{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,12]],"date-time":"2026-08-12T13:31:56Z","timestamp":1786541516710,"version":"3.56.0"},"reference-count":46,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T00:00:00Z","timestamp":1777680000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T00:00:00Z","timestamp":1777680000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Oper Res Int J"],"published-print":{"date-parts":[[2026,9]]},"DOI":"10.1007\/s12351-026-01049-w","type":"journal-article","created":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T09:18:57Z","timestamp":1777713537000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Asymmetric stochastic games: an evolutionary approach"],"prefix":"10.1007","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9599-5319","authenticated-orcid":false,"given":"Divya","family":"Murali","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A. J.","family":"Shaiju","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,5,2]]},"reference":[{"key":"1049_CR1","unstructured":"Altman E, Hayel Y, Tembine H, ElAzouzi R (2010) Markov decision evolutionary games with time average expected fitness criterion. In 3rd International ICST Conference on Performance Evaluation Methodologies and Tools, vol.\u00a05. ICST"},{"key":"1049_CR2","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1016\/j.jet.2005.08.008","volume":"133","author":"D Balkenborg","year":"2007","unstructured":"Balkenborg D, Schlag K (2007) On the evolutionary selection of sets of nash equilibria. J Econ Theory 133:295\u2013315","journal-title":"J Econ Theory"},{"issue":"1","key":"1049_CR3","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1214\/aoms\/1177698513","volume":"39","author":"D Blackwell","year":"1968","unstructured":"Blackwell D, Ferguson TS (1968) The big match. Ann Math Statist 39(1):159\u2013163","journal-title":"Ann Math Statist"},{"issue":"1","key":"1049_CR4","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1142\/S0219525902000535","volume":"5","author":"VS Borkar","year":"2002","unstructured":"Borkar VS (2002) Reinforcement learning in markovian evolutionary games. Adv Complex Syst 5(1):55\u201372","journal-title":"Adv Complex Syst"},{"key":"1049_CR5","doi-asserted-by":"crossref","unstructured":"Brunetti I, Hayel Y, Altman E (2015) State policy couple dynamics in evolutionary games. In 2015 American Control Conference (ACC), pp. 1758\u20131763","DOI":"10.1109\/ACC.2015.7170987"},{"key":"1049_CR6","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/2884.001.0001","volume-title":"Evolutionary Dynamics and Extensive Form Games","author":"R Cressman","year":"2003","unstructured":"Cressman R (2003) Evolutionary Dynamics and Extensive Form Games. MIT Press, Cambridge"},{"key":"1049_CR7","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1007\/BF00280661","volume":"18","author":"I Eshel","year":"1983","unstructured":"Eshel I, Akin E (1983) Coevolutionary instability of mixed nash solutions. J Math Biol 18:123\u2013133","journal-title":"J Math Biol"},{"key":"1049_CR8","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2023.114068","volume":"175","author":"M Feng","year":"2023","unstructured":"Feng M, Han S, Li Q, Wu J, Kurths J (2023) Harmful strong agents and asymmetric interaction can promote the frequency of cooperation in the snowdrift game. Chaos Solitons & Fractals 175:114068","journal-title":"Chaos Solitons & Fractals"},{"issue":"1","key":"1049_CR9","doi-asserted-by":"publisher","first-page":"609","DOI":"10.1109\/TSMC.2023.3315963","volume":"54","author":"M Feng","year":"2024","unstructured":"Feng M, Pi B, Deng L-J, Kurths J (2024) An