[{"publication_identifier":{"issn":["2153-0785"],"eissn":["2153-0793"]},"oa":1,"title":"Time-dependent strategies in repeated asymmetric public goods games","doi":"10.1007/s13235-025-00627-5","type":"journal_article","corr_author":"1","scopus_import":"1","publication":"Dynamic Games and Applications","author":[{"orcid":"0009-0001-5009-4987","first_name":"Valentin","id":"2c8aa207-dc7d-11ea-9b2f-f22972ecd910","last_name":"Hübner","full_name":"Hübner, Valentin"},{"last_name":"Hilbe","id":"2FDF8F3C-F248-11E8-B48F-1D18A9856A87","full_name":"Hilbe, Christian","orcid":"0000-0001-5116-955X","first_name":"Christian"},{"first_name":"Manuel","last_name":"Staab","full_name":"Staab, Manuel"},{"full_name":"Kleshnina, Maria","id":"4E21749C-F248-11E8-B48F-1D18A9856A87","last_name":"Kleshnina","orcid":"0000-0002-5518-8317","first_name":"Maria"},{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu","orcid":"0000-0002-4561-241X"}],"date_created":"2025-02-23T23:01:57Z","article_processing_charge":"Yes (via OA deal)","project":[{"call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","grant_number":"863818"},{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411"}],"related_material":{"record":[{"id":"19903","relation":"dissertation_contains","status":"public"}]},"quality_controlled":"1","page":"1617-1645","volume":15,"language":[{"iso":"eng"}],"department":[{"_id":"KrCh"}],"publication_status":"published","month":"11","ddc":["000"],"OA_type":"hybrid","date_published":"2025-11-01T00:00:00Z","PlanS_conform":"1","has_accepted_license":"1","fulldoi":"https://doi.org/10.1007/s13235-025-00627-5","article_type":"original","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"OA_place":"publisher","date_updated":"2026-09-16T06:58:23Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ec_funded":1,"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","external_id":{"isi":["001415587800001"]},"file":[{"success":1,"file_id":"20888","file_name":"2025_DynGamesAppl_Huebner.pdf","file_size":1126178,"date_created":"2025-12-30T08:01:35Z","checksum":"de0a412cbb7d98bf5e6a551c26acbefa","access_level":"open_access","relation":"main_file","date_updated":"2025-12-30T08:01:35Z","content_type":"application/pdf","creator":"dernst"}],"intvolume":"        15","status":"public","_id":"19074","oa_version":"Published Version","day":"01","isi":1,"year":"2025","citation":{"chicago":"Hübner, Valentin, Christian Hilbe, Manuel Staab, Maria Kleshnina, and Krishnendu Chatterjee. “Time-Dependent Strategies in Repeated Asymmetric Public Goods Games.” <i>Dynamic Games and Applications</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s13235-025-00627-5\">https://doi.org/10.1007/s13235-025-00627-5</a>.","mla":"Hübner, Valentin, et al. “Time-Dependent Strategies in Repeated Asymmetric Public Goods Games.” <i>Dynamic Games and Applications</i>, vol. 15, Springer Nature, 2025, pp. 1617–45, doi:<a href=\"https://doi.org/10.1007/s13235-025-00627-5\">10.1007/s13235-025-00627-5</a>.","short":"V. Hübner, C. Hilbe, M. Staab, M. Kleshnina, K. Chatterjee, Dynamic Games and Applications 15 (2025) 1617–1645.","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. <i>Dynamic Games and Applications</i>. 2025;15:1617-1645. doi:<a href=\"https://doi.org/10.1007/s13235-025-00627-5\">10.1007/s13235-025-00627-5</a>","apa":"Hübner, V., Hilbe, C., Staab, M., Kleshnina, M., &#38; Chatterjee, K. (2025). Time-dependent strategies in repeated asymmetric public goods games. <i>Dynamic Games and Applications</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s13235-025-00627-5\">https://doi.org/10.1007/s13235-025-00627-5</a>","ieee":"V. Hübner, C. Hilbe, M. Staab, M. Kleshnina, and K. Chatterjee, “Time-dependent strategies in repeated asymmetric public goods games,” <i>Dynamic Games and Applications</i>, vol. 15. Springer Nature, pp. 1617–1645, 2025."},"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).","publisher":"Springer Nature"},{"doi":"10.1007/s13235-025-00636-4","type":"journal_article","publication_identifier":{"issn":["2153-0785"],"eissn":["2153-0793"]},"title":"Random zero-sum dynamic games on infinite directed graphs","oa":1,"scopus_import":"1","corr_author":"1","author":[{"last_name":"Attia","full_name":"Attia, Luc","first_name":"Luc"},{"first_name":"Lyuben","id":"9aa8388e-d003-11ee-8458-c4c1d7447977","last_name":"Lichev","full_name":"Lichev, Lyuben"},{"last_name":"Mitsche","full_name":"Mitsche, Dieter","first_name":"Dieter"},{"first_name":"Raimundo J","orcid":"0000-0001-5103-038X","id":"BD1DF4C4-D767-11E9-B658-BC13E6697425","last_name":"Saona Urmeneta","full_name":"Saona Urmeneta, Raimundo J"},{"full_name":"Ziliotto, Bruno","last_name":"Ziliotto","first_name":"Bruno"}],"publication":"Dynamic Games and Applications","date_created":"2025-04-06T22:01:32Z","article_processing_charge":"Yes (via OA deal)","quality_controlled":"1","related_material":{"record":[{"id":"20234","relation":"dissertation_contains","status":"public"}]},"project":[{"name":"Formal Methods for Stochastic Models: Algorithms and Applications","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","call_identifier":"H2020","grant_number":"863818"}],"language":[{"iso":"eng"}],"department":[{"_id":"MaKw"},{"_id":"KrCh"}],"volume":15,"publication_status":"published","page":"1517-1535","month":"11","article_type":"original","fulldoi":"https://doi.org/10.1007/s13235-025-00636-4","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"ddc":["000"],"date_published":"2025-11-01T00:00:00Z","has_accepted_license":"1","PlanS_conform":"1","OA_type":"hybrid","OA_place":"publisher","date_updated":"2026-09-16T07:00:33Z","abstract":[{"lang":"eng","text":"We consider random two-player zero-sum dynamic games with perfect information on a class of infinite directed graphs. Starting from a fixed vertex, the players take turns to move a token along the edges of the graph. Every vertex is assigned a payoff known in advance by both players. Every time the token visits a vertex, Player 2 pays Player 1 the corresponding payoff. We consider a distribution over such games by assigning i.i.d. payoffs to the vertices. On the one hand, for acyclic directed graphs of bounded degree and sub-exponential expansion, we show that, when the duration of the game tends to infinity, the value converges almost surely to a constant at an exponential rate dominated in terms of the expansion. On the other hand, for the infinite d-ary tree (that does not fall into the previous class of graphs), we show convergence at a double-exponential rate."}],"ec_funded":1,"file_date_updated":"2025-12-30T08:13:04Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"access_level":"open_access","checksum":"b3a1b7eef40c9ac2acf3fef563081694","relation":"main_file","creator":"dernst","content_type":"application/pdf","date_updated":"2025-12-30T08:13:04Z","success":1,"file_id":"20891","date_created":"2025-12-30T08:13:04Z","file_size":570994,"file_name":"2025_DynGamesAppl_Attia.pdf"}],"intvolume":"        15","external_id":{"isi":["001449708900001"]},"oa_version":"Published Version","status":"public","_id":"19508","year":"2025","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). This work was supported by the French Agence Nationale de la Recherche (ANR) under references ANR-21-CE40-0020 (CONVERGENCE project) and ANR-20-CE40-0002 (GrHyDy), by Fondecyt grant 1220174, by ANID Chile grant ACT210005, and by the ERC CoG 863818 (ForM-SMArt) grant. This collaboration was mainly conducted during a 1-year visit of Bruno Ziliotto to the Center for Mathematical Modeling (CMM) at University of Chile in 2023, under the IRL program of CNRS. This work was supported by Fondation CFM pour la Recherche. This paper has also been funded by the Agence Nationale de la Recherche under grant ANR-17-EURE-0010 (Investissements d’Avenir program).","citation":{"chicago":"Attia, Luc, Lyuben Lichev, Dieter Mitsche, Raimundo J Saona Urmeneta, and Bruno Ziliotto. “Random Zero-Sum Dynamic Games on Infinite Directed Graphs.” <i>Dynamic Games and Applications</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s13235-025-00636-4\">https://doi.org/10.1007/s13235-025-00636-4</a>.","mla":"Attia, Luc, et al. “Random Zero-Sum Dynamic Games on Infinite Directed Graphs.” <i>Dynamic Games and Applications</i>, vol. 15, Springer Nature, 2025, pp. 1517–35, doi:<a href=\"https://doi.org/10.1007/s13235-025-00636-4\">10.1007/s13235-025-00636-4</a>.","short":"L. Attia, L. Lichev, D. Mitsche, R.J. Saona Urmeneta, B. Ziliotto, Dynamic Games and Applications 15 (2025) 1517–1535.","ama":"Attia L, Lichev L, Mitsche D, Saona Urmeneta RJ, Ziliotto B. Random zero-sum dynamic games on infinite directed graphs. <i>Dynamic Games and Applications</i>. 2025;15:1517-1535. doi:<a href=\"https://doi.org/10.1007/s13235-025-00636-4\">10.1007/s13235-025-00636-4</a>","ista":"Attia L, Lichev L, Mitsche D, Saona Urmeneta RJ, Ziliotto B. 2025. Random zero-sum dynamic games on infinite directed graphs. Dynamic Games and Applications. 15, 1517–1535.","apa":"Attia, L., Lichev, L., Mitsche, D., Saona Urmeneta, R. J., &#38; Ziliotto, B. (2025). Random zero-sum dynamic games on infinite directed graphs. <i>Dynamic Games and Applications</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s13235-025-00636-4\">https://doi.org/10.1007/s13235-025-00636-4</a>","ieee":"L. Attia, L. Lichev, D. Mitsche, R. J. Saona Urmeneta, and B. Ziliotto, “Random zero-sum dynamic games on infinite directed graphs,” <i>Dynamic Games and Applications</i>, vol. 15. Springer Nature, pp. 1517–1535, 2025."