{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T14:54:00Z","timestamp":1773759240861,"version":"3.50.1"},"reference-count":89,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T00:00:00Z","timestamp":1772323200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T00:00:00Z","timestamp":1772323200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2025,12,3]],"date-time":"2025-12-03T00:00:00Z","timestamp":1764720000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004837","name":"Ministerio de Ciencia e Innovaci\u00f3n","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004837","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014440","name":"Gobierno de Espa\u00f1a Ministerio de Ciencia e Innovaci\u00f3n","doi-asserted-by":"publisher","award":["PID2022-143241OB-I00"],"award-info":[{"award-number":["PID2022-143241OB-I00"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Games and Economic Behavior"],"published-print":{"date-parts":[[2026,3]]},"DOI":"10.1016\/j.geb.2025.11.012","type":"journal-article","created":{"date-parts":[[2025,12,5]],"date-time":"2025-12-05T00:33:53Z","timestamp":1764894833000},"page":"1-21","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Algorithmic collusion and a folk theorem from learning with bounded rationality"],"prefix":"10.1016","volume":"157","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7426-4645","authenticated-orcid":false,"given":"\u00c1lvaro","family":"Cartea","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3610-0164","authenticated-orcid":false,"given":"Patrick","family":"Chang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1793-9642","authenticated-orcid":false,"given":"Jos\u00e9","family":"Penalva","sequence":"additional","affiliation":[]},{"given":"Harrison","family":"Waldon","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"issue":"9","key":"10.1016\/j.geb.2025.11.012_bib0001","doi-asserted-by":"crossref","first-page":"5042","DOI":"10.1287\/mnsc.2022.4623","article-title":"Artificial intelligence: can seemingly collusive outcomes be avoided?","volume":"69","author":"Abada","year":"2023","journal-title":"Manage. Sci."},{"issue":"2","key":"10.1016\/j.geb.2025.11.012_bib0002","doi-asserted-by":"crossref","first-page":"383","DOI":"10.2307\/1911077","article-title":"On the theory of infinitely repeated games with discounting","volume":"56","author":"Abreu","year":"1988","journal-title":"Econometrica"},{"issue":"4","key":"10.1016\/j.geb.2025.11.012_bib0003","doi-asserted-by":"crossref","first-page":"939","DOI":"10.2307\/2951739","article-title":"The folk theorem for repeated games: a neu condition","volume":"62","author":"Abreu","year":"1994","journal-title":"Econometrica"},{"issue":"5","key":"10.1016\/j.geb.2025.11.012_bib0004","doi-asserted-by":"crossref","first-page":"1041","DOI":"10.2307\/2938299","article-title":"Toward a theory of discounted repeated games with imperfect monitoring","volume":"58","author":"Abreu","year":"1990","journal-title":"Econometrica"},{"issue":"6","key":"10.1016\/j.geb.2025.11.012_bib0005","doi-asserted-by":"crossref","first-page":"1259","DOI":"10.2307\/1913097","article-title":"The structure of nash equilibrium in repeated games with finite automata","volume":"56","author":"Abreu","year":"1988","journal-title":"Econometrica"},{"issue":"2","key":"10.1016\/j.geb.2025.11.012_bib0006","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1016\/j.geb.2009.08.004","article-title":"The logit-response dynamics","volume":"68","author":"Al\u00f3s-Ferrer","year":"2010","journal-title":"Games Econ. Behav."},{"key":"10.1016\/j.geb.2025.11.012_bib0007","unstructured":"Askenazi-Golan, G., Cecchelli, D. M., Plumb, E., 2024. Reinforcement learning, collusion, and the folk theorem. Available at arXiv:2411.12725."