-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Manuel","full_name":"Staab, Manuel","last_name":"Staab"},{"orcid":"0000-0002-5518-8317","id":"4E21749C-F248-11E8-B48F-1D18A9856A87","last_name":"Kleshnina","full_name":"Kleshnina, Maria","first_name":"Maria"},{"orcid":"0000-0002-4561-241X","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu"}],"article_processing_charge":"Yes (via OA deal)","title":"Time-dependent strategies in repeated asymmetric public goods games","year":"2025","page":"1617-1645","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2025-11-01T00:00:00Z","oa_version":"Published Version","volume":15},{"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.).","author":[{"full_name":"Hübner, Valentin","first_name":"Valentin","last_name":"Hübner","id":"2c8aa207-dc7d-11ea-9b2f-f22972ecd910","orcid":"0009-0001-5009-4987"},{"id":"38B437DE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6978-7329","full_name":"Schmid, Laura","first_name":"Laura","last_name":"Schmid"},{"orcid":"0000-0001-5116-955X","id":"2FDF8F3C-F248-11E8-B48F-1D18A9856A87","last_name":"Hilbe","first_name":"Christian","full_name":"Hilbe, Christian"},{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu","last_name":"Chatterjee"}],"article_number":"pgaf154","ddc":["000"],"external_id":{"pmid":["40417077"]},"year":"2025","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2025-05-01T00:00:00Z","oa_version":"Published Version","volume":4,"pmid":1,"article_processing_charge":"Yes","title":"Stable strategies of direct and indirect reciprocity across all social dilemmas","has_accepted_license":"1","status":"public","corr_author":"1","publisher":"Oxford University Press","publication":"PNAS Nexus","OA_place":"publisher","publication_identifier":{"eissn":["2752-6542"]},"month":"05","intvolume":" 4","publication_status":"published","date_created":"2025-06-15T22:01:30Z","tmp":{"image":"/images/cc_by_nc.png","legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode","name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","short":"CC BY-NC (4.0)"},"type":"journal_article","doi":"10.1093/pnasnexus/pgaf154","department":[{"_id":"KrCh"}],"file":[{"date_updated":"2025-06-23T08:09:50Z","file_name":"2025_PNASNexus_Huebner.pdf","checksum":"efd6648db3fc3ea0cdd7155d667e5f11","access_level":"open_access","success":1,"content_type":"application/pdf","date_created":"2025-06-23T08:09:50Z","file_size":2551195,"creator":"dernst","relation":"main_file","file_id":"19867"}],"article_type":"original","day":"01","project":[{"grant_number":"863818","name":"Formal Methods for Stochastic Models: Algorithms and Applications","call_identifier":"H2020","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E"}],"OA_type":"gold","scopus_import":"1","ec_funded":1,"license":"https://creativecommons.org/licenses/by-nc/4.0/","abstract":[{"lang":"eng","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."}],"language":[{"iso":"eng"}],"oa":1,"file_date_updated":"2025-06-23T08:09:50Z","related_material":{"record":[{"status":"public","id":"19903","relation":"dissertation_contains"}]},"DOAJ_listed":"1","quality_controlled":"1","date_updated":"2026-04-07T12:30:56Z","citation":{"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.","ama":"Hübner V, Schmid L, Hilbe C, Chatterjee K. Stable strategies of direct and indirect reciprocity across all social dilemmas. PNAS Nexus. 2025;4(5). doi:10.1093/pnasnexus/pgaf154","apa":"Hübner, V., Schmid, L., Hilbe, C., & Chatterjee, K. (2025). Stable strategies of direct and indirect reciprocity across all social dilemmas. PNAS Nexus. Oxford University Press. https://doi.org/10.1093/pnasnexus/pgaf154","ieee":"V. Hübner, L. Schmid, C. Hilbe, and K. Chatterjee, “Stable strategies of direct and indirect reciprocity across all social dilemmas,” PNAS Nexus, vol. 4, no. 5. Oxford University Press, 2025.","mla":"Hübner, Valentin, et al. “Stable Strategies of Direct and Indirect Reciprocity across All Social Dilemmas.” PNAS Nexus, vol. 4, no. 5, pgaf154, Oxford University Press, 2025, doi:10.1093/pnasnexus/pgaf154.","short":"V. Hübner, L. Schmid, C. Hilbe, K. Chatterjee, PNAS Nexus 4 (2025).","chicago":"Hübner, Valentin, Laura Schmid, Christian Hilbe, and Krishnendu Chatterjee. “Stable Strategies of Direct and Indirect Reciprocity across All Social Dilemmas.” PNAS Nexus. Oxford University Press, 2025. https://doi.org/10.1093/pnasnexus/pgaf154."},"_id":"19843","issue":"5"},{"intvolume":" 122","month":"06","publication_identifier":{"issn":["0027-8424"],"eissn":["1091-6490"]},"OA_place":"publisher","publication":"Proceedings of the National Academy of Sciences","publisher":"National Academy of Sciences","status":"public","has_accepted_license":"1","title":"Unilateral incentive alignment in two-agent stochastic games","article_processing_charge":"Yes (in subscription journal)","oa_version":"Published Version","volume":122,"pmid":1,"date_published":"2025-06-24T00:00:00Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","year":"2025","external_id":{"pmid":["40523172"],"isi":["001522351900001"]},"article_number":"e2319927121","ddc":["000"],"author":[{"full_name":"Mcavoy, Alex","first_name":"Alex","last_name":"Mcavoy"},{"last_name":"Sehwag","first_name":"Udari Madhushani","full_name":"Sehwag, Udari Madhushani"},{"full_name":"Hilbe, Christian","first_name":"Christian","last_name":"Hilbe","id":"2FDF8F3C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5116-955X"},{"first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X"},{"last_name":"Barfuss","full_name":"Barfuss, Wolfram","first_name":"Wolfram"},{"last_name":"Su","first_name":"Qi","full_name":"Su, Qi"},{"last_name":"Leonard","full_name":"Leonard, Naomi Ehrich","first_name":"Naomi Ehrich"},{"last_name":"Plotkin","first_name":"Joshua B.","full_name":"Plotkin, Joshua B."}],"acknowledgement":"We gratefully acknowledge the support from the European Research Council (Starting Grant 850529: E-DIRECT) and the Max Planck Society (C.H.), the European Research Council (Consolidator Grant 863818: ForM-SMArt) (K.C.), the Shanghai Pujiang Program (No. 23PJ1405500) (Q.S.), the Army Research Office (Grant No. W911NF-18-1-0325) (N.E.L.), and the John Templeton Foundation (Grant No. 62281) (J.B.P.).","_id":"19965","issue":"25","quality_controlled":"1","date_updated":"2025-09-30T13:47:14Z","citation":{"chicago":"Mcavoy, Alex, Udari Madhushani Sehwag, Christian Hilbe, Krishnendu Chatterjee, Wolfram Barfuss, Qi Su, Naomi Ehrich Leonard, and Joshua B. Plotkin. “Unilateral Incentive Alignment in Two-Agent Stochastic Games.” Proceedings of the National Academy of Sciences. National Academy of Sciences, 2025. https://doi.org/10.1073/pnas.2319927121.","short":"A. Mcavoy, U.M. Sehwag, C. Hilbe, K. Chatterjee, W. Barfuss, Q. Su, N.E. Leonard, J.B. Plotkin, Proceedings of the National Academy of Sciences 122 (2025).","mla":"Mcavoy, Alex, et al. “Unilateral Incentive Alignment in Two-Agent Stochastic Games.” Proceedings of the National Academy of Sciences, vol. 122, no. 25, e2319927121, National Academy of Sciences, 2025, doi:10.1073/pnas.2319927121.","ieee":"A. Mcavoy et al., “Unilateral incentive alignment in two-agent stochastic games,” Proceedings of the National Academy of Sciences, vol. 122, no. 25. National Academy of Sciences, 2025.","apa":"Mcavoy, A., Sehwag, U. M., Hilbe, C., Chatterjee, K., Barfuss, W., Su, Q., … Plotkin, J. B. (2025). Unilateral incentive alignment in two-agent stochastic games. Proceedings of the National Academy of Sciences. National Academy of Sciences. https://doi.org/10.1073/pnas.2319927121","ama":"Mcavoy A, Sehwag UM, Hilbe C, et al. Unilateral incentive alignment in two-agent stochastic games. Proceedings of the National Academy of Sciences. 2025;122(25). doi:10.1073/pnas.2319927121","ista":"Mcavoy A, Sehwag UM, Hilbe C, Chatterjee K, Barfuss W, Su Q, Leonard NE, Plotkin JB. 2025. Unilateral incentive alignment in two-agent stochastic games. Proceedings of the National Academy of Sciences. 122(25), e2319927121."},"language":[{"iso":"eng"}],"oa":1,"file_date_updated":"2025-07-08T05:52:26Z","abstract":[{"lang":"eng","text":"Multiagent learning is challenging when agents face mixed-motivation interactions, where conflicts of interest arise as agents independently try to optimize their respective outcomes. Recent advancements in evolutionary game theory have identified a class of “zero-determinant” strategies, which confer an agent with significant unilateral control over outcomes in repeated games. Building on these insights, we present a comprehensive generalization of zero-determinant strategies to stochastic games, encompassing dynamic environments. We propose an algorithm that allows an agent to discover strategies enforcing predetermined linear (or approximately linear) payoff relationships. Of particular interest is the relationship in which both payoffs are equal, which serves as a proxy for fairness in symmetric games. We demonstrate that an agent can discover strategies enforcing such relationships through experience alone, without coordinating with an opponent. In finding and using such a strategy, an agent (“enforcer”) can incentivize optimal and equitable outcomes, circumventing potential exploitation. In particular, from the opponent’s viewpoint, the enforcer transforms a mixed-motivation problem into a cooperative problem, paving the way for more collaboration and fairness in multiagent systems."}],"license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","ec_funded":1,"scopus_import":"1","OA_type":"hybrid","project":[{"grant_number":"863818","name":"Formal Methods for Stochastic Models: Algorithms and Applications","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","call_identifier":"H2020"}],"day":"24","isi":1,"article_type":"original","file":[{"checksum":"3b35befd959a3e37aa9080a64a6afaf3","access_level":"open_access","success":1,"date_updated":"2025-07-08T05:52:26Z","file_name":"2025_PNAS_McAvoy.pdf","content_type":"application/pdf","creator":"dernst","date_created":"2025-07-08T05:52:26Z","file_size":29525932,"file_id":"19972","relation":"main_file"}],"department":[{"_id":"KrCh"}],"doi":"10.1073/pnas.2319927121","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)"},"type":"journal_article","publication_status":"published","date_created":"2025-07-06T22:01:23Z"},{"has_accepted_license":"1","status":"public","corr_author":"1","publisher":"National Academy of Sciences","publication":"Proceedings of the National Academy of Sciences of the United States of America","OA_place":"publisher","publication_identifier":{"issn":["0027-8424"],"eissn":["1091-6490"]},"month":"03","intvolume":" 121","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.).","author":[{"last_name":"Hübner","full_name":"Hübner, Valentin","first_name":"Valentin","orcid":"0009-0001-5009-4987","id":"2c8aa207-dc7d-11ea-9b2f-f22972ecd910"},{"last_name":"Staab","full_name":"Staab, Manuel","first_name":"Manuel"},{"orcid":"0000-0001-5116-955X","id":"2FDF8F3C-F248-11E8-B48F-1D18A9856A87","last_name":"Hilbe","full_name":"Hilbe, Christian","first_name":"Christian"},{"last_name":"Chatterjee","first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Kleshnina","first_name":"Maria","full_name":"Kleshnina, Maria"}],"article_number":"e2315558121","ddc":["000"],"external_id":{"pmid":["38408249"],"isi":["001207786500004"]},"year":"2024","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","volume":121,"pmid":1,"oa_version":"Published Version","date_published":"2024-03-05T00:00:00Z","article_processing_charge":"Yes (in subscription journal)","title":"Efficiency and resilience of cooperation in asymmetric social dilemmas","OA_type":"hybrid","scopus_import":"1","ec_funded":1,"abstract":[{"lang":"eng","text":"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."