},"publisher":"Springer Nature","day":"01","isi":1},{"external_id":{"isi":["000753777100001"]},"file":[{"date_updated":"2022-02-21T08:54:17Z","content_type":"application/pdf","creator":"dernst","access_level":"open_access","checksum":"cd53b07e96f9030ddb348f305e5b58c7","relation":"main_file","file_name":"2022_DynamicGamesApplic_Graham.pdf","file_size":1890512,"date_created":"2022-02-21T08:54:17Z","success":1,"file_id":"10781"}],"intvolume":"        13","day":"01","isi":1,"year":"2023","citation":{"mla":"Graham, Thomas, et al. “Where Do Mistakes Lead? A Survey of Games with Incompetent Players.” <i>Dynamic Games and Applications</i>, vol. 13, Springer Nature, 2023, pp. 231–64, doi:<a href=\"https://doi.org/10.1007/s13235-022-00425-3\">10.1007/s13235-022-00425-3</a>.","short":"T. Graham, M. Kleshnina, J.A. Filar, Dynamic Games and Applications 13 (2023) 231–264.","chicago":"Graham, Thomas, Maria Kleshnina, and Jerzy A. Filar. “Where Do Mistakes Lead? A Survey of Games with Incompetent Players.” <i>Dynamic Games and Applications</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s13235-022-00425-3\">https://doi.org/10.1007/s13235-022-00425-3</a>.","ieee":"T. Graham, M. Kleshnina, and J. A. Filar, “Where do mistakes lead? A survey of games with incompetent players,” <i>Dynamic Games and Applications</i>, vol. 13. Springer Nature, pp. 231–264, 2023.","apa":"Graham, T., Kleshnina, M., &#38; Filar, J. A. (2023). Where do mistakes lead? A survey of games with incompetent players. <i>Dynamic Games and Applications</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s13235-022-00425-3\">https://doi.org/10.1007/s13235-022-00425-3</a>","ista":"Graham T, Kleshnina M, Filar JA. 2023. Where do mistakes lead? A survey of games with incompetent players. Dynamic Games and Applications. 13, 231–264.","ama":"Graham T, Kleshnina M, Filar JA. Where do mistakes lead? A survey of games with incompetent players. <i>Dynamic Games and Applications</i>. 2023;13:231-264. doi:<a href=\"https://doi.org/10.1007/s13235-022-00425-3\">10.1007/s13235-022-00425-3</a>"},"acknowledgement":"The authors would like to acknowledge stimulating email discussions with Dr Wayne Lobb of W.A. Lobb LLC on the topic of evolutionary games. We also thank Dr Thomas Taimre for his input to the material in Sect. 3.\r\nThe authors would like to acknowledge partial support from the Australian Research Council under the Discovery grant DP180101602 and support by the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement #754411.","publisher":"Springer Nature","status":"public","_id":"10770","oa_version":"Published Version","ddc":["000"],"has_accepted_license":"1","date_published":"2023-03-01T00:00:00Z","fulldoi":"https://doi.org/10.1007/s13235-022-00425-3","article_type":"original","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"text":"Mathematical models often aim to describe a complicated mechanism in a cohesive and simple manner. However, reaching perfect balance between being simple enough or overly simplistic is a challenging task. Frequently, game-theoretic models have an underlying assumption that players, whenever they choose to execute a specific action, do so perfectly. In fact, it is rare that action execution perfectly coincides with intentions of individuals, giving rise to behavioural mistakes. The concept of incompetence of players was suggested to address this issue in game-theoretic settings. Under the assumption of incompetence, players have non-zero probabilities of executing a different strategy from the one they chose, leading to stochastic outcomes of the interactions. In this article, we survey results related to the concept of incompetence in classic as well as evolutionary game theory and provide several new results. We also suggest future extensions of the model and argue why it is important to take into account behavioural mistakes when analysing interactions among players in both economic and biological settings.","lang":"eng"}],"file_date_updated":"2022-02-21T08:54:17Z","ec_funded":1,"date_updated":"2025-04-14T07:43:48Z","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411"}],"quality_controlled":"1","date_created":"2022-02-20T23:01:32Z","article_processing_charge":"No","month":"03","page":"231-264","language":[{"iso":"eng"}],"volume":13,"department":[{"_id":"KrCh"}],"publication_status":"published","publication_identifier":{"eissn":["2153-0793"],"issn":["2153-0785"]},"oa":1,"title":"Where do mistakes lead? A survey of games with incompetent players","doi":"10.1007/s13235-022-00425-3","type":"journal_article","publication":"Dynamic Games and Applications","author":[{"full_name":"Graham, Thomas","last_name":"Graham","first_name":"Thomas"},{"full_name":"Kleshnina, Maria","id":"4E21749C-F248-11E8-B48F-1D18A9856A87","last_name":"Kleshnina","first_name":"Maria"},{"last_name":"Filar","full_name":"Filar, Jerzy A.","first_name":"Jerzy A."}],"scopus_import":"1"}]