evolutionary game with the game transitions based on the markov process. IEEE Trans Syst Man Cybernetics Syst 54(1):609\u2013621","journal-title":"IEEE Trans Syst Man Cybernetics Syst"},{"issue":"8","key":"1049_CR10","doi-asserted-by":"publisher","first-page":"5123","DOI":"10.1109\/TSMC.2024.3389095","volume":"54","author":"M Feng","year":"2024","unstructured":"Feng M, Zeng Z, Li Q, Perc M, Kurths J (2024) Information dynamics in evolving networks based on the birth-death process: Random drift and natural selection perspective. IEEE Trans Syst Man Cybernetics Syst 54(8):5123\u20135136","journal-title":"IEEE Trans Syst Man Cybernetics Syst"},{"key":"1049_CR11","volume-title":"Competitive Markov Decision Processes","author":"J Filar","year":"1997","unstructured":"Filar J, Vrieze K (1997) Competitive Markov Decision Processes. Springer-Verlag, New York"},{"issue":"1","key":"1049_CR12","first-page":"89","volume":"28","author":"AM Fink","year":"1964","unstructured":"Fink AM (1964) Equilibrium in a stochastic n-person game. J Sci Hiroshima Univ Ser A-I Math 28(1):89\u201393","journal-title":"J Sci Hiroshima Univ Ser A-I Math"},{"key":"1049_CR13","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1007\/s13235-012-0059-2","volume":"3","author":"J Flesch","year":"2013","unstructured":"Flesch J, Parthasarathy T, Thuijsman F, Uyttendaele P (2013) Evolutionary Stochastic Games Dyn Games Appl 3:207\u2013219","journal-title":"Evolutionary Stochastic Games Dyn Games Appl"},{"key":"1049_CR14","volume-title":"Representable infinite games","author":"D Gillette","year":"1953","unstructured":"Gillette D (1953) Representable infinite games. University of California, Berkeley, PhD.Thesis"},{"key":"1049_CR15","first-page":"179","volume":"39","author":"D Gillette","year":"1957","unstructured":"Gillette D (1957) Stochastic games with zero stop probabilities. Contributions to the Theory of Games, Vol. III Annals Math Stud 39:179\u2013187","journal-title":"III Annals Math Stud"},{"key":"1049_CR16","doi-asserted-by":"crossref","unstructured":"Hennes D, Tuyls K, Rauterberg M (2009) State-coupled replicator dynamics. In Proceedings of The 8th International Conference on Autonomous Agents and Multiagent Systems, pp. 789\u2013796. International Foundation for Autonomous Agents and Multiagent Systems","DOI":"10.65109\/RBSY8382"},{"key":"1049_CR17","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1038\/s41586-018-0277-x","volume":"559","author":"C Hilbe","year":"2018","unstructured":"Hilbe C, \u0160imsa \u0160, Chatterjee K, Nowak MA (2018) Evolution of cooperation in stochastic games. Nature 559:246\u2013249","journal-title":"Nature"},{"key":"1049_CR18","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139173179","volume-title":"Evolutionary Games and Population Dynamics","author":"J Hofbauer","year":"1998","unstructured":"Hofbauer J, Sigmund K (1998) Evolutionary Games and Population Dynamics. Cambridge University Press, Cambridge"},{"key":"1049_CR19","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.107.044301","volume":"107","author":"K Hu","year":"2023","unstructured":"Hu K, Wang P, He J, Perc M, Shi L (2023) Complex evolutionary interactions in multiple populations. Phys Rev E 107:044301","journal-title":"Phys Rev E"},{"issue":"2","key":"1049_CR20","doi-asserted-by":"publisher","DOI":"10.1063\/5.0192619","volume":"34","author":"Y Jing","year":"2024","unstructured":"Jing Y, Han S, Feng M, Kurths J (2024) Co-evolution of heterogeneous cognition in spatial snowdrift game with asymmetric cost. Chaos Interdisciplinary J Nonlinear Sci 34(2):023109","journal-title":"Chaos Interdisciplinary J Nonlinear