}],"oa":1,"language":[{"iso":"eng"}],"file_date_updated":"2024-03-12T13:12:22Z","related_material":{"link":[{"url":"https://ista.ac.at/en/news/what-math-tells-us-about-social-dilemmas/","relation":"press_release","description":"News on ISTA Website"}],"record":[{"status":"public","id":"15108","relation":"research_data"},{"status":"public","id":"19903","relation":"dissertation_contains"}]},"quality_controlled":"1","date_updated":"2026-04-07T12:30:56Z","citation":{"chicago":"Hübner, Valentin, Manuel Staab, Christian Hilbe, Krishnendu Chatterjee, and Maria Kleshnina. “Efficiency and Resilience of Cooperation in Asymmetric Social Dilemmas.” Proceedings of the National Academy of Sciences of the United States of America. National Academy of Sciences, 2024. https://doi.org/10.1073/pnas.2315558121.","short":"V. Hübner, M. Staab, C. Hilbe, K. Chatterjee, M. Kleshnina, Proceedings of the National Academy of Sciences of the United States of America 121 (2024).","mla":"Hübner, Valentin, et al. “Efficiency and Resilience of Cooperation in Asymmetric Social Dilemmas.” Proceedings of the National Academy of Sciences of the United States of America, vol. 121, no. 10, e2315558121, National Academy of Sciences, 2024, doi:10.1073/pnas.2315558121.","ieee":"V. Hübner, M. Staab, C. Hilbe, K. Chatterjee, and M. Kleshnina, “Efficiency and resilience of cooperation in asymmetric social dilemmas,” Proceedings of the National Academy of Sciences of the United States of America, vol. 121, no. 10. National Academy of Sciences, 2024.","apa":"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 of the United States of America. National Academy of Sciences. https://doi.org/10.1073/pnas.2315558121","ama":"Hübner V, Staab M, Hilbe C, Chatterjee K, Kleshnina M. Efficiency and resilience of cooperation in asymmetric social dilemmas. Proceedings of the National Academy of Sciences of the United States of America. 2024;121(10). doi:10.1073/pnas.2315558121","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 of the United States of America. 121(10), e2315558121."},"_id":"15083","issue":"10","publication_status":"published","date_created":"2024-03-05T09:18:49Z","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)"},"APC_amount":"3041,76 EUR","department":[{"_id":"KrCh"}],"doi":"10.1073/pnas.2315558121","file":[{"creator":"dernst","file_size":2203220,"date_created":"2024-03-12T13:12:22Z","relation":"main_file","file_id":"15109","access_level":"open_access","success":1,"checksum":"068520e3efd4d008bb9177e8aedb7d22","file_name":"2024_PNAS_Huebner.pdf","date_updated":"2024-03-12T13:12:22Z","content_type":"application/pdf"}],"article_type":"original","isi":1,"day":"05","project":[{"call_identifier":"H2020","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","name":"Formal Methods for Stochastic Models: Algorithms and Applications","grant_number":"863818"},{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}]},{"status":"public","has_accepted_license":"1","publication":"Nature Communications","publisher":"Springer Nature","publication_identifier":{"eissn":["2041-1723"]},"intvolume":" 14","month":"04","author":[{"last_name":"Schmid","first_name":"Laura","full_name":"Schmid, Laura","orcid":"0000-0002-6978-7329","id":"38B437DE-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Ekbatani, Farbod","first_name":"Farbod","last_name":"Ekbatani"},{"orcid":"0000-0001-5116-955X","id":"2FDF8F3C-F248-11E8-B48F-1D18A9856A87","last_name":"Hilbe","full_name":"Hilbe, Christian","first_name":"Christian"},{"first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X"}],"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.). L.S. received additional partial support by the Austrian Science Fund (FWF) under grant Z211-N23 (Wittgenstein Award), and also thanks the support by the Stochastic Analysis and Application Research Center (SAARC) under National Research Foundation of Korea grant NRF-2019R1A5A1028324. The authors additionally thank Stefan Schmid for providing access to his lab infrastructure at the University of Vienna for the purpose of collecting simulation data.","external_id":{"pmid":["37045828"],"isi":["001003644100020"]},"ddc":["000"],"article_number":"2086","volume":14,"date_published":"2023-04-12T00:00:00Z","oa_version":"Published Version","pmid":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","year":"2023","title":"Quantitative assessment can stabilize indirect reciprocity under imperfect information","article_processing_charge":"No","scopus_import":"1","oa":1,"file_date_updated":"2023-04-25T09:13:53Z","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"The field of indirect reciprocity investigates how social norms can foster cooperation when individuals continuously monitor and assess each other’s social interactions. By adhering to certain social norms, cooperating individuals can improve their reputation and, in turn, receive benefits from others. Eight social norms, known as the “leading eight,\" have been shown to effectively promote the evolution of cooperation as long as information is public and reliable. These norms categorize group members as either ’good’ or ’bad’. In this study, we examine a scenario where individuals instead assign nuanced reputation scores to each other, and only cooperate with those whose reputation exceeds a certain threshold. We find both analytically and through simulations that such quantitative assessments are error-correcting, thus facilitating cooperation in situations where information is private and unreliable. Moreover, our results identify four specific norms that are robust to such conditions, and may be relevant for helping to sustain cooperation in natural populations."}],"ec_funded":1,"quality_controlled":"1","citation":{"ieee":"L. Schmid, F. Ekbatani, C. Hilbe, and K. Chatterjee, “Quantitative assessment can stabilize indirect reciprocity under imperfect information,” Nature Communications, vol. 14. Springer Nature, 2023.","mla":"Schmid, Laura, et al. “Quantitative Assessment Can Stabilize Indirect Reciprocity under Imperfect Information.” Nature Communications, vol. 14, 2086, Springer Nature, 2023, doi:10.1038/s41467-023-37817-x.","short":"L. Schmid, F. Ekbatani, C. Hilbe, K. Chatterjee, Nature Communications 14 (2023).","chicago":"Schmid, Laura, Farbod Ekbatani, Christian Hilbe, and Krishnendu Chatterjee. “Quantitative Assessment Can Stabilize Indirect Reciprocity under Imperfect Information.” Nature Communications. Springer Nature, 2023. https://doi.org/10.1038/s41467-023-37817-x.","ista":"Schmid L, Ekbatani F, Hilbe C, Chatterjee K. 2023. Quantitative assessment can stabilize indirect reciprocity under imperfect information. Nature Communications. 14, 2086.","ama":"Schmid L, Ekbatani F, Hilbe C, Chatterjee K. Quantitative assessment can stabilize indirect reciprocity under imperfect information. Nature Communications. 2023;14. doi:10.1038/s41467-023-37817-x","apa":"Schmid, L., Ekbatani, F., Hilbe, C., & Chatterjee, K. (2023). Quantitative assessment can stabilize indirect reciprocity under imperfect information. Nature Communications. Springer Nature. https://doi.org/10.1038/s41467-023-37817-x"},"date_updated":"2025-04-15T06:26:15Z","_id":"12861","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"type":"journal_article","date_created":"2023-04-23T22:01:03Z","publication_status":"published","file":[{"file_name":"2023_NatureComm_Schmid.pdf","date_updated":"2023-04-25T09:13:53Z","success":1,"access_level":"open_access","checksum":"a4b3b7b36fbef068cabf4fb99501fef6","content_type":"application/pdf","file_size":1786475,"date_created":"2023-04-25T09:13:53Z","creator":"dernst","relation":"main_file","file_id":"12868"}],"doi":"10.1038/s41467-023-37817-x","department":[{"_id":"KrCh"}],"article_type":"original","project":[{"name":"Formal Methods for Stochastic Models: Algorithms and Applications","grant_number":"863818","call_identifier":"H2020","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E"},{"call_identifier":"FWF","_id":"25F42A32-B435-11E9-9278-68D0E5697425","name":"Formal methods for the design and analysis of complex systems","grant_number":"Z211"}],"isi":1,"day":"12"},{"_id":"13258","related_material":{"record":[{"status":"public","id":"13336","relation":"research_data"}]},"quality_controlled":"1","date_updated":"2025-04-14T07:43:55Z","citation":{"ama":"Kleshnina M, Hilbe C, Simsa S, Chatterjee K, Nowak MA. The effect of environmental information on evolution of cooperation in stochastic games. Nature Communications. 2023;14. doi:10.1038/s41467-023-39625-9","apa":"Kleshnina, M., Hilbe, C., Simsa, S., Chatterjee, K., & Nowak, M. A. (2023). The effect of environmental information on evolution of cooperation in stochastic games. Nature Communications. Springer Nature. https://doi.org/10.1038/s41467-023-39625-9","ista":"Kleshnina M, Hilbe C, Simsa S, Chatterjee K, Nowak MA. 2023. The effect of environmental information on evolution of cooperation in stochastic games. Nature Communications. 14, 4153.","short":"M. Kleshnina, C. Hilbe, S. Simsa, K. Chatterjee, M.A. Nowak, Nature Communications 14 (2023).","chicago":"Kleshnina, Maria, Christian Hilbe, Stepan Simsa, Krishnendu Chatterjee, and Martin A. Nowak. “The Effect of Environmental Information on Evolution of Cooperation in Stochastic Games.” Nature Communications. Springer Nature, 2023. https://doi.org/10.1038/s41467-023-39625-9.","ieee":"M. Kleshnina, C. Hilbe, S. Simsa, K. Chatterjee, and M. A. Nowak, “The effect of environmental information on evolution of cooperation in stochastic games,” Nature Communications, vol. 14. Springer Nature, 2023.","mla":"Kleshnina, Maria, et al. “The Effect of Environmental Information on Evolution of Cooperation in Stochastic Games.” Nature Communications, vol. 14, 4153, Springer Nature, 2023, doi:10.1038/s41467-023-39625-9."},"ec_funded":1,"file_date_updated":"2023-07-31T11:32:36Z","oa":1,"language":[{"iso":"eng"}],"abstract":[{"text":"Many human interactions feature the characteristics of social dilemmas where individual actions have consequences for the group and the environment. The feedback between behavior and environment can be studied with the framework of stochastic games. In stochastic games, the state of the environment can change, depending on the choices made by group members. Past work suggests that such feedback can reinforce cooperative behaviors. In particular, cooperation can evolve in stochastic games even if it is infeasible in each separate repeated game. In stochastic games, participants have an interest in conditioning their strategies on the state of the environment. Yet in many applications, precise information about the state could be scarce. Here, we study how the availability of information (or lack thereof) shapes evolution of cooperation. Already for simple examples of two state games we find surprising effects. In some cases, cooperation is only possible if there is precise information about the state of the environment. In other cases, cooperation is most abundant when there is no information about the state of the environment. We systematically analyze all stochastic games of a given complexity class, to determine when receiving information about the environment is better, neutral, or worse for evolution of cooperation.","lang":"eng"}],"scopus_import":"1","isi":1,"day":"12","project":[{"name":"Formal Methods for Stochastic Models: Algorithms and