{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T16:08:05Z","timestamp":1773936485429,"version":"3.50.1"},"reference-count":30,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2025,12,20]],"date-time":"2025-12-20T00:00:00Z","timestamp":1766188800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["ECCS-2336842"],"award-info":[{"award-number":["ECCS-2336842"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["ECCS-2342073"],"award-info":[{"award-number":["ECCS-2342073"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Systems &amp; Control Letters"],"published-print":{"date-parts":[[2026,1]]},"DOI":"10.1016\/j.sysconle.2025.106326","type":"journal-article","created":{"date-parts":[[2025,12,22]],"date-time":"2025-12-22T11:58:32Z","timestamp":1766404712000},"page":"106326","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["On zero-sum game representation for replicator dynamics"],"prefix":"10.1016","volume":"208","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0181-3922","authenticated-orcid":false,"given":"Haoyu","family":"Yin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0135-0606","authenticated-orcid":false,"given":"Xudong","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5778-4879","authenticated-orcid":false,"given":"Bruno","family":"Sinopoli","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"issue":"2","key":"10.1016\/j.sysconle.2025.106326_b1","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1006\/jtbi.2002.3067","article-title":"Replicator dynamics for optional public good games","volume":"218","author":"Hauert","year":"2002","journal-title":"J. Theoret. Biol."},{"key":"10.1016\/j.sysconle.2025.106326_b2","series-title":"Evolutionary Game Theory","author":"Weibull","year":"1997"},{"key":"10.1016\/j.sysconle.2025.106326_b3","series-title":"Evolutionary Games and Population Dynamics","author":"Hofbauer","year":"1998"},{"key":"10.1016\/j.sysconle.2025.106326_b4","series-title":"Population Games and Evolutionary Dynamics","author":"Sandholm","year":"2010"},{"key":"10.1016\/j.sysconle.2025.106326_b5","series-title":"Differential equation approximations for population games using elementary probability","author":"Kara","year":"2023"},{"key":"10.1016\/j.sysconle.2025.106326_b6","series-title":"Payoff dynamics model and evolutionary dynamics model: Feedback and convergence to equilibria","author":"Park","year":"2019"},{"issue":"1","key":"10.1016\/j.sysconle.2025.106326_b7","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1007\/s00182-025-00929-3","article-title":"On the discrete-time origins of the replicator dynamics: From convergence to instability and chaos","volume":"54","author":"Falniowski","year":"2025","journal-title":"Int. J. Game Theory"},{"key":"10.1016\/j.sysconle.2025.106326_b8","series-title":"Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms","first-page":"2703","article-title":"Cycles in adversarial regularized learning","author":"Mertikopoulos","year":"2018"},{"issue":"4","key":"10.1016\/j.sysconle.2025.106326_b9","article-title":"Replicator dynamics: Old and new.","volume":"7","author":"Sorin","year":"2020","journal-title":"J. Dyn. Games"},{"key":"10.1016\/j.sysconle.2025.106326_b10","doi-asserted-by":"crossref","unstructured":"D. Hennes, D. Morrill, S. Omidshafiei, R. Munos, J. Perolat, M. Lanctot, A. Gruslys, J.B. Lespiau, P. Parmas, E. Du\u00e9\u00f1ez Guzm\u00e1n, et al., Neural replicator dynamics: Multiagent learning via hedging policy gradients, in: Proceedings of the 19th International Conference on Autonomous Agents and Multiagent Systems, 2020, pp. 492\u2013501.","DOI":"10.65109\/GJMW6851"},{"key":"10.1016\/j.sysconle.2025.106326_b11","series-title":"International Conference on Quantitative Evaluation of Systems and Formal Modeling and Analysis of Timed Systems","first-page":"302","article-title":"Multi-agent path finding for timed tasks using evolutionary games","author":"Paul","year":"2024"},{"key":"10.1016\/j.sysconle.2025.106326_b12","doi-asserted-by":"crossref","unstructured":"T. Mai, M. Mihail, I. Panageas, W. Ratcliff, V. Vazirani, P. Yunker, Cycles in zero-sum differential games and biological diversity, in: Proceedings of the 2018 ACM Conference on Economics and Computation, 2018, pp. 339\u2013350.","DOI":"10.1145\/3219166.3219227"},{"key":"10.1016\/j.sysconle.2025.106326_b13","article-title":"Permanence in Lotka-Volterra and replicator equations","author":"Amann","year":"1985","journal-title":"Lotka-Volterra Approach Coop. Comp\u00e9t. Dyn. Syst. Berl."