},{"key":"10.1016\/j.geb.2025.11.012_bib0008","doi-asserted-by":"crossref","first-page":"452","DOI":"10.1257\/pandp.20221059","article-title":"Artificial intelligence, algorithm design, and pricing","volume":"112","author":"Asker","year":"2022","journal-title":"AEA Papers Proc."},{"key":"10.1016\/j.geb.2025.11.012_bib0009","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1111\/jems.12516","article-title":"The impact of AI design on pricing","volume":"33","author":"Asker","year":"2023","journal-title":"J. Econ. Manage. Strategy"},{"issue":"3","key":"10.1016\/j.geb.2025.11.012_bib0010","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1093\/oxrep\/grab011","article-title":"Autonomous algorithmic collusion: economic research and policy implications","volume":"37","author":"Assad","year":"2021","journal-title":"Oxford Rev. Econ. Policy"},{"issue":"1","key":"10.1016\/j.geb.2025.11.012_bib0011","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1016\/j.jet.2008.04.003","article-title":"Repeated games with one-memory","volume":"144","author":"Barlo","year":"2009","journal-title":"J. Econ. Theory"},{"key":"10.1016\/j.geb.2025.11.012_bib0012","doi-asserted-by":"crossref","first-page":"728","DOI":"10.1016\/j.jet.2016.03.001","article-title":"Bounded memory folk theorem","volume":"163","author":"Barlo","year":"2016","journal-title":"J. Econ. Theory"},{"key":"10.1016\/j.geb.2025.11.012_bib0013","series-title":"Proceedings of the 39th International Conference on Machine Learning","first-page":"1664","article-title":"Fictitious play and best-Response dynamics in identical interest and zero-sum stochastic games","author":"Baudin","year":"2022"},{"key":"10.1016\/j.geb.2025.11.012_bib0014","series-title":"Advances in Neural Information Processing Systems","first-page":"20243","article-title":"Smooth fictitious play in stochastic games with perturbed payoffs and unknown transitions","author":"Baudin","year":"2022"},{"issue":"1","key":"10.1016\/j.geb.2025.11.012_bib0015","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jet.2004.03.008","article-title":"On the convergence of reinforcement learning","volume":"122","author":"Beggs","year":"2005","journal-title":"J. Econ. Theory"},{"key":"10.1016\/j.geb.2025.11.012_bib0016","series-title":"S\u00e9minaire de Probabilit\u00e9s XXXIII","first-page":"1","article-title":"Dynamics of stochastic approximation algorithms","author":"Bena\u00efm","year":"1999"},{"issue":"1","key":"10.1016\/j.geb.2025.11.012_bib0017","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1006\/game.1999.0717","article-title":"Mixed equilibria and dynamical systems arising from fictitious play in perturbed games","volume":"29","author":"Bena\u00efm","year":"1999","journal-title":"Games Econ. Behav."},{"key":"10.1016\/j.geb.2025.11.012_bib0018","series-title":"Adaptive Algorithms and Stochastic Approximations","author":"Benveniste","year":"1990"},{"key":"10.1016\/j.geb.2025.11.012_bib0019","series-title":"Stochastic Approximation: a Dynamical Systems Viewpoint","author":"Borkar","year":"2008"},{"issue":"1","key":"10.1016\/j.geb.2025.11.012_bib0020","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1239\/aap\/1035227996","article-title":"The dynamic system method and the traps","volume":"30","author":"Brandi\u00e8re","year":"1998","journal-title":"Adv. Appl. Probab."},{"issue":"2","key":"10.1016\/j.geb.2025.11.012_bib0021","first-page":"109","article-title":"Competition in pricing algorithms","volume":"15","author":"Brown","year":"2023","journal-title":"Am. Econ. Rev."},{"issue":"1","key":"10.1016\/j.geb.2025.11.012_bib0022","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1006\/jeth.1997.2319","article-title":"Learning through reinforcement and replicator dynamics","volume":"77","author":"B\u00f6rgers","year":"1997","journal-title":"J. Econ. Theory"},{"issue":"10","key":"10.1016\/j.geb.2025.11.012_bib0023","doi-asserted-by":"crossref","first-page":"3267","DOI":"10.1257\/aer.20190623","article-title":"Artificial intelligence, algorithmic pricing, and collusion","volume":"110","author":"Calvano","year":"2020","journal-title":"Am. Econ. Rev."