Applications","grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","call_identifier":"H2020"},{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"article_type":"original","file":[{"content_type":"application/pdf","file_name":"2023_NatureComm_Kleshnina.pdf","date_updated":"2023-07-31T11:32:36Z","access_level":"open_access","success":1,"checksum":"5aceefdfe76686267b93ae4fe81899f1","file_id":"13337","relation":"main_file","file_size":1601682,"date_created":"2023-07-31T11:32:36Z","creator":"dernst"}],"department":[{"_id":"KrCh"}],"doi":"10.1038/s41467-023-39625-9","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"type":"journal_article","date_created":"2023-07-23T22:01:11Z","publication_status":"published","month":"07","intvolume":" 14","publication_identifier":{"eissn":["2041-1723"]},"publisher":"Springer Nature","publication":"Nature Communications","status":"public","has_accepted_license":"1","corr_author":"1","article_processing_charge":"Yes","title":"The effect of environmental information on evolution of cooperation in stochastic games","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2023","pmid":1,"volume":14,"date_published":"2023-07-12T00:00:00Z","oa_version":"Published Version","external_id":{"isi":["001029450400031"],"pmid":["37438341"]},"article_number":"4153","ddc":["000"],"author":[{"id":"4E21749C-F248-11E8-B48F-1D18A9856A87","first_name":"Maria","full_name":"Kleshnina, Maria","last_name":"Kleshnina"},{"first_name":"Christian","full_name":"Hilbe, Christian","last_name":"Hilbe","id":"2FDF8F3C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5116-955X"},{"id":"409d615c-2f95-11ee-b934-90a352102c1e","orcid":"0000-0001-6687-1210","full_name":"Simsa, Stepan","first_name":"Stepan","last_name":"Simsa"},{"orcid":"0000-0002-4561-241X","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu"},{"full_name":"Nowak, Martin A.","first_name":"Martin A.","last_name":"Nowak"}],"acknowledgement":"This work was supported by the European Research Council CoG 863818 (ForM-SMArt) (to K.C.), 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 Sklodowska-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.)."},{"file":[{"relation":"main_file","file_id":"12460","creator":"dernst","date_created":"2023-01-30T11:28:13Z","file_size":3143222,"content_type":"application/pdf","checksum":"31b6b311b6731f1658277a9dfff6632c","success":1,"access_level":"open_access","date_updated":"2023-01-30T11:28:13Z","file_name":"2022_PlosCompBio_Schmid.pdf"}],"department":[{"_id":"KrCh"}],"doi":"10.1371/journal.pcbi.1010149","type":"journal_article","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"publication_status":"published","date_created":"2023-01-16T10:02:51Z","project":[{"_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","call_identifier":"H2020","grant_number":"863818","name":"Formal Methods for Stochastic Models: Algorithms and Applications"}],"isi":1,"day":"14","article_type":"original","language":[{"iso":"eng"}],"oa":1,"file_date_updated":"2023-01-30T11:28:13Z","abstract":[{"text":"In repeated interactions, players can use strategies that respond to the outcome of previous rounds. Much of the existing literature on direct reciprocity assumes that all competing individuals use the same strategy space. Here, we study both learning and evolutionary dynamics of players that differ in the strategy space they explore. We focus on the infinitely repeated donation game and compare three natural strategy spaces: memory-1 strategies, which consider the last moves of both players, reactive strategies, which respond to the last move of the co-player, and unconditional strategies. These three strategy spaces differ in the memory capacity that is needed. We compute the long term average payoff that is achieved in a pairwise learning process. We find that smaller strategy spaces can dominate larger ones. For weak selection, unconditional players dominate both reactive and memory-1 players. For intermediate selection, reactive players dominate memory-1 players. Only for strong selection and low cost-to-benefit ratio, memory-1 players dominate the others. We observe that the supergame between strategy spaces can be a social dilemma: maximum payoff is achieved if both players explore a larger strategy space, but smaller strategy spaces dominate.","lang":"eng"}],"ec_funded":1,"scopus_import":"1","issue":"6","_id":"12280","quality_controlled":"1","citation":{"ista":"Schmid L, Hilbe C, Chatterjee K, Nowak M. 2022. Direct reciprocity between individuals that use different strategy spaces. PLOS Computational Biology. 18(6), e1010149.","apa":"Schmid, L., Hilbe, C., Chatterjee, K., & Nowak, M. (2022). Direct reciprocity between individuals that use different strategy spaces. PLOS Computational Biology. Public Library of Science. https://doi.org/10.1371/journal.pcbi.1010149","ama":"Schmid L, Hilbe C, Chatterjee K, Nowak M. Direct reciprocity between individuals that use different strategy spaces. PLOS Computational Biology. 2022;18(6). doi:10.1371/journal.pcbi.1010149","mla":"Schmid, Laura, et al. “Direct Reciprocity between Individuals That Use Different Strategy Spaces.” PLOS Computational Biology, vol. 18, no. 6, e1010149, Public Library of Science, 2022, doi:10.1371/journal.pcbi.1010149.","ieee":"L. Schmid, C. Hilbe, K. Chatterjee, and M. Nowak, “Direct reciprocity between individuals that use different strategy spaces,” PLOS Computational Biology, vol. 18, no. 6. Public Library of Science, 2022.","chicago":"Schmid, Laura, Christian Hilbe, Krishnendu Chatterjee, and Martin Nowak. “Direct Reciprocity between Individuals That Use Different Strategy Spaces.” PLOS Computational Biology. Public Library of Science, 2022. https://doi.org/10.1371/journal.pcbi.1010149.","short":"L. Schmid, C. Hilbe, K. Chatterjee, M. Nowak, PLOS Computational Biology 18 (2022)."},"date_updated":"2025-04-14T07:52:47Z","external_id":{"pmid":["35700167"],"isi":["000843626800031"]},"ddc":["000","570"],"article_number":"e1010149","author":[{"orcid":"0000-0002-6978-7329","id":"38B437DE-F248-11E8-B48F-1D18A9856A87","last_name":"Schmid","full_name":"Schmid, Laura","first_name":"Laura"},{"full_name":"Hilbe, Christian","first_name":"Christian","last_name":"Hilbe","id":"2FDF8F3C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5116-955X"},{"last_name":"Chatterjee","first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Nowak","first_name":"Martin","full_name":"Nowak, Martin"}],"acknowledgement":"This work was supported by the European Research Council (https://erc.europa.eu/)\r\nCoG 863818 (ForM-SMArt) (to K.C.), and the European Research Council Starting Grant 850529: E-DIRECT (to C.H.). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.","title":"Direct reciprocity between individuals that use different strategy spaces","article_processing_charge":"No","volume":18,"date_published":"2022-06-14T00:00:00Z","pmid":1,"oa_version":"Published Version","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","year":"2022","publication":"PLOS Computational Biology","publisher":"Public Library of Science","corr_author":"1","status":"public","has_accepted_license":"1","intvolume":" 18","keyword":["Computational Theory and Mathematics","Cellular and Molecular Neuroscience","Genetics","Molecular Biology","Ecology","Modeling and Simulation","Ecology","Evolution","Behavior and Systematics"],"month":"06","publication_identifier":{"eissn":["1553-7358"]}},{"file":[{"file_id":"17400","relation":"main_file","creator":"dernst","file_size":2410962,"date_created":"2024-08-06T07:33:30Z","content_type":"application/pdf","access_level":"open_access","success":1,"checksum":"79a8e3e4be7e8a2b407b4efddd65f3f3","file_name":"2022_PNASNexus_McAvoy.pdf","date_updated":"2024-08-06T07:33:30Z"}],"doi":"10.1093/pnasnexus/pgac141","department":[{"_id":"KrCh"}],"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"type":"journal_article","publication_status":"published","date_created":"2024-05-28T14:23:12Z","project":[{"_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","call_identifier":"H2020","grant_number":"863818","name":"Formal Methods for Stochastic Models: Algorithms and Applications"}],"day":"01","article_type":"original","file_date_updated":"2024-08-06T07:33:30Z","language":[{"iso":"eng"}],"oa":1,"abstract":[{"lang":"eng","text":"Across many domains of interaction, both natural and artificial, individuals use past experience to shape future behaviors. The results of such learning processes depend on what individuals wish to maximize. A natural objective is one’s own success. However, when two such “selfish” learners interact with each other, the outcome can be detrimental to both, especially when there are conflicts of interest. Here, we explore how a learner can align incentives with a selfish opponent. Moreover, we consider the dynamics that arise when learning rules themselves are subject to evolutionary pressure. By combining extensive simulations and analytical techniques, we demonstrate that selfish learning is unstable in most classical two-player repeated games. If evolution operates on the level of long-run payoffs, selection instead favors learning rules that incorporate social (other-regarding) preferences. To further corroborate these results, we analyze data from a repeated prisoner’s dilemma experiment. We find that selfish learning is insufficient to explain human behavior when there is a trade-off between payoff maximization and fairness."}],"ec_funded":1,"scopus_import":"1","_id":"17061","issue":"4","citation":{"ama":"McAvoy A, Kates-Harbeck J, Chatterjee K, Hilbe C. Evolutionary instability of selfish learning in repeated games. PNAS Nexus. 2022;1(4). doi:10.1093/pnasnexus/pgac141","apa":"McAvoy, A., Kates-Harbeck, J., Chatterjee, K., & Hilbe, C. (2022). Evolutionary instability of selfish learning in repeated games. PNAS Nexus. Oxford University Press. https://doi.org/10.1093/pnasnexus/pgac141","ista":"McAvoy A, Kates-Harbeck J, Chatterjee K, Hilbe C. 2022. Evolutionary instability of selfish learning in repeated games. PNAS Nexus. 1(4), pgac141.","short":"A. McAvoy, J. Kates-Harbeck, K. Chatterjee, C. Hilbe, PNAS Nexus 1 (2022).","chicago":"McAvoy, Alex, Julian Kates-Harbeck, Krishnendu Chatterjee, and Christian Hilbe. “Evolutionary Instability of Selfish Learning in Repeated Games.” PNAS Nexus. Oxford University Press, 2022. https://doi.org/10.1093/pnasnexus/pgac141.","ieee":"A. McAvoy, J. Kates-Harbeck, K. Chatterjee, and C. Hilbe, “Evolutionary instability of selfish learning in repeated games,” PNAS Nexus, vol. 1, no. 4. Oxford University Press, 2022.","mla":"McAvoy, Alex, et al. “Evolutionary Instability of Selfish Learning in Repeated Games.” PNAS Nexus, vol. 1, no. 4, pgac141, Oxford University Press, 2022, doi:10.1093/pnasnexus/pgac141."