Sci"},{"key":"1049_CR21","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1016\/j.ress.2018.08.014","volume":"181","author":"KC Lalropuia","year":"2019","unstructured":"Lalropuia KC, Gupta V (2019) Modeling cyber-physical attacks based on stochastic game and markov processes. Reliability Eng Syst Safety 181:28\u201337","journal-title":"Reliability Eng Syst Safety"},{"key":"1049_CR22","doi-asserted-by":"publisher","DOI":"10.1016\/j.jet.2020.105095","volume":"189","author":"DS Leslie","year":"2020","unstructured":"Leslie DS, Perkins S, Xu Z (2020) Best-response dynamics in zero-sum stochastic games. J Econ Theory 189:105095","journal-title":"J Econ Theory"},{"issue":"1","key":"1049_CR23","doi-asserted-by":"publisher","first-page":"322","DOI":"10.2307\/3003416","volume":"11","author":"D Levhari","year":"1980","unstructured":"Levhari D, Mirman LJ (1980) The great fish war: An example using a dynamic cournot-nash solution. Bell J Econ 11(1):322\u2013334","journal-title":"Bell J Econ"},{"key":"1049_CR24","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1038\/246015a0","volume":"246","author":"J Maynard Smith","year":"1973","unstructured":"Maynard Smith J, Price GR (1973) The logic of animal conflict. Nature 246:15\u201318","journal-title":"Nature"},{"key":"1049_CR25","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1007\/BF01769259","volume":"10","author":"J Mertens","year":"1981","unstructured":"Mertens J, Neymen A (1981) Stochastic games. Internat. J. Game Theory 10:53\u201366","journal-title":"Game Theory"},{"key":"1049_CR26","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139343275","volume-title":"Repeated Games","author":"J Mertens","year":"2015","unstructured":"Mertens J, Sorin S, Zamir S (2015) Repeated Games. Cambridge University Press, Cambridge, UK"},{"issue":"3","key":"1049_CR27","doi-asserted-by":"publisher","first-page":"270","DOI":"10.3934\/jdg.2023004","volume":"10","author":"D Murali","year":"2023","unstructured":"Murali D, Shaiju AJ (2023) Dynamic stability of the set of nash equilibria in stable stochastic games. J Dynamics Games 10(3):270\u2013286","journal-title":"J Dynamics Games"},{"issue":"4","key":"1049_CR28","doi-asserted-by":"publisher","first-page":"2350010","DOI":"10.1142\/S021919892350010X","volume":"25","author":"D Murali","year":"2023","unstructured":"Murali D, Shaiju AJ (2023) Best-response dynamics for evolutionary stochastic games. Int Game Theory Rev 25(4):2350010","journal-title":"Int Game Theory Rev"},{"issue":"6","key":"1049_CR29","doi-asserted-by":"publisher","DOI":"10.1063\/5.0215761","volume":"34","author":"B Pi","year":"2024","unstructured":"Pi B, Feng M, Deng L-J (2024) A memory-based spatial evolutionary game with the dynamic interaction between learners and profiteers. Chaos Interdisciplinary J Nonlinear Sci 34(6):063120","journal-title":"Chaos Interdisciplinary J Nonlinear Sci"},{"key":"1049_CR30","doi-asserted-by":"crossref","unstructured":"Raghavan TES, Ferguson TS, Parthsarathy T, (Eds.) Vrieze OJ (1991) Stochastic games and related topics. Springer Dordrecht, Kluwer Academic Publishers","DOI":"10.1007\/978-94-011-3760-7"},{"issue":"6","key":"1049_CR31","doi-asserted-by":"publisher","first-page":"1371","DOI":"10.2307\/2171774","volume":"63","author":"K Ritzberger","year":"1995","unstructured":"Ritzberger K, Weibull J (1995) Evolutionary selection in normal-form games. Econometrica 63(6):1371\u20131399","journal-title":"Econometrica"},{"key":"1049_CR32","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1016\/0022-0531(92)90041-F","volume":"57","author":"L Samuelson","year":"1992","unstructured":"Samuelson L, Zhang J (1992) Evolutionary