},{"key":"10.1016\/j.geb.2025.11.012_bib0024","doi-asserted-by":"crossref","DOI":"10.1016\/j.ijindorg.2021.102712","article-title":"Algorithmic collusion with imperfect monitoring","volume":"79","author":"Calvano","year":"2021","journal-title":"Int. J. Ind Organiz"},{"issue":"2","key":"10.1016\/j.geb.2025.11.012_bib0025","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/2465769.2465776","article-title":"Near-potential games: geometry and dynamics","volume":"1","author":"Candogan","year":"2013","journal-title":"ACM Trans. Econ. Comput. (TEAC)"},{"key":"10.1016\/j.geb.2025.11.012_bib0026","article-title":"The algorithmic learning equations: evolving strategies in dynamic games","author":"Cartea","year":"2022","journal-title":"Available at SSRN 4175239"},{"issue":"2","key":"10.1016\/j.geb.2025.11.012_bib0027","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/j.jet.2004.12.001","article-title":"Learning aspiration in repeated games","volume":"124","author":"Cho","year":"2005","journal-title":"J. Econ. Theory"},{"issue":"5","key":"10.1016\/j.geb.2025.11.012_bib0028","doi-asserted-by":"crossref","first-page":"2179","DOI":"10.1093\/restud\/rdab016","article-title":"Record-keeping and cooperation in large societies","volume":"88","author":"Clark","year":"2021","journal-title":"Rev. Econ. Stud."},{"issue":"3","key":"10.1016\/j.geb.2025.11.012_bib0029","doi-asserted-by":"crossref","first-page":"369","DOI":"10.3982\/TE632","article-title":"A theory of regular Markov perfect equilibria in dynamic stochastic games: genericity, stability, and purification","volume":"5","author":"Doraszelski","year":"2010","journal-title":"Theoretical Econ."},{"issue":"3","key":"10.1016\/j.geb.2025.11.012_bib0030","doi-asserted-by":"crossref","first-page":"567","DOI":"10.2307\/2297904","article-title":"Cooperation in the prisoner\u2019s dilemma with anonymous random matching","volume":"61","author":"Ellison","year":"1994","journal-title":"Rev. Econ. Stud."},{"issue":"4","key":"10.1016\/j.geb.2025.11.012_bib0031","first-page":"848","article-title":"Predicting how people play games: reinforcement learning in experimental games with unique, mixed strategy equilibria","volume":"88","author":"Erev","year":"1998","journal-title":"Am. Econ. Rev."},{"issue":"1","key":"10.1016\/j.geb.2025.11.012_bib0032","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1006\/game.1997.0595","article-title":"Calibrated learning and correlated equilibrium","volume":"21","author":"Foster","year":"1997","journal-title":"Games Econ. Behav."},{"issue":"22","key":"10.1016\/j.geb.2025.11.012_bib0033","doi-asserted-by":"crossref","first-page":"12848","DOI":"10.1073\/pnas.211534898","article-title":"On the impossibility of predicting the behavior of rational agents","volume":"98","author":"Foster","year":"2001","journal-title":"Proc. Nat. Acad. Sci."},{"issue":"1","key":"10.1016\/j.geb.2025.11.012_bib0034","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/S0899-8256(03)00025-3","article-title":"Learning, hypothesis testing, and nash equilibrium","volume":"45","author":"Foster","year":"2003","journal-title":"Games Econ. Behav."},{"issue":"1","key":"10.1016\/j.geb.2025.11.012_bib0035","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/j.jet.2005.04.006","article-title":"Imitation processes with small mutations","volume":"131","author":"Fudenberg","year":"2006","journal-title":"J. Econ. Theory"},{"issue":"1","key":"10.1016\/j.geb.2025.11.012_bib0036","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.jet.2007.08.002","article-title":"Monotone imitation dynamics in large populations","volume":"140","author":"Fudenberg","year":"2008","journal-title":"J. Econ. Theory"},{"issue":"3","key":"10.1016\/j.geb.2025.11.012_bib0037","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1006\/game.1993.1021","article-title":"Learning mixed equilibria","volume":"5","author":"Fudenberg","year":"1993","journal-title":"Games Econ. Behav."