},{"key":"10.1016\/j.sysconle.2025.106326_b14","series-title":"Dynamical Systems: Proceedings of an IIASA Workshop on Mathematics of Dynamic Processes Held at Sopron, Hungary, September 9\u201313, 1985","first-page":"70","article-title":"Permanence for replicator equations","author":"Hofbauer","year":"1987"},{"key":"10.1016\/j.sysconle.2025.106326_b15","first-page":"11343","article-title":"Evolutionary game theory squared: Evolving agents in endogenously evolving zero-sum games","volume":"vol. 35, no. 13","author":"Skoulakis","year":"2021"},{"key":"10.1016\/j.sysconle.2025.106326_b16","series-title":"2019 IEEE 58th Conference on Decision and Control","first-page":"6584","article-title":"From population games to payoff dynamics models: A passivity-based approach","author":"Park","year":"2019"},{"issue":"3","key":"10.1016\/j.sysconle.2025.106326_b17","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1109\/MCS.2022.3157119","article-title":"Dissipativity theory in game theory: On the role of dissipativity and passivity in Nash equilibrium seeking","volume":"42","author":"Pavel","year":"2022","journal-title":"IEEE Control Syst. Mag."},{"issue":"1","key":"10.1016\/j.sysconle.2025.106326_b18","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1109\/TCNS.2020.3029990","article-title":"Dissipativity tools for convergence to Nash equilibria in population games","volume":"8","author":"Arcak","year":"2020","journal-title":"IEEE Trans. Control. Netw. Syst."},{"key":"10.1016\/j.sysconle.2025.106326_b19","series-title":"2018 IEEE Conference on Decision and Control","first-page":"3553","article-title":"Passivity and evolutionary game dynamics","author":"Park","year":"2018"},{"key":"10.1016\/j.sysconle.2025.106326_b20","series-title":"International Conference on Algorithmic Learning Theory","first-page":"161","article-title":"The attractor of the replicator dynamic in zero-sum games","author":"Biggar","year":"2024"},{"key":"10.1016\/j.sysconle.2025.106326_b21","series-title":"Global Theory of Dynamical Systems: Proceedings of an International Conference Held at Northwestern University, Evanston, Illinois, June 18\u201322, 1979","first-page":"471","article-title":"Population dynamics from game theory","author":"Zeeman","year":"2006"},{"issue":"3","key":"10.1016\/j.sysconle.2025.106326_b22","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/BF00318088","article-title":"Lotka-Volterra equation and replicator dynamics: A two-dimensional classification","volume":"48","author":"Bomze","year":"1983","journal-title":"Biol. Cybernet."},{"issue":"5","key":"10.1016\/j.sysconle.2025.106326_b23","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1007\/BF00201420","article-title":"Lotka-Volterra equation and replicator dynamics: New issues in classification","volume":"72","author":"Bomze","year":"1995","journal-title":"Biol. Cybernet."},{"key":"10.1016\/j.sysconle.2025.106326_b24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2020.05.004","article-title":"Networks beyond pairwise interactions: Structure and dynamics","volume":"874","author":"Battiston","year":"2020","journal-title":"Phys. Rep."},{"key":"10.1016\/j.sysconle.2025.106326_b25","series-title":"Replicator Dynamics with Alternate Growth Functions, Delay, and Quasiperiodic Forcing","author":"Wesson","year":"2015"},{"key":"10.1016\/j.sysconle.2025.106326_b26","series-title":"Introduction to Complex Analysis in Several Variables","author":"Scheidemann","year":"2005"},{"key":"10.1016\/j.sysconle.2025.106326_b27","series-title":"Elements of Algebra","author":"Euler","year":"2012"},{"key":"10.1016\/j.sysconle.2025.106326_b28","series-title":"Analytic Combinatorics","author":"Flajolet","year":"2009"},{"key":"10.1016\/j.sysconle.2025.106326_b29","series-title":"Matrix Computations","author":"Golub","year":"2013"},{"key":"10.1016\/j.sysconle.2025.106326_b30","series-title":"Theory of Approximation of Functions of a Real Variable","author":"Timan","year":"2014"}],"container-title":["Systems &amp; Control Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0167691125003081?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0167691125003081?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T14:14:11Z","timestamp":1773929651000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0167691125003081"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1]]},"references-count":30,"alternative-id":["S0167691125003081"],"URL":"https:\/\/doi.org\/10.1016\/j.sysconle.2025.106326","relation":{},"ISSN":["0167-6911"],"issn-type":[{"value":"0167-6911","type":"print"}],"subject":[],"published":{"date-parts":[[2026,1]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"On zero-sum game representation for replicator dynamics","name":"articletitle","label":"Article Title"},{"value":"Systems & Control Letters","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.sysconle.2025.106326","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"Published by Elsevier B.V.","name":"copyright","label":"Copyright"}],"article-number":"106326"}}