},"quality_controlled":"1","date_updated":"2025-06-11T13:54:20Z","related_material":{"link":[{"url":"https://github.com/alexmcavoy/fmtl/","relation":"software"}]},"external_id":{"arxiv":["2105.06199"],"pmid":["36714856"]},"ddc":["000"],"article_number":"pgac141","author":[{"first_name":"Alex","full_name":"McAvoy, Alex","last_name":"McAvoy"},{"first_name":"Julian","full_name":"Kates-Harbeck, Julian","last_name":"Kates-Harbeck"},{"last_name":"Chatterjee","first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Hilbe, Christian","first_name":"Christian","last_name":"Hilbe","id":"2FDF8F3C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5116-955X"}],"acknowledgement":"The authors are grateful to Jörg Oechssler for many helpful comments. A.M. was supported by a Simons Postdoctoral Fellowship (Math+X) at the University of Pennsylvania; K.C. was supported by the European Research Council Consolidator Grant 863818 (ForM-SMArt); and C.H. was supported by the European Research Council Starting Grant 850529 (E-DIRECT).","title":"Evolutionary instability of selfish learning in repeated games","article_processing_charge":"Yes","pmid":1,"oa_version":"Published Version","volume":1,"date_published":"2022-09-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2022","publication":"PNAS Nexus","publisher":"Oxford University Press","arxiv":1,"status":"public","has_accepted_license":"1","intvolume":" 1","month":"09","publication_identifier":{"issn":["2752-6542"]}},{"scopus_import":"1","file_date_updated":"2023-11-07T08:27:23Z","language":[{"iso":"eng"}],"oa":1,"abstract":[{"lang":"eng","text":"Direct and indirect reciprocity are key mechanisms for the evolution of cooperation. Direct reciprocity means that individuals use their own experience to decide whether to cooperate with another person. Indirect reciprocity means that they also consider the experiences of others. Although these two mechanisms are intertwined, they are typically studied in isolation. Here, we introduce a mathematical framework that allows us to explore both kinds of reciprocity simultaneously. We show that the well-known ‘generous tit-for-tat’ strategy of direct reciprocity has a natural analogue in indirect reciprocity, which we call ‘generous scoring’. Using an equilibrium analysis, we characterize under which conditions either of the two strategies can maintain cooperation. With simulations, we additionally explore which kind of reciprocity evolves when members of a population engage in social learning to adapt to their environment. Our results draw unexpected connections between direct and indirect reciprocity while highlighting important differences regarding their evolvability."}],"ec_funded":1,"date_updated":"2026-07-08T22:30:53Z","citation":{"ieee":"L. Schmid, K. Chatterjee, C. Hilbe, and M. A. Nowak, “A unified framework of direct and indirect reciprocity,” Nature Human Behaviour, vol. 5, no. 10. Springer Nature, pp. 1292–1302, 2021.","mla":"Schmid, Laura, et al. “A Unified Framework of Direct and Indirect Reciprocity.” Nature Human Behaviour, vol. 5, no. 10, Springer Nature, 2021, pp. 1292–1302, doi:10.1038/s41562-021-01114-8.","short":"L. Schmid, K. Chatterjee, C. Hilbe, M.A. Nowak, Nature Human Behaviour 5 (2021) 1292–1302.","chicago":"Schmid, Laura, Krishnendu Chatterjee, Christian Hilbe, and Martin A. Nowak. “A Unified Framework of Direct and Indirect Reciprocity.” Nature Human Behaviour. Springer Nature, 2021. https://doi.org/10.1038/s41562-021-01114-8.","ista":"Schmid L, Chatterjee K, Hilbe C, Nowak MA. 2021. A unified framework of direct and indirect reciprocity. Nature Human Behaviour. 5(10), 1292–1302.","ama":"Schmid L, Chatterjee K, Hilbe C, Nowak MA. A unified framework of direct and indirect reciprocity. Nature Human Behaviour. 2021;5(10):1292–1302. doi:10.1038/s41562-021-01114-8","apa":"Schmid, L., Chatterjee, K., Hilbe, C., & Nowak, M. A. (2021). A unified framework of direct and indirect reciprocity. Nature Human Behaviour. Springer Nature. https://doi.org/10.1038/s41562-021-01114-8"},"quality_controlled":"1","related_material":{"link":[{"description":"News on IST Homepage","relation":"press_release","url":"https://ist.ac.at/en/news/the-emergence-of-cooperation/"}],"record":[{"id":"10293","relation":"dissertation_contains","status":"public"}]},"_id":"9402","issue":"10","type":"journal_article","publication_status":"published","date_created":"2021-05-18T16:56:57Z","file":[{"content_type":"application/pdf","file_name":"2021_NatureHumanBehaviour_Schmid_accepted.pdf","date_updated":"2023-11-07T08:27:23Z","access_level":"open_access","success":1,"checksum":"34f55e173f90dc1dab731063458ac780","file_id":"14496","relation":"main_file","file_size":5232761,"date_created":"2023-11-07T08:27:23Z","creator":"dernst"}],"department":[{"_id":"KrCh"},{"_id":"GradSch"}],"doi":"10.1038/s41562-021-01114-8","article_type":"original","project":[{"call_identifier":"H2020","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","grant_number":"863818","name":"Formal Methods for Stochastic Models: Algorithms and Applications"},{"grant_number":"279307","name":"Quantitative Graph Games: Theory and Applications","_id":"2581B60A-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"day":"13","isi":1,"corr_author":"1","status":"public","has_accepted_license":"1","publication":"Nature Human Behaviour","publisher":"Springer Nature","publication_identifier":{"eissn":["2397-3374"]},"intvolume":" 5","month":"05","author":[{"orcid":"0000-0002-6978-7329","id":"38B437DE-F248-11E8-B48F-1D18A9856A87","last_name":"Schmid","full_name":"Schmid, Laura","first_name":"Laura"},{"last_name":"Chatterjee","first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Hilbe","first_name":"Christian","full_name":"Hilbe, Christian","orcid":"0000-0001-5116-955X","id":"2FDF8F3C-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Nowak, Martin A.","first_name":"Martin A.","last_name":"Nowak"}],"acknowledgement":"This work was supported by the European Research Council CoG 863818 (ForM-SMArt) (to K.C.), the European Research Council Start Grant 279307: Graph Games (to K.C.), and the European Research Council Starting Grant 850529: E-DIRECT (to C.H.). The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.","external_id":{"pmid":["33986519"],"isi":["000650304000002"]},"ddc":["000"],"oa_version":"Submitted Version","volume":5,"pmid":1,"date_published":"2021-05-13T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2021","page":"1292–1302","title":"A unified framework of direct and indirect reciprocity","article_processing_charge":"No"},{"date_created":"2023-05-23T16:11:22Z","author":[{"id":"2CDC32B8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8214-4758","first_name":"Barbara","full_name":"Milutinovic, Barbara","last_name":"Milutinovic"},{"id":"42462816-F248-11E8-B48F-1D18A9856A87","last_name":"Stock","first_name":"Miriam","full_name":"Stock, Miriam"},{"first_name":"Anna V","full_name":"Grasse, Anna V","last_name":"Grasse","id":"406F989C-F248-11E8-B48F-1D18A9856A87"},{"id":"31757262-F248-11E8-B48F-1D18A9856A87","first_name":"Elisabeth","full_name":"Naderlinger, Elisabeth","last_name":"Naderlinger"},{"first_name":"Christian","full_name":"Hilbe, Christian","last_name":"Hilbe","id":"2FDF8F3C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5116-955X"},{"last_name":"Cremer","full_name":"Cremer, Sylvia","first_name":"Sylvia","orcid":"0000-0002-2193-3868","id":"2F64EC8C-F248-11E8-B48F-1D18A9856A87"}],"tmp":{"short":"CC0 (1.0)","name":"Creative Commons Public Domain Dedication (CC0 1.0)","image":"/images/cc_0.png","legal_code_url":"https://creativecommons.org/publicdomain/zero/1.0/legalcode"},"type":"research_data_reference","department":[{"_id":"SyCr"},{"_id":"KrCh"}],"ddc":["570"],"doi":"10.5061/DRYAD.CRJDFN318","year":"2020","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","date_published":"2020-12-19T00:00:00Z","day":"19","article_processing_charge":"No","title":"Social immunity modulates competition between coinfecting pathogens","status":"public","corr_author":"1","license":"https://creativecommons.org/publicdomain/zero/1.0/","publisher":"Dryad","abstract":[{"lang":"eng","text":"Coinfections with multiple pathogens can result in complex within-host dynamics affecting virulence and transmission. Whilst multiple infections are intensively studied in solitary hosts, it is so far unresolved how social host interactions interfere with pathogen competition, and if this depends on coinfection diversity. We studied how the collective disease defenses of ants – their social immunity – influence pathogen competition in coinfections of same or different fungal pathogen species. Social immunity reduced virulence for all pathogen combinations, but interfered with spore production only in different-species coinfections. Here, it decreased overall pathogen sporulation success, whilst simultaneously increasing co-sporulation on individual cadavers and maintaining a higher pathogen diversity at the community-level. Mathematical modeling revealed that host sanitary care alone can modulate competitive outcomes between pathogens, giving advantage to fast-germinating, thus less grooming-sensitive ones. Host social interactions can hence modulate infection dynamics in coinfected group members, thereby altering pathogen communities at the host- and population-level."}],"oa":1,"related_material":{"record":[{"id":"7343","relation":"used_in_publication","status":"public"}]},"main_file_link":[{"url":"https://doi.org/10.5061/dryad.crjdfn318","open_access":"1"}],"citation":{"apa":"Milutinovic, B., Stock, M., Grasse, A. V., Naderlinger, E., Hilbe, C., & Cremer, S. (2020). Social immunity modulates competition between coinfecting pathogens. Dryad. https://doi.org/10.5061/DRYAD.CRJDFN318","ama":"Milutinovic B, Stock M, Grasse AV, Naderlinger E, Hilbe C, Cremer S. Social immunity modulates competition between coinfecting pathogens. 2020. doi:10.5061/DRYAD.CRJDFN318","ista":"Milutinovic B, Stock M, Grasse AV, Naderlinger E, Hilbe C, Cremer S. 2020. Social immunity modulates competition between coinfecting pathogens, Dryad, 10.5061/DRYAD.CRJDFN318.","chicago":"Milutinovic, Barbara, Miriam Stock, Anna V Grasse, Elisabeth Naderlinger, Christian Hilbe, and Sylvia Cremer. “Social Immunity Modulates Competition between Coinfecting Pathogens.” Dryad, 2020. https://doi.org/10.5061/DRYAD.CRJDFN318.","short":"B. Milutinovic, M. Stock, A.V. Grasse, E. Naderlinger, C. Hilbe, S. Cremer, (2020).","mla":"Milutinovic, Barbara, et al. Social Immunity Modulates Competition between Coinfecting Pathogens. Dryad, 2020, doi:10.5061/DRYAD.CRJDFN318.","ieee":"B. Milutinovic, M. Stock, A. V. Grasse, E. Naderlinger, C. Hilbe, and S. Cremer, “Social immunity modulates competition between coinfecting pathogens.” Dryad, 2020."},"date_updated":"2025-06-12T07:32:35Z","month":"12","_id":"13060"},{"scopus_import":"1","oa":1,"file_date_updated":"2020-11-19T11:27:10Z","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"Coinfections with multiple pathogens can result in complex within‐host dynamics affecting virulence and transmission. While multiple infections are intensively studied in solitary hosts, it is so far unresolved how social host interactions interfere with pathogen competition, and if this depends on coinfection diversity. We studied how the collective disease defences of ants – their social immunity – influence pathogen competition in coinfections of same or different fungal pathogen species. Social immunity reduced virulence for all pathogen combinations, but interfered with spore production only in different‐species coinfections. Here, it decreased overall pathogen sporulation success while increasing co‐sporulation on individual cadavers and maintaining a higher pathogen diversity at the community level. Mathematical modelling revealed that host sanitary care alone can modulate competitive outcomes between pathogens, giving advantage to fast‐germinating, thus less grooming‐sensitive ones. Host social interactions can hence modulate infection dynamics in coinfected group members, thereby altering pathogen communities at the host level and population level."}],"ec_funded":1,"acknowledged_ssus":[{"_id":"LifeSc"}],"citation":{"ista":"Milutinovic B, Stock M, Grasse AV, Naderlinger E, Hilbe C, Cremer S. 2020. Social immunity modulates competition between coinfecting pathogens. Ecology Letters. 23(3), 565–574.","ama":"Milutinovic B, Stock M, Grasse AV, Naderlinger E, Hilbe C, Cremer S. Social immunity modulates competition between coinfecting pathogens. Ecology Letters. 