},{"issue":"5","key":"10.1016\/j.geb.2025.11.012_bib0038","doi-asserted-by":"crossref","first-page":"997","DOI":"10.2307\/2951505","article-title":"The folk theorem with imperfect public information","volume":"62","author":"Fudenberg","year":"1994","journal-title":"Econometrica"},{"key":"10.1016\/j.geb.2025.11.012_bib0039","series-title":"The Theory of Learning in Games","author":"Fudenberg","year":"1998"},{"issue":"1","key":"10.1016\/j.geb.2025.11.012_bib0040","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1006\/game.1998.0705","article-title":"Conditional universal consistency","volume":"29","author":"Fudenberg","year":"1999","journal-title":"Games Econ. Behav."},{"issue":"1","key":"10.1016\/j.geb.2025.11.012_bib0041","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1146\/annurev.economics.050708.142930","article-title":"Learning and equilibrium","volume":"1","author":"Fudenberg","year":"2009","journal-title":"Annu. Rev. Econom."},{"issue":"3","key":"10.1016\/j.geb.2025.11.012_bib0042","doi-asserted-by":"crossref","first-page":"533","DOI":"10.2307\/1911307","article-title":"The folk theorem in repeated games with discounting or with incomplete information","volume":"54","author":"Fudenberg","year":"1986","journal-title":"Econometrica"},{"issue":"2","key":"10.1016\/j.geb.2025.11.012_bib0043","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1016\/S0899-8256(03)00149-0","article-title":"A short proof of Harsanyi\u2019s purification theorem","volume":"45","author":"Govindan","year":"2003","journal-title":"Games Econ. Behav."},{"key":"10.1016\/j.geb.2025.11.012_bib0044","series-title":"The Oxford Handbook of International Antitrust Economics, Volume 2","first-page":"464","article-title":"Tacit collusion in oligopoly","author":"Green","year":"2014"},{"issue":"1","key":"10.1016\/j.geb.2025.11.012_bib0045","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1287\/mksc.2020.1276","article-title":"Frontiers: algorithmic collusion: supra-competitive prices via independent algorithms","volume":"40","author":"Hansen","year":"2021","journal-title":"Marketing Sci."},{"issue":"3","key":"10.1016\/j.geb.2025.11.012_bib0046","first-page":"331","article-title":"Developing competition law for collusion by autonomous artificial agents","volume":"14","author":"Harrington","year":"2018","journal-title":"J. Compet. Law Econom."},{"issue":"1","key":"10.1016\/j.geb.2025.11.012_bib0047","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01737554","article-title":"Games with randomly disturbed payoffs: a new rationale for mixed-Strategy equilibrium points","volume":"2","author":"Harsanyi","year":"1973","journal-title":"Int. J. Game Theory"},{"key":"10.1016\/j.geb.2025.11.012_bib0048","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1007\/BF01737572","article-title":"Oddness of the number of equilibrium points: a new proof","volume":"2","author":"Harsanyi","year":"1973","journal-title":"Inte. J. Game Theory"},{"issue":"2","key":"10.1016\/j.geb.2025.11.012_bib0049","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/S0899-8256(02)00502-X","article-title":"Evolutionary dynamics and backward induction","volume":"41","author":"Hart","year":"2002","journal-title":"Games Econ. Behav."},{"issue":"5","key":"10.1016\/j.geb.2025.11.012_bib0050","doi-asserted-by":"crossref","first-page":"1127","DOI":"10.1111\/1468-0262.00153","article-title":"A simple adaptive procedure leading to correlated equilibrium","volume":"68","author":"Hart","year":"2000","journal-title":"Econometrica"},{"key":"10.1016\/j.geb.2025.11.012_bib0051","series-title":"A Reinforcement Procedure Leading to Correlated Equilibrium","first-page":"181","author":"Hart","year":"2001"},{"issue":"5","key":"10.1016\/j.geb.2025.11.012_bib0052","doi-asserted-by":"crossref","first-page":"1830","DOI":"10.1257\/000282803322655581","article-title":"Uncoupled dynamics do not lead to nash equilibrium","volume":"93","author":"Hart","year":"2003","journal-title":"Am. Econ. Rev."},{"key":"10.1016\/j.geb.2025.11.012_bib0053","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.geb.2004.06.006","article-title":"Learning in perturbed asymmetric games","volume":"52","author":"Hofbauer","year":"2005","journal-title":"Games Econ. Behav."},{"issue":"6","key":"10.1016\/j.geb.2025.11.012_bib0054","doi-asserted-by":"crossref","first-page":"2265","DOI":"10.1111\/1468-0262.00376","article-title":"On the global convergence of stochastic fictitious play","volume":"70","author":"Hofbauer","year":"2002","journal-title":"Econometrica"},{"issue":"6","key":"10.1016\/j.geb.2025.11.012_bib0055","doi-asserted-by":"crossref","first-page":"2141","DOI":"10.1111\/1468-0262.00372","article-title":"Two competing models of how people learn in games","volume":"70","author":"Hopkins","year":"2002","journal-title":"Econometrica"},{"issue":"1","key":"10.1016\/j.geb.2025.11.012_bib0056","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1016\/j.geb.2004.08.002","article-title":"Attainability of boundary points under reinforcement learning","volume":"53","author":"Hopkins","year":"2005","journal-title":"Games Econ. Behav."},{"issue":"31","key":"10.1016\/j.geb.2025.11.012_bib0057","doi-asserted-by":"crossref","first-page":"10797","DOI":"10.1073\/pnas.0502589102","article-title":"Evolutionary cycles of cooperation and defection","volume":"102","author":"Imhof","year":"2005","journal-title":"Proc. Nat. Acad. Sci."},{"key":"10.1016\/j.geb.2025.11.012_bib0058","doi-asserted-by":"crossref","DOI":"10.1016\/j.jet.2022.105551","article-title":"Learning efficient equilibria in repeated games","volume":"205","author":"Jindani","year":"2022","journal-title":"J. Econ. Theory"},{"issue":"2","key":"10.1016\/j.geb.2025.11.012_bib0059","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1006\/jeth.1995.1082","article-title":"Limited horizon forecast in repeated alternate games","volume":"67","author":"J\u00e9hiel","year":"1995","journal-title":"J. Econ. Theory"},{"issue":"2","key":"10.1016\/j.geb.2025.11.012_bib0060","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1006\/game.1997.0589","article-title":"Learning to play limited forecast equilibria","volume":"22","author":"J\u00e9hiel","year":"1998","journal-title":"Games Econ Behav"},{"issue":"2","key":"10.1016\/j.geb.2025.11.012_bib0061","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.jet.2004.09.004","article-title":"Learning to play games in extensive form by valuation","volume":"124","author":"J\u00e9hiel","year":"2005","journal-title":"J. Econ. Theory"},{"issue":"5","key":"10.1016\/j.geb.2025.11.012_bib0062","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.2307\/2951492","article-title":"Rational learning leads to nash equilibrium","volume":"61","author":"Kalai","year":"1993","journal-title":"Econometrica"},{"issue":"1","key":"10.1016\/j.geb.2025.11.012_bib0063","doi-asserted-by":"crossref","first-page":"81","DOI":"10.2307\/2297926","article-title":"Repeated games played by overlapping generations of players","volume":"59","author":"Kandori","year":"1992","journal-title":"Rev. Econ. Stud"},{"issue":"2","key":"10.1016\/j.geb.2025.11.012_bib0064","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1006\/jeth.1997.2379","article-title":"Evolving aspirations and