2020;23(3):565-574. doi:10.1111/ele.13458","apa":"Milutinovic, B., Stock, M., Grasse, A. V., Naderlinger, E., Hilbe, C., & Cremer, S. (2020). Social immunity modulates competition between coinfecting pathogens. Ecology Letters. Wiley. https://doi.org/10.1111/ele.13458","ieee":"B. Milutinovic, M. Stock, A. V. Grasse, E. Naderlinger, C. Hilbe, and S. Cremer, “Social immunity modulates competition between coinfecting pathogens,” Ecology Letters, vol. 23, no. 3. Wiley, pp. 565–574, 2020.","mla":"Milutinovic, Barbara, et al. “Social Immunity Modulates Competition between Coinfecting Pathogens.” Ecology Letters, vol. 23, no. 3, Wiley, 2020, pp. 565–74, doi:10.1111/ele.13458.","short":"B. Milutinovic, M. Stock, A.V. Grasse, E. Naderlinger, C. Hilbe, S. Cremer, Ecology Letters 23 (2020) 565–574.","chicago":"Milutinovic, Barbara, Miriam Stock, Anna V Grasse, Elisabeth Naderlinger, Christian Hilbe, and Sylvia Cremer. “Social Immunity Modulates Competition between Coinfecting Pathogens.” Ecology Letters. Wiley, 2020. https://doi.org/10.1111/ele.13458."},"date_updated":"2025-06-12T07:32:35Z","quality_controlled":"1","related_material":{"record":[{"id":"13060","relation":"research_data","status":"public"}],"link":[{"description":"News on IST Homepage","relation":"press_release","url":"https://ist.ac.at/en/news/social-ants-shapes-disease-outcome/"}]},"issue":"3","_id":"7343","tmp":{"image":"/images/cc_by_nc.png","legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode","name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","short":"CC BY-NC (4.0)"},"type":"journal_article","date_created":"2020-01-20T13:32:12Z","publication_status":"published","file":[{"checksum":"0cd8be386fa219db02845b7c3991ce04","access_level":"open_access","success":1,"date_updated":"2020-11-19T11:27:10Z","file_name":"2020_EcologyLetters_Milutinovic.pdf","content_type":"application/pdf","creator":"dernst","date_created":"2020-11-19T11:27:10Z","file_size":561749,"file_id":"8776","relation":"main_file"}],"doi":"10.1111/ele.13458","department":[{"_id":"SyCr"},{"_id":"KrCh"}],"article_type":"letter_note","project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"},{"name":"Host-Parasite Coevolution","grant_number":"CR-118/3-1","_id":"25DAF0B2-B435-11E9-9278-68D0E5697425"}],"isi":1,"day":"01","corr_author":"1","status":"public","has_accepted_license":"1","publication":"Ecology Letters","publisher":"Wiley","publication_identifier":{"eissn":["1461-0248"],"issn":["1461-023X"]},"intvolume":" 23","month":"03","author":[{"id":"2CDC32B8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8214-4758","full_name":"Milutinovic, Barbara","first_name":"Barbara","last_name":"Milutinovic"},{"id":"42462816-F248-11E8-B48F-1D18A9856A87","last_name":"Stock","full_name":"Stock, Miriam","first_name":"Miriam"},{"id":"406F989C-F248-11E8-B48F-1D18A9856A87","last_name":"Grasse","full_name":"Grasse, Anna V","first_name":"Anna V"},{"id":"31757262-F248-11E8-B48F-1D18A9856A87","last_name":"Naderlinger","full_name":"Naderlinger, Elisabeth","first_name":"Elisabeth"},{"orcid":"0000-0001-5116-955X","id":"2FDF8F3C-F248-11E8-B48F-1D18A9856A87","last_name":"Hilbe","first_name":"Christian","full_name":"Hilbe, Christian"},{"id":"2F64EC8C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2193-3868","full_name":"Cremer, Sylvia","first_name":"Sylvia","last_name":"Cremer"}],"acknowledgement":"We thank Bernhardt Steinwender and Jorgen Eilenberg for the fungal strains, Xavier Espadaler, Mireia Diaz, Christiane Wanke, Lumi Viljakainen and the Social Immunity Team at IST Austria, for help with ant collection, and Wanda Gorecka and Gertraud Stift of the IST Austria Life Science Facility for technical support. We are thankful to Dieter Ebert for input at all stages of the project, Roger Mundry for statistical advice, Hinrich Schulenburg, Paul Schmid-Hempel, Yuko\r\nUlrich and Joachim Kurtz for project discussion, Bor Kavcic for advice on growth curves, Marcus Roper for advice on modelling work and comments on the manuscript, as well as Marjon de Vos, Weini Huang and the Social Immunity Team for comments on the manuscript.\r\nThis study was funded by the German Research Foundation (DFG) within the Priority Programme 1399 Host-parasite Coevolution (CR 118/3 to S.C.) and the People Programme\r\n(Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement no 291734 (ISTFELLOW to B.M.). ","external_id":{"pmid":["31950595"],"isi":["000507515900001"]},"ddc":["570"],"pmid":1,"volume":23,"date_published":"2020-03-01T00:00:00Z","oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"565-574","year":"2020","title":"Social immunity modulates competition between coinfecting pathogens","article_processing_charge":"Yes (via OA deal)"},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2019","page":"524-527","date_published":"2019-08-22T00:00:00Z","oa_version":"Submitted Version","volume":572,"article_processing_charge":"No","title":"Social dilemmas among unequals","author":[{"first_name":"Oliver P.","full_name":"Hauser, Oliver P.","last_name":"Hauser"},{"orcid":"0000-0001-5116-955X","id":"2FDF8F3C-F248-11E8-B48F-1D18A9856A87","last_name":"Hilbe","first_name":"Christian","full_name":"Hilbe, Christian"},{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu","last_name":"Chatterjee"},{"first_name":"Martin A.","full_name":"Nowak, Martin A.","last_name":"Nowak"}],"external_id":{"isi":["000482219600045"]},"ddc":["000"],"publication_identifier":{"eissn":["1476-4687"],"issn":["0028-0836"]},"month":"08","intvolume":" 572","status":"public","has_accepted_license":"1","publisher":"Springer Nature","publication":"Nature","article_type":"letter_note","day":"22","isi":1,"project":[{"grant_number":"279307","name":"Quantitative Graph Games: Theory and Applications","_id":"2581B60A-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"_id":"25832EC2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Rigorous Systems Engineering","grant_number":"S 11407_N23"},{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"type":"journal_article","date_created":"2019-09-01T22:00:56Z","publication_status":"published","file":[{"file_id":"7828","relation":"main_file","date_created":"2020-05-14T10:00:32Z","file_size":18577756,"creator":"dernst","content_type":"application/pdf","date_updated":"2020-07-14T12:47:42Z","file_name":"2019_Nature_Hauser.pdf","checksum":"a6e0e3168bf62de624e7772cdfaeb26f","access_level":"open_access"}],"doi":"10.1038/s41586-019-1488-5","department":[{"_id":"KrCh"}],"related_material":{"link":[{"description":"News on IST Homepage","relation":"press_release","url":"https://ist.ac.at/en/news/too-much-inequality-impedes-support-for-public-goods-according-to-research-published-in-nature/"}]},"quality_controlled":"1","date_updated":"2025-07-10T11:53:55Z","citation":{"ama":"Hauser OP, Hilbe C, Chatterjee K, Nowak MA. Social dilemmas among unequals. Nature. 2019;572(7770):524-527. doi:10.1038/s41586-019-1488-5","apa":"Hauser, O. P., Hilbe, C., Chatterjee, K., & Nowak, M. A. (2019). Social dilemmas among unequals. Nature. Springer Nature. https://doi.org/10.1038/s41586-019-1488-5","ista":"Hauser OP, Hilbe C, Chatterjee K, Nowak MA. 2019. Social dilemmas among unequals. Nature. 572(7770), 524–527.","short":"O.P. Hauser, C. Hilbe, K. Chatterjee, M.A. Nowak, Nature 572 (2019) 524–527.","chicago":"Hauser, Oliver P., Christian Hilbe, Krishnendu Chatterjee, and Martin A. Nowak. “Social Dilemmas among Unequals.” Nature. Springer Nature, 2019. https://doi.org/10.1038/s41586-019-1488-5.","ieee":"O. P. Hauser, C. Hilbe, K. Chatterjee, and M. A. Nowak, “Social dilemmas among unequals,” Nature, vol. 572, no. 7770. Springer Nature, pp. 524–527, 2019.","mla":"Hauser, Oliver P., et al. “Social Dilemmas among Unequals.” Nature, vol. 572, no. 7770, Springer Nature, 2019, pp. 524–27, doi:10.1038/s41586-019-1488-5."},"issue":"7770","_id":"6836","scopus_import":"1","ec_funded":1,"oa":1,"language":[{"iso":"eng"}],"file_date_updated":"2020-07-14T12:47:42Z","abstract":[{"text":"Direct reciprocity is a powerful mechanism for the evolution of cooperation on the basis of repeated interactions1,2,3,4. It requires that interacting individuals are sufficiently equal, such that everyone faces similar consequences when they cooperate or defect. Yet inequality is ubiquitous among humans5,6 and is generally considered to undermine cooperation and welfare7,8,9,10. Most previous models of reciprocity do not include inequality11,12,13,14,15. These models assume that individuals are the same in all relevant aspects. Here we introduce a general framework to study direct reciprocity among unequal individuals. Our model allows for multiple sources of inequality. Subjects can differ in their endowments, their productivities and in how much they benefit from public goods. We find that extreme inequality prevents cooperation. But if subjects differ in productivity, some endowment inequality can be necessary for cooperation to prevail. Our mathematical predictions are supported by a behavioural experiment in which we vary the endowments and productivities of the subjects. We observe that overall welfare is maximized when the two sources of heterogeneity are aligned, such that more productive individuals receive higher endowments. By contrast, when endowments and productivities are misaligned, cooperation quickly breaks down. Our findings have implications for policy-makers concerned with equity, efficiency and the provisioning of public goods.","lang":"eng"}]},{"quality_controlled":"1","citation":{"ista":"Hoffman M, Hilbe C, Nowak M. 2018. The signal-burying game can explain why we obscure positive traits and good deeds. Nature Human Behaviour. 2, 397–404.","ama":"Hoffman M, Hilbe C, Nowak M. The signal-burying game can explain why we obscure positive traits and good deeds. Nature Human Behaviour. 2018;2:397-404. doi:10.1038/s41562-018-0354-z","apa":"Hoffman, M., Hilbe, C., & Nowak, M. (2018). The signal-burying game can explain why we obscure positive traits and good deeds. Nature Human Behaviour. Nature Publishing Group. https://doi.org/10.1038/s41562-018-0354-z","ieee":"M. Hoffman, C. Hilbe, and M. Nowak, “The signal-burying game can explain why we obscure positive traits and good deeds,” Nature Human Behaviour, vol. 2. Nature Publishing Group, pp. 397–404, 2018.","mla":"Hoffman, Moshe, et al. “The Signal-Burying Game Can Explain Why We Obscure Positive Traits and Good Deeds.” Nature Human Behaviour, vol. 2, Nature Publishing Group, 2018, pp. 397–404, doi:10.1038/s41562-018-0354-z.","short":"M. Hoffman, C. Hilbe, M. Nowak, Nature Human Behaviour 2 (2018) 397–404.","chicago":"Hoffman, Moshe, Christian Hilbe, and Martin Nowak. “The Signal-Burying Game Can Explain Why We Obscure Positive Traits and Good Deeds.” Nature Human Behaviour. Nature Publishing Group, 2018. https://doi.org/10.1038/s41562-018-0354-z."