cooperation","volume":"80","author":"Karandikar","year":"1998","journal-title":"J. Econ. Theory"},{"key":"10.1016\/j.geb.2025.11.012_bib0065","series-title":"Stochastic Approximation Methods for Constrained and Unconstrained Systems","author":"Kushner","year":"1978"},{"key":"10.1016\/j.geb.2025.11.012_bib0066","doi-asserted-by":"crossref","unstructured":"Lamba, R., Zhuk, S., 2023. Pricing with algorithms. Available at SSRN 4085069.","DOI":"10.2139\/ssrn.4085069"},{"key":"10.1016\/j.geb.2025.11.012_bib0067","article-title":"Less than meets the eye: simultaneous experiments as a source of algorithmic seeming collusion","author":"Lambin","year":"2023","journal-title":"Available at SSRN 4498926"},{"key":"10.1016\/j.geb.2025.11.012_bib0068","series-title":"International Conference on Learning Representations","article-title":"Global convergence of multi-agent policy gradient in markov potential games","author":"Leonardos","year":"2022"},{"key":"10.1016\/j.geb.2025.11.012_bib0069","doi-asserted-by":"crossref","DOI":"10.1016\/j.jet.2020.105095","article-title":"Best-response dynamics in zero-sum stochastic games","volume":"189","author":"Leslie","year":"2020","journal-title":"J. Econ. Theory"},{"issue":"1","key":"10.1016\/j.geb.2025.11.012_bib0070","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/0304-4149(90)90120-H","article-title":"Stochastic approximations for finite-state Markov chains","volume":"35","author":"Ma","year":"1990","journal-title":"Stoch. Process. Their Appl."},{"key":"10.1016\/j.geb.2025.11.012_bib0071","unstructured":"Maheshwari, C., Wu, M., Pai, D., Sastry, S. S., 2023. Independent and decentralized learning in Markov potential games. Available at arXiv:2205.14590v4."},{"key":"10.1016\/j.geb.2025.11.012_bib0072","series-title":"Repeated Games and Reputations: Long-Run Relationships","author":"Mailath","year":"2006"},{"issue":"2","key":"10.1016\/j.geb.2025.11.012_bib0073","doi-asserted-by":"crossref","first-page":"788","DOI":"10.1016\/j.geb.2012.03.006","article-title":"Revisiting log-linear learning: asynchrony, completeness and payoff-based implementation","volume":"75","author":"Marden","year":"2012","journal-title":"Games Econ. Behav."},{"key":"10.1016\/j.geb.2025.11.012_bib0074","series-title":"International Conference on Machine Learning (ICML)","first-page":"7688","article-title":"Learning in nonzero-sum stochastic games with potentials","author":"Mguni","year":"2021"},{"issue":"1","key":"10.1016\/j.geb.2025.11.012_bib0075","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1006\/game.1996.0044","article-title":"Potential games","volume":"14","author":"Monderer","year":"1996","journal-title":"Games Econ. Behav."},{"issue":"2","key":"10.1016\/j.geb.2025.11.012_bib0076","doi-asserted-by":"crossref","first-page":"275","DOI":"10.2307\/2171894","article-title":"Prediction, optimization, and learning in repeated games","volume":"65","author":"Nachbar","year":"1997","journal-title":"Econometrica"},{"issue":"6983","key":"10.1016\/j.geb.2025.11.012_bib0077","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1038\/nature02414","article-title":"Emergence of cooperation and evolutionary stability in finite populations","volume":"428","author":"Nowak","year":"2004","journal-title":"Nature"},{"issue":"2","key":"10.1016\/j.geb.2025.11.012_bib0078","doi-asserted-by":"crossref","first-page":"698","DOI":"10.1214\/aop\/1176990853","article-title":"Nonconvergence to unstable points in urn models and stochastic approximations","volume":"18","author":"Pemantle","year":"1990","journal-title":"Ann. Probab."},{"issue":"2","key":"10.1016\/j.geb.2025.11.012_bib0079","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1287\/11-SSY056","article-title":"Asynchronous stochastic approximation with differential inclusions","volume":"2","author":"Perkins","year":"2012","journal-title":"Stochastic Syst."},{"issue":"1","key":"10.1016\/j.geb.2025.11.012_bib0080","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1016\/0022-0531(92)90075-S","article-title":"Finite automata equilibria with discounting","volume":"56","author":"Piccione","year":"1992","journal-title":"J. Econ. Theory"},{"issue":"1427","key":"10.1016\/j.geb.2025.11.012_bib0081","doi-asserted-by":"crossref","first-page":"1427","DOI":"10.1098\/rspb.1999.0797","article-title":"The efficiency of adapting aspiration levels","volume":"266","author":"Posch","year":"1999","journal-title":"Proc. Biol. Sci."},{"key":"10.1016\/j.geb.2025.11.012_bib0082","unstructured":"Salcedo, B., 2015. Pricing algorithms and tacit collusion."},{"key":"10.1016\/j.geb.2025.11.012_bib0083","first-page":"18320","article-title":"Decentralized Q-learning in zero-sum Markov games","volume":"35","author":"Sayin","year":"2021","journal-title":"Adv. Neural Inf. Process. Syst."},{"issue":"4","key":"10.1016\/j.geb.2025.11.012_bib0084","doi-asserted-by":"crossref","first-page":"2095","DOI":"10.1137\/21M1426675","article-title":"Fictitious play in zero-Sum stochastic games","volume":"60","author":"Sayin","year":"2022","journal-title":"SIAM J. Control Optim."},{"issue":"3","key":"10.1016\/j.geb.2025.11.012_bib0085","doi-asserted-by":"crossref","first-page":"1175","DOI":"10.3982\/TE3820","article-title":"Common learning and cooperation in repeated games","volume":"15","author":"Sugaya","year":"2020","journal-title":"Theoretical Econ."},{"issue":"10","key":"10.1016\/j.geb.2025.11.012_bib0086","doi-asserted-by":"crossref","first-page":"3275","DOI":"10.1016\/j.jedc.2008.01.003","article-title":"Q-learning agents in a cournot oligopoly model","volume":"32","author":"Waltman","year":"2008","journal-title":"J. Econ. Dyn. Control"},{"key":"10.1016\/j.geb.2025.11.012_bib0087","doi-asserted-by":"crossref","DOI":"10.1016\/j.jedc.2022.104567","article-title":"Learning and equilibrium transitions: stochastic stability in discounted stochastic fictitious play","volume":"145","author":"Williams","year":"2022","journal-title":"J. Econ. Dyn. Control"},{"issue":"2","key":"10.1016\/j.geb.2025.11.012_bib0088","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1111\/j.1468-0262.2005.00589.x","article-title":"A partial folk theorem for games with unknown payoff distributions","volume":"73","author":"Wiseman","year":"2005","journal-title":"Econometrica"},{"issue":"2","key":"10.1016\/j.geb.2025.11.012_bib0089","doi-asserted-by":"crossref","first-page":"217","DOI":"10.3982\/TE913","article-title":"A partial folk theorem for games with private learning","volume":"7","author":"Wiseman","year":"2012","journal-title":"Theoretical Economics"}],"container-title":["Games and Economic Behavior"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0899825625001745?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0899825625001745?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T12:34:16Z","timestamp":1773750856000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0899825625001745"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3]]},"references-count":89,"alternative-id":["S0899825625001745"],"URL":"https:\/\/doi.org\/10.1016\/j.geb.2025.11.012","relation":{},"ISSN":["0899-8256"],"issn-type":[{"value":"0899-8256","type":"print"}],"subject":[],"published":{"date-parts":[[2026,3]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Algorithmic collusion and a folk theorem from learning with bounded rationality","name":"articletitle","label":"Article Title"},{"value":"Games and Economic Behavior","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.geb.2025.11.012","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2025 The Author(s). Published by Elsevier Inc.","name":"copyright","label":"Copyright"}]}}