},"date_updated":"2025-04-15T06:50:21Z","publist_id":"7588","related_material":{"link":[{"url":"https://ist.ac.at/en/news/the-logic-of-modesty-why-it-pays-to-be-humble/","description":"News on IST Homepage","relation":"press_release"}]},"_id":"293","scopus_import":"1","language":[{"iso":"eng"}],"file_date_updated":"2020-07-14T12:45:54Z","oa":1,"abstract":[{"text":"People sometimes make their admirable deeds and accomplishments hard to spot, such as by giving anonymously or avoiding bragging. Such ‘buried’ signals are hard to reconcile with standard models of signalling or indirect reciprocity, which motivate costly pro-social behaviour by reputational gains. To explain these phenomena, we design a simple game theory model, which we call the signal-burying game. This game has the feature that senders can bury their signal by deliberately reducing the probability of the signal being observed. If the signal is observed, however, it is identified as having been buried. We show under which conditions buried signals can be maintained, using static equilibrium concepts and calculations of the evolutionary dynamics. We apply our analysis to shed light on a number of otherwise puzzling social phenomena, including modesty, anonymous donations, subtlety in art and fashion, and overeagerness.","lang":"eng"}],"ec_funded":1,"article_type":"original","project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"day":"28","isi":1,"type":"journal_article","publication_status":"published","date_created":"2018-12-11T11:45:39Z","file":[{"file_id":"7051","relation":"main_file","date_created":"2019-11-19T08:17:23Z","file_size":194734,"creator":"dernst","content_type":"application/pdf","date_updated":"2020-07-14T12:45:54Z","file_name":"2018_NatureHumanBeh_Hoffman.pdf","checksum":"32efaf06a597495c184df91b3fbb19c0","access_level":"open_access"}],"doi":"10.1038/s41562-018-0354-z","department":[{"_id":"KrCh"}],"intvolume":" 2","month":"05","corr_author":"1","status":"public","has_accepted_license":"1","publication":"Nature Human Behaviour","publisher":"Nature Publishing Group","date_published":"2018-05-28T00:00:00Z","oa_version":"Submitted Version","volume":2,"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","year":"2018","page":"397 - 404","title":"The signal-burying game can explain why we obscure positive traits and good deeds","article_processing_charge":"No","author":[{"last_name":"Hoffman","full_name":"Hoffman, Moshe","first_name":"Moshe"},{"first_name":"Christian","full_name":"Hilbe, Christian","last_name":"Hilbe","id":"2FDF8F3C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5116-955X"},{"first_name":"Martin","full_name":"Nowak, Martin","last_name":"Nowak"}],"acknowledgement":"This work was supported by a grant from the John Templeton Foundation and by the Office of Naval Research Grant N00014-16-1-2914 (M.A.N.). C.H. acknowledges generous support from the ISTFELLOW programme and by the Schrödinger scholarship of the Austrian Science Fund (FWF) J3475.","external_id":{"isi":["000435551300009"]},"ddc":["000"]},{"scopus_import":"1","ec_funded":1,"file_date_updated":"2020-07-14T12:45:02Z","language":[{"iso":"eng"}],"oa":1,"abstract":[{"text":"Social dilemmas occur when incentives for individuals are misaligned with group interests 1-7 . According to the 'tragedy of the commons', these misalignments can lead to overexploitation and collapse of public resources. The resulting behaviours can be analysed with the tools of game theory 8 . The theory of direct reciprocity 9-15 suggests that repeated interactions can alleviate such dilemmas, but previous work has assumed that the public resource remains constant over time. Here we introduce the idea that the public resource is instead changeable and depends on the strategic choices of individuals. An intuitive scenario is that cooperation increases the public resource, whereas defection decreases it. Thus, cooperation allows the possibility of playing a more valuable game with higher payoffs, whereas defection leads to a less valuable game. We analyse this idea using the theory of stochastic games 16-19 and evolutionary game theory. We find that the dependence of the public resource on previous interactions can greatly enhance the propensity for cooperation. For these results, the interaction between reciprocity and payoff feedback is crucial: neither repeated interactions in a constant environment nor single interactions in a changing environment yield similar cooperation rates. Our framework shows which feedbacks between exploitation and environment - either naturally occurring or designed - help to overcome social dilemmas.","lang":"eng"}],"publist_id":"7764","related_material":{"link":[{"description":"News on IST Homepage","relation":"press_release","url":"https://ist.ac.at/en/news/engineering-cooperation/"}]},"date_updated":"2025-04-15T06:30:08Z","quality_controlled":"1","citation":{"chicago":"Hilbe, Christian, Štepán Šimsa, Krishnendu Chatterjee, and Martin Nowak. “Evolution of Cooperation in Stochastic Games.” Nature. Nature Publishing Group, 2018. https://doi.org/10.1038/s41586-018-0277-x.","short":"C. Hilbe, Š. Šimsa, K. Chatterjee, M. Nowak, Nature 559 (2018) 246–249.","mla":"Hilbe, Christian, et al. “Evolution of Cooperation in Stochastic Games.” Nature, vol. 559, no. 7713, Nature Publishing Group, 2018, pp. 246–49, doi:10.1038/s41586-018-0277-x.","ieee":"C. Hilbe, Š. Šimsa, K. Chatterjee, and M. Nowak, “Evolution of cooperation in stochastic games,” Nature, vol. 559, no. 7713. Nature Publishing Group, pp. 246–249, 2018.","apa":"Hilbe, C., Šimsa, Š., Chatterjee, K., & Nowak, M. (2018). Evolution of cooperation in stochastic games. Nature. Nature Publishing Group. https://doi.org/10.1038/s41586-018-0277-x","ama":"Hilbe C, Šimsa Š, Chatterjee K, Nowak M. Evolution of cooperation in stochastic games. Nature. 2018;559(7713):246-249. doi:10.1038/s41586-018-0277-x","ista":"Hilbe C, Šimsa Š, Chatterjee K, Nowak M. 2018. Evolution of cooperation in stochastic games. Nature. 559(7713), 246–249."},"_id":"157","issue":"7713","type":"journal_article","publication_status":"published","date_created":"2018-12-11T11:44:56Z","file":[{"file_size":2834442,"date_created":"2019-11-19T08:09:57Z","creator":"dernst","relation":"main_file","file_id":"7049","file_name":"2018_Nature_Hilbe.pdf","date_updated":"2020-07-14T12:45:02Z","access_level":"open_access","checksum":"011ab905cf9a410bc2b96f15174d654d","content_type":"application/pdf"}],"department":[{"_id":"KrCh"}],"doi":"10.1038/s41586-018-0277-x","day":"04","isi":1,"project":[{"grant_number":"S11407","name":"Game Theory","call_identifier":"FWF","_id":"25863FF4-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FP7","_id":"2581B60A-B435-11E9-9278-68D0E5697425","grant_number":"279307","name":"Quantitative Graph Games: Theory and Applications"},{"grant_number":"P 23499-N23","name":"Modern Graph Algorithmic Techniques in Formal Verification","call_identifier":"FWF","_id":"2584A770-B435-11E9-9278-68D0E5697425"},{"grant_number":"S 11407_N23","name":"Rigorous Systems Engineering","_id":"25832EC2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"status":"public","has_accepted_license":"1","publisher":"Nature Publishing Group","publication":"Nature","month":"07","intvolume":" 559","author":[{"orcid":"0000-0001-5116-955X","id":"2FDF8F3C-F248-11E8-B48F-1D18A9856A87","last_name":"Hilbe","first_name":"Christian","full_name":"Hilbe, Christian"},{"last_name":"Šimsa","first_name":"Štepán","full_name":"Šimsa, Štepán"},{"full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X"},{"last_name":"Nowak","first_name":"Martin","full_name":"Nowak, Martin"}],"acknowledgement":"European Research Council Start Grant 279307, Austrian Science Fund (FWF) grant P23499-N23, \r\nC.H. acknowledges support from the ISTFELLOW programme.","external_id":{"isi":["000438240900054"]},"ddc":["000"],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","year":"2018","page":"246 - 249","oa_version":"Submitted Version","date_published":"2018-07-04T00:00:00Z","volume":559,"article_processing_charge":"No","title":"Evolution of cooperation in stochastic games"},{"abstract":[{"text":"Direct reciprocity is a mechanism for cooperation among humans. Many of our daily interactions are repeated. We interact repeatedly with our family, friends, colleagues, members of the local and even global community. In the theory of repeated games, it is a tacit assumption that the various games that a person plays simultaneously have no effect on each other. Here we introduce a general framework that allows us to analyze “crosstalk” between a player’s concurrent games. In the presence of crosstalk, the action a person experiences in one game can alter the person’s decision in another. We find that crosstalk impedes the maintenance of cooperation and requires stronger levels of forgiveness. The magnitude of the effect depends on the population structure. In more densely connected social groups, crosstalk has a stronger effect. A harsh retaliator, such as Tit-for-Tat, is unable to counteract crosstalk. The crosstalk framework provides a unified interpretation of direct and upstream reciprocity in the context of repeated games.","lang":"eng"}],"oa":1,"file_date_updated":"2020-07-14T12:46:31Z","language":[{"iso":"eng"}],"ec_funded":1,"scopus_import":"1","issue":"1","_id":"454","quality_controlled":"1","citation":{"ama":"Reiter J, Hilbe C, Rand D, Chatterjee K, Nowak M. Crosstalk in concurrent repeated games impedes direct reciprocity and requires stronger levels of forgiveness. Nature Communications. 2018;9(1). doi:10.1038/s41467-017-02721-8","apa":"Reiter, J., Hilbe, C., Rand, D., Chatterjee, K., & Nowak, M. (2018). Crosstalk in concurrent repeated games impedes direct reciprocity and requires stronger levels of forgiveness. Nature Communications. Nature Publishing Group. https://doi.org/10.1038/s41467-017-02721-8","ista":"Reiter J, Hilbe C, Rand D, Chatterjee K, Nowak M. 2018. Crosstalk in concurrent repeated games impedes direct reciprocity and requires stronger levels of forgiveness. Nature Communications. 9(1), 555.","short":"J. Reiter, C. Hilbe, D. Rand, K. Chatterjee, M. Nowak, Nature Communications 9 (2018).","chicago":"Reiter, Johannes, Christian Hilbe, David Rand, Krishnendu Chatterjee, and Martin Nowak. “Crosstalk in Concurrent Repeated Games Impedes Direct Reciprocity and Requires Stronger Levels of Forgiveness.” Nature Communications. Nature Publishing Group, 2018. https://doi.org/10.1038/s41467-017-02721-8.","ieee":"J. Reiter, C. Hilbe, D. Rand, K. Chatterjee, and M. Nowak, “Crosstalk in concurrent repeated games impedes direct reciprocity and requires stronger levels of forgiveness,” Nature Communications, vol. 9, no. 1. Nature Publishing Group, 2018.","mla":"Reiter, Johannes, et al. “Crosstalk in Concurrent Repeated Games Impedes Direct Reciprocity and Requires Stronger Levels of Forgiveness.” Nature Communications, vol. 9, no. 1, 555, Nature Publishing Group, 2018, doi:10.1038/s41467-017-02721-8."},"date_updated":"2025-04-15T06:30:05Z","publist_id":"7368","department":[{"_id":"KrCh"}],"doi":"10.1038/s41467-017-02721-8","file":[{"relation":"main_file","file_id":"4741","creator":"system","date_created":"2018-12-12T10:09:18Z","file_size":843646,"content_type":"application/pdf","checksum":"b6b90367545b4c615891c960ab0567f1","access_level":"open_access","date_updated":"2020-07-14T12:46:31Z","file_name":"IST-2018-964-v1+1_2018_Hilbe_Crosstalk_in.pdf"}],"publication_status":"published","date_created":"2018-12-11T11:46:34Z","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"type":"journal_article","project":[{"call_identifier":"FP7","_id":"2581B60A-B435-11E9-9278-68D0E5697425","name":"Quantitative Graph Games: Theory and Applications","grant_number":"279307"},{"_id":"2584A770-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"P 23499-N23","name":"Modern Graph Algorithmic Techniques in Formal Verification"},{"grant_number":"S11407","name":"Game Theory","_id":"25863FF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"291734","name":"International IST Postdoc Fellowship Programme"}],"isi":1,"day":"07","publication":"Nature Communications","publisher":"Nature Publishing Group","has_accepted_license":"1","status":"public","pubrep_id":"964","intvolume":" 9","month":"02","ddc":["004"],"article_number":"555","external_id":{"isi":["000424318200001"]},"acknowledgement":"This work was supported by the European Research Council (ERC) start grant 279307: Graph Games (C.K.), Austrian Science Fund (FWF) grant no P23499-N23 (C.K.), FWF\r\nNFN grant no S11407-N23 RiSE/SHiNE (C.K.), Office of Naval Research grant N00014-16-1-2914 (M.A.N.), National Cancer Institute grant CA179991 (M.A.N.) and by the John Templeton Foundation. J.G.R. is supported by an Erwin Schrödinger fellowship\r\n(Austrian Science Fund FWF J-3996). C.H. acknowledges generous support from the\r\nISTFELLOW program. The Program for Evolutionary Dynamics is supported in part by\r\na gift from B Wu and Eric Larson.","author":[{"orcid":"0000-0002-0170-7353","id":"4A918E98-F248-11E8-B48F-1D18A9856A87","last_name":"Reiter","first_name":"Johannes","full_name":"Reiter, Johannes"},{"orcid":"0000-0001-5116-955X","id":"2FDF8F3C-F248-11E8-B48F-1D18A9856A87","last_name":"Hilbe","full_name":"Hilbe, Christian","first_name":"Christian"},{"last_name":"Rand","first_name":"David","full_name":"Rand, David"},{"first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X"},{"first_name":"Martin","full_name":"Nowak, Martin","last_name":"Nowak"}],"title":"Crosstalk in concurrent repeated games impedes direct reciprocity and requires stronger levels of forgiveness","article_processing_charge":"No","oa_version":"Published Version","volume":9,"date_published":"2018-02-07T00:00:00Z","year":"2018","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1"},{"intvolume":" 2","month":"03","corr_author":"1","status":"public","has_accepted_license":"1","publication":"Nature Human Behaviour","publisher":"Nature Publishing Group","oa_version":"Submitted Version","date_published":"2018-03-19T00:00:00Z","volume":2,"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","page":"469–477","year":"2018","title":"Partners and rivals in direct reciprocity","article_processing_charge":"No","author":[{"first_name":"Christian","full_name":"Hilbe, Christian","last_name":"Hilbe","id":"2FDF8F3C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5116-955X"},{"orcid":"0000-0002-4561-241X","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu"},{"last_name":"Nowak","full_name":"Nowak, Martin","first_name":"Martin"}],"external_id":{"isi":["000446612000016"]},"ddc":["000"],"quality_controlled":"1","citation":{"ista":"Hilbe C, Chatterjee K, Nowak M. 2018. Partners and rivals in direct reciprocity. Nature Human Behaviour. 2, 469–477.","apa":"Hilbe, C., Chatterjee, K., & Nowak, M. (2018). Partners and rivals in direct reciprocity. Nature Human Behaviour. Nature Publishing Group. https://doi.org/10.1038/s41562-018-0320-9","ama":"Hilbe C, Chatterjee K, Nowak M. Partners and rivals in direct reciprocity. Nature Human Behaviour. 2018;2:469–477. doi:10.1038/s41562-018-0320-9","mla":"Hilbe, Christian, et al. “Partners and Rivals in Direct Reciprocity.” Nature Human Behaviour, vol. 2, Nature Publishing Group, 2018, pp. 469–477, doi:10.1038/s41562-018-0320-9.","ieee":"C. Hilbe, K. Chatterjee, and M. Nowak, “Partners and rivals in direct reciprocity,” Nature Human Behaviour, vol. 2. Nature Publishing Group, pp. 469–477, 2018.","chicago":"Hilbe, Christian, Krishnendu Chatterjee, and Martin Nowak. “Partners and Rivals in Direct Reciprocity.” Nature Human Behaviour. Nature Publishing Group, 2018. https://doi.org/10.1038/s41562-018-0320-9.","short":"C. Hilbe, K. Chatterjee, M. Nowak, Nature Human Behaviour 2 (2018) 469–477."},"date_updated":"2025-04-15T06:50:00Z","publist_id":"7404","related_material":{"link":[{"relation":"erratum","url":"http://doi.org/10.1038/s41562-018-0342-3"}]},"_id":"419","scopus_import":"1","file_date_updated":"2020-07-14T12:46:25Z","oa":1,"language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"Reciprocity is a major factor in human social life and accounts for a large part of cooperation in our communities. Direct reciprocity arises when repeated interactions occur between the same individuals. The framework of iterated games formalizes this phenomenon. Despite being introduced more than five decades ago, the concept keeps offering beautiful surprises. Recent theoretical research driven by new mathematical tools has proposed a remarkable dichotomy among the crucial strategies: successful individuals either act as partners or as rivals. Rivals strive for unilateral advantages by applying selfish or extortionate strategies. Partners aim to share the payoff for mutual cooperation, but are ready to fight back when being exploited. Which of these behaviours evolves depends on the environment. Whereas small population sizes and a limited number of rounds favour rivalry, partner strategies are selected when populations are large and relationships stable. Only partners allow for evolution of cooperation, while the rivals’ attempt to put themselves first leads to defection. Hilbe et al. synthesize recent theoretical work on zero-determinant and ‘rival’ versus ‘partner’ strategies in social dilemmas. They describe the environments under which these contrasting selfish or cooperative strategies emerge in evolution."}],"ec_funded":1,"article_type":"review","project":[{"grant_number":"279307","name":"Quantitative Graph Games: Theory and Applications","call_identifier":"FP7","_id":"2581B60A-B435-11E9-9278-68D0E5697425"},{"name":"Modern Graph Algorithmic Techniques in Formal Verification","grant_number":"P 23499-N23","call_identifier":"FWF","_id":"2584A770-B435-11E9-9278-68D0E5697425"},{"grant_number":"S 11407_N23","name":"Rigorous Systems Engineering","_id":"25832EC2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"}],"day":"19","isi":1,"type":"journal_article","date_created":"2018-12-11T11:46:22Z","publication_status":"published","file":[{"content_type":"application/pdf","date_updated":"2020-07-14T12:46:25Z","file_name":"2018_NatureHumanBeh_Hilbe.pdf","checksum":"571b8cc0ba14e8d5d8b18e439a9835eb","access_level":"open_access","file_id":"7052","relation":"main_file","date_created":"2019-11-19T08:19:51Z","file_size":598033,"creator":"dernst"}],"doi":"10.1038/s41562-018-0320-9","department":[{"_id":"KrCh"}]},{"date_published":"2018-11-27T00:00:00Z","oa_version":"Submitted Version","pmid":1,"volume":115,"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","page":"12241-12246","year":"2018","title":"Indirect reciprocity with private, noisy, and incomplete information","article_processing_charge":"No","author":[{"last_name":"Hilbe","full_name":"Hilbe, Christian","first_name":"Christian","orcid":"0000-0001-5116-955X","id":"2FDF8F3C-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-6978-7329","id":"38B437DE-F248-11E8-B48F-1D18A9856A87","last_name":"Schmid","full_name":"Schmid, Laura","first_name":"Laura"},{"first_name":"Josef","full_name":"Tkadlec, Josef","last_name":"Tkadlec","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1097-9684"},{"full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X"},{"last_name":"Nowak","first_name":"Martin","full_name":"Nowak, Martin"}],"external_id":{"isi":["000451351000063"],"pmid":["30429320"]},"main_file_link":[{"url":"https://www.ncbi.nlm.nih.gov/pubmed/30429320","open_access":"1"}],"intvolume":" 115","month":"11","status":"public","publication":"PNAS","publisher":"National Academy of Sciences","project":[{"_id":"2581B60A-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Quantitative Graph Games: Theory and Applications","grant_number":"279307"},{"grant_number":"P 23499-N23","name":"Modern Graph Algorithmic Techniques in Formal Verification","call_identifier":"FWF","_id":"2584A770-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","_id":"25832EC2-B435-11E9-9278-68D0E5697425","name":"Rigorous Systems Engineering","grant_number":"S 11407_N23"},{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"}],"isi":1,"day":"27","type":"journal_article","publication_status":"published","date_created":"2018-12-11T11:44:05Z","doi":"10.1073/pnas.1810565115","department":[{"_id":"KrCh"}],"citation":{"ieee":"C. Hilbe, L. Schmid, J. Tkadlec, K. Chatterjee, and M. Nowak, “Indirect reciprocity with private, noisy, and incomplete information,” PNAS, vol. 115, no. 48. National Academy of Sciences, pp. 12241–12246, 2018.","mla":"Hilbe, Christian, et al. “Indirect Reciprocity with Private, Noisy, and Incomplete Information.” PNAS, vol. 115, no. 48, National Academy of Sciences, 2018, pp. 12241–46, doi:10.1073/pnas.1810565115.","short":"C. Hilbe, L. Schmid, J. Tkadlec, K. Chatterjee, M. Nowak, PNAS 115 (2018) 12241–12246.","chicago":"Hilbe, Christian, Laura Schmid, Josef Tkadlec, Krishnendu Chatterjee, and Martin Nowak. “Indirect Reciprocity with Private, Noisy, and Incomplete Information.” PNAS. National Academy of Sciences, 2018. https://doi.org/10.1073/pnas.1810565115.","ista":"Hilbe C, Schmid L, Tkadlec J, Chatterjee K, Nowak M. 2018. Indirect reciprocity with private, noisy, and incomplete information. PNAS. 115(48), 12241–12246.","ama":"Hilbe C, Schmid L, Tkadlec J, Chatterjee K, Nowak M. Indirect reciprocity with private, noisy, and incomplete information. PNAS. 2018;115(48):12241-12246. doi:10.1073/pnas.1810565115","apa":"Hilbe, C., Schmid, L., Tkadlec, J., Chatterjee, K., & Nowak, M. (2018). Indirect reciprocity with private, noisy, and incomplete information. PNAS. National Academy of Sciences. https://doi.org/10.1073/pnas.1810565115"},"quality_controlled":"1","date_updated":"2026-07-08T22:30:53Z","related_material":{"record":[{"relation":"dissertation_contains","id":"10293","status":"public"}],"link":[{"url":"https://ist.ac.at/en/news/no-cooperation-without-open-communication/","relation":"press_release","description":"News on IST Homepage"}]},"issue":"48","_id":"2","scopus_import":"1","language":[{"iso":"eng"}],"oa":1,"abstract":[{"text":"Indirect reciprocity explores how humans act when their reputation is at stake, and which social norms they use to assess the actions of others. A crucial question in indirect reciprocity is which social norms can maintain stable cooperation in a society. Past research has highlighted eight such norms, called “leading-eight” strategies. This past research, however, is based on the assumption that all relevant information about other population members is publicly available and that everyone agrees on who is good or bad. Instead, here we explore the reputation dynamics when information is private and noisy. We show that under these conditions, most leading-eight strategies fail to evolve. Those leading-eight strategies that do evolve are unable to sustain full cooperation.Indirect reciprocity is a mechanism for cooperation based on shared moral systems and individual reputations. It assumes that members of a community routinely observe and assess each other and that they use this information to decide who is good or bad, and who deserves cooperation. When information is transmitted publicly, such that all community members agree on each other’s reputation, previous research has highlighted eight crucial moral systems. These “leading-eight” strategies can maintain cooperation and resist invasion by defectors. However, in real populations individuals often hold their own private views of others. Once two individuals disagree about their opinion of some third party, they may also see its subsequent actions in a different light. Their opinions may further diverge over time. Herein, we explore indirect reciprocity when information transmission is private and noisy. We find that in the presence of perception errors, most leading-eight strategies cease to be stable. Even if a leading-eight strategy evolves, cooperation rates may drop considerably when errors are common. Our research highlights the role of reliable information and synchronized reputations to maintain stable moral systems.","lang":"eng"}],"ec_funded":1},{"title":"Memory-n strategies of direct reciprocity","article_processing_charge":"Yes (in subscription journal)","oa_version":"Published Version","date_published":"2017-05-02T00:00:00Z","pmid":1,"volume":114,"page":"4715 - 4720","year":"2017","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["000"],"external_id":{"isi":["000400358000050"],"pmid":["28420786"]},"author":[{"orcid":"0000-0001-5116-955X","id":"2FDF8F3C-F248-11E8-B48F-1D18A9856A87","last_name":"Hilbe","full_name":"Hilbe, Christian","first_name":"Christian"},{"last_name":"Martinez","first_name":"Vaquero","full_name":"Martinez, Vaquero"},{"orcid":"0000-0002-4561-241X","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu"},{"last_name":"Nowak","first_name":"Martin","full_name":"Nowak, Martin"}],"intvolume":" 114","month":"05","main_file_link":[{"url":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5422766/","open_access":"1"}],"publication_identifier":{"issn":["0027-8424"]},"publication":"PNAS","publisher":"National Academy of Sciences","corr_author":"1","status":"public","project":[{"_id":"2581B60A-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"279307","name":"Quantitative Graph Games: Theory and Applications"},{"name":"Modern Graph Algorithmic Techniques in Formal Verification","grant_number":"P 23499-N23","_id":"2584A770-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"grant_number":"S11407","name":"Game Theory","_id":"25863FF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"isi":1,"day":"02","doi":"10.1073/pnas.1621239114","department":[{"_id":"KrCh"}],"date_created":"2018-12-11T11:47:50Z","publication_status":"published","type":"journal_article","_id":"671","issue":"18","date_updated":"2026-06-18T19:11:14Z","citation":{"apa":"Hilbe, C., Martinez, V., Chatterjee, K., & Nowak, M. (2017). Memory-n strategies of direct reciprocity. PNAS. National Academy of Sciences. https://doi.org/10.1073/pnas.1621239114","ama":"Hilbe C, Martinez V, Chatterjee K, Nowak M. Memory-n strategies of direct reciprocity. PNAS. 2017;114(18):4715-4720. doi:10.1073/pnas.1621239114","ista":"Hilbe C, Martinez V, Chatterjee K, Nowak M. 2017. Memory-n strategies of direct reciprocity. PNAS. 114(18), 4715–4720.","chicago":"Hilbe, Christian, Vaquero Martinez, Krishnendu Chatterjee, and Martin Nowak. “Memory-n Strategies of Direct Reciprocity.” PNAS. National Academy of Sciences, 2017. https://doi.org/10.1073/pnas.1621239114.","short":"C. Hilbe, V. Martinez, K. Chatterjee, M. Nowak, PNAS 114 (2017) 4715–4720.","mla":"Hilbe, Christian, et al. “Memory-n Strategies of Direct Reciprocity.” PNAS, vol. 114, no. 18, National Academy of Sciences, 2017, pp. 4715–20, doi:10.1073/pnas.1621239114.","ieee":"C. Hilbe, V. Martinez, K. Chatterjee, and M. Nowak, “Memory-n strategies of direct reciprocity,” PNAS, vol. 114, no. 18. National Academy of Sciences, pp. 4715–4720, 2017."},"quality_controlled":"1","publist_id":"7053","abstract":[{"lang":"eng","text":"Humans routinely use conditionally cooperative strategies when interacting in repeated social dilemmas. They are more likely to cooperate if others cooperated before, and are ready to retaliate if others defected. To capture the emergence of reciprocity, most previous models consider subjects who can only choose from a restricted set of representative strategies, or who react to the outcome of the very last round only. As players memorize more rounds, the dimension of the strategy space increases exponentially. This increasing computational complexity renders simulations for individuals with higher cognitive abilities infeasible, especially if multiplayer interactions are taken into account. Here, we take an axiomatic approach instead. We propose several properties that a robust cooperative strategy for a repeated multiplayer dilemma should have. These properties naturally lead to a unique class of cooperative strategies, which contains the classical Win-Stay Lose-Shift rule as a special case. A comprehensive numerical analysis for the prisoner's dilemma and for the public goods game suggests that strategies of this class readily evolve across various memory-n spaces. Our results reveal that successful strategies depend not only on how cooperative others were in the past but also on the respective context of cooperation."}],"language":[{"iso":"eng"}],"oa":1,"ec_funded":1,"scopus_import":"1"},{"abstract":[{"lang":"eng","text":"In antagonistic symbioses, such as host–parasite interactions, one population’s success is the other’s loss. In mutualistic symbioses, such as division of labor, both parties can gain, but they might have different preferences over the possible mutualistic arrangements. The rates of evolution of the two populations in a symbiosis are important determinants of which population will be more successful: Faster evolution is thought to be favored in antagonistic symbioses (the “Red Queen effect”), but disfavored in certain mutualistic symbioses (the “Red King effect”). However, it remains unclear which biological parameters drive these effects. Here, we analyze the effects of the various determinants of evolutionary rate: generation time, mutation rate, population size, and the intensity of natural selection. Our main results hold for the case where mutation is infrequent. Slower evolution causes a long-term advantage in an important class of mutualistic interactions. Surprisingly, less intense selection is the strongest driver of this Red King effect, whereas relative mutation rates and generation times have little effect. In antagonistic interactions, faster evolution by any means is beneficial. Our results provide insight into the demographic evolution of symbionts. "}],"oa":1,"language":[{"iso":"eng"}],"scopus_import":"1","issue":"27","_id":"699","quality_controlled":"1","date_updated":"2025-09-10T11:11:07Z","citation":{"apa":"Veller, C., Hayward, L., Nowak, M., & Hilbe, C. (2017). The red queen and king in finite populations. PNAS. National Academy of Sciences. https://doi.org/10.1073/pnas.1702020114","ama":"Veller C, Hayward L, Nowak M, Hilbe C. The red queen and king in finite populations. PNAS. 2017;114(27):E5396-E5405. doi:10.1073/pnas.1702020114","ista":"Veller C, Hayward L, Nowak M, Hilbe C. 2017. The red queen and king in finite populations. PNAS. 114(27), E5396–E5405.","chicago":"Veller, Carl, Laura Hayward, Martin Nowak, and Christian Hilbe. “The Red Queen and King in Finite Populations.” PNAS. National Academy of Sciences, 2017. https://doi.org/10.1073/pnas.1702020114.","short":"C. Veller, L. Hayward, M. Nowak, C. Hilbe, PNAS 114 (2017) E5396–E5405.","mla":"Veller, Carl, et al. “The Red Queen and King in Finite Populations.” PNAS, vol. 114, no. 27, National Academy of Sciences, 2017, pp. E5396–405, doi:10.1073/pnas.1702020114.","ieee":"C. Veller, L. Hayward, M. Nowak, and C. Hilbe, “The red queen and king in finite populations,” PNAS, vol. 114, no. 27. National Academy of Sciences, pp. E5396–E5405, 2017."},"publist_id":"7002","doi":"10.1073/pnas.1702020114","department":[{"_id":"KrCh"}],"publication_status":"published","date_created":"2018-12-11T11:48:00Z","type":"journal_article","isi":1,"day":"03","publication":"PNAS","publisher":"National Academy of Sciences","status":"public","intvolume":" 114","month":"07","main_file_link":[{"open_access":"1","url":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5502615/"}],"publication_identifier":{"issn":["0027-8424"]},"external_id":{"isi":["000404576100017"],"pmid":["28630336"]},"author":[{"full_name":"Veller, Carl","first_name":"Carl","last_name":"Veller"},{"last_name":"Hayward","first_name":"Laura","full_name":"Hayward, Laura"},{"last_name":"Nowak","first_name":"Martin","full_name":"Nowak, Martin"},{"orcid":"0000-0001-5116-955X","id":"2FDF8F3C-F248-11E8-B48F-1D18A9856A87","last_name":"Hilbe","first_name":"Christian","full_name":"Hilbe, Christian"}],"title":"The red queen and king in finite populations","article_processing_charge":"No","pmid":1,"volume":114,"oa_version":"Submitted Version","date_published":"2017-07-03T00:00:00Z","page":"E5396 - E5405","year":"2017","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345"},{"isi":1,"day":"01","project":[{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"department":[{"_id":"KrCh"}],"doi":"10.1016/j.plrev.2016.10.004","file":[{"file_id":"4855","relation":"main_file","date_created":"2018-12-12T10:11:02Z","file_size":171352,"creator":"system","content_type":"application/pdf","date_updated":"2020-07-14T12:44:39Z","file_name":"IST-2017-798-v1+1_comment_adami.pdf","checksum":"95e6dc78278334b99dacbf8822509364","access_level":"open_access"}],"date_created":"2018-12-11T11:50:40Z","publication_status":"published","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)"},"type":"journal_article","_id":"1200","publist_id":"6150","quality_controlled":"1","date_updated":"2025-09-22T09:42:11Z","citation":{"ista":"Hilbe C, Traulsen A. 2016. Only the combination of mathematics and agent based simulations can leverage the full potential of evolutionary modeling: Comment on “Evolutionary game theory using agent-based methods” by C. Adami, J. Schossau and A. Hintze. Physics of Life Reviews. 19, 29–31.","apa":"Hilbe, C., & Traulsen, A. (2016). Only the combination of mathematics and agent based simulations can leverage the full potential of evolutionary modeling: Comment on “Evolutionary game theory using agent-based methods” by C. Adami, J. Schossau and A. Hintze. Physics of Life Reviews. Elsevier. https://doi.org/10.1016/j.plrev.2016.10.004","ama":"Hilbe C, Traulsen A. Only the combination of mathematics and agent based simulations can leverage the full potential of evolutionary modeling: Comment on “Evolutionary game theory using agent-based methods” by C. Adami, J. Schossau and A. Hintze. Physics of Life Reviews. 2016;19:29-31. doi:10.1016/j.plrev.2016.10.004","mla":"Hilbe, Christian, and Arne Traulsen. “Only the Combination of Mathematics and Agent Based Simulations Can Leverage the Full Potential of Evolutionary Modeling: Comment on ‘Evolutionary Game Theory Using Agent-Based Methods’ by C. Adami, J. Schossau and A. Hintze.” Physics of Life Reviews, vol. 19, Elsevier, 2016, pp. 29–31, doi:10.1016/j.plrev.2016.10.004.","ieee":"C. Hilbe and A. Traulsen, “Only the combination of mathematics and agent based simulations can leverage the full potential of evolutionary modeling: Comment on ‘Evolutionary game theory using agent-based methods’ by C. Adami, J. Schossau and A. Hintze,” Physics of Life Reviews, vol. 19. Elsevier, pp. 29–31, 2016.","chicago":"Hilbe, Christian, and Arne Traulsen. “Only the Combination of Mathematics and Agent Based Simulations Can Leverage the Full Potential of Evolutionary Modeling: Comment on ‘Evolutionary Game Theory Using Agent-Based Methods’ by C. Adami, J. Schossau and A. Hintze.” Physics of Life Reviews. Elsevier, 2016. https://doi.org/10.1016/j.plrev.2016.10.004.","short":"C. Hilbe, A. Traulsen, Physics of Life Reviews 19 (2016) 29–31."},"ec_funded":1,"oa":1,"language":[{"iso":"eng"}],"file_date_updated":"2020-07-14T12:44:39Z","scopus_import":"1","article_processing_charge":"No","title":"Only the combination of mathematics and agent based simulations can leverage the full potential of evolutionary modeling: Comment on “Evolutionary game theory using agent-based methods” by C. Adami, J. Schossau and A. Hintze","page":"29 - 31","year":"2016","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_published":"2016-12-01T00:00:00Z","volume":19,"oa_version":"Submitted Version","ddc":["530"],"external_id":{"isi":["000390640200003"]},"acknowledgement":"C.H. acknowledges generous support from the ISTFELLOW program.","author":[{"last_name":"Hilbe","full_name":"Hilbe, Christian","first_name":"Christian","orcid":"0000-0001-5116-955X","id":"2FDF8F3C-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Arne","full_name":"Traulsen, Arne","last_name":"Traulsen"}],"month":"12","intvolume":" 19","publisher":"Elsevier","publication":"Physics of Life Reviews","has_accepted_license":"1","pubrep_id":"798","status":"public"}]