stability in asymmetric games. J Econ Theory 57:363\u2013391","journal-title":"J Econ Theory"},{"key":"1049_CR33","volume-title":"Population Games and Evolutionary Dynamics","author":"W Sandholm","year":"2010","unstructured":"Sandholm W (2010) Population Games and Evolutionary Dynamics. MIT Press, Cambridge"},{"key":"1049_CR34","doi-asserted-by":"publisher","DOI":"10.1515\/9781400880881","volume-title":"Game Theory in Action: An Introduction to Classical and Evolutionary Models","author":"S Schecter","year":"2016","unstructured":"Schecter S, Gintis H (2016) Game Theory in Action: An Introduction to Classical and Evolutionary Models. Princeton University Press, Princeton"},{"key":"1049_CR35","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1016\/S0022-5193(80)81038-1","volume":"84","author":"R Selten","year":"1980","unstructured":"Selten R (1980) A note on evolutionarily stable strategies in asymmetric animal conflicts. J Theor Biol 84:93\u2013101","journal-title":"J Theor Biol"},{"issue":"10","key":"1049_CR36","doi-asserted-by":"publisher","first-page":"1095","DOI":"10.1073\/pnas.39.10.1095","volume":"39","author":"LS Shapley","year":"1953","unstructured":"Shapley LS (1953) Stochastic games. Proc Natl Acad Sci USA 39(10):1095\u20131100","journal-title":"Proc Natl Acad Sci USA"},{"key":"1049_CR37","doi-asserted-by":"crossref","unstructured":"Sigmund K (2011) Introduction to evolutionary game theory. In Evolutionary game dynamics, vol.\u00a069 of Proc. Sympos. Appl. Math., pp. 1\u201325. Amer. Math. Soc., Providence, RI","DOI":"10.1090\/psapm\/069\/2882632"},{"key":"1049_CR38","doi-asserted-by":"publisher","DOI":"10.1017\/9781009029704","volume-title":"A Course in Stochastic Game Theory","author":"E Solan","year":"2022","unstructured":"Solan E (2022) A Course in Stochastic Game Theory. Cambridge University Press, Cambridge, UK"},{"issue":"45","key":"1049_CR39","doi-asserted-by":"publisher","first-page":"13743","DOI":"10.1073\/pnas.1513508112","volume":"112","author":"E Solan","year":"2015","unstructured":"Solan E, Vieille N (2015) Stochastic games. Proc Natl Acad Sci 112(45):13743\u201313746","journal-title":"Proc Natl Acad Sci"},{"key":"1049_CR40","doi-asserted-by":"publisher","first-page":"23633","DOI":"10.1038\/srep23633","volume":"6","author":"A Szolnoki","year":"2016","unstructured":"Szolnoki A, Perc M (2016) Leaders should not be conformists in evolutionary social dilemmas. Sci Rep 6:23633","journal-title":"Sci Rep"},{"issue":"1","key":"1049_CR41","first-page":"95","volume":"28","author":"M Takahashi","year":"1964","unstructured":"Takahashi M (1964) Equilibrium points of stochastic non-cooperative n-person games. J Sci Hiroshima Univ Ser A-I Math 28(1):95\u201399","journal-title":"J Sci Hiroshima Univ Ser A-I Math"},{"key":"1049_CR42","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1016\/0025-5564(78)90077-9","volume":"40","author":"PD Taylor","year":"1978","unstructured":"Taylor PD, Jonker LB (1978) Evolutionarily stable strategies and game dynamics. Math Biosci 40:145\u2013156","journal-title":"Math Biosci"},{"key":"1049_CR43","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1007\/BF00276549","volume":"22","author":"B Thomas","year":"1985","unstructured":"Thomas B (1985) On evolutionarily stable sets. J Math Biol 22:105\u2013115","journal-title":"J Math Biol"},{"key":"1049_CR44","doi-asserted-by":"crossref","unstructured":"Vrieze OJ (2003) Stochastic games and stationary strategies In Neyman A Sorin S (eds) Stochastic Games and Applications NATO Science Series 570:37\u201350","DOI":"10.1007\/978-94-010-0189-2_4"},{"key":"1049_CR45","volume-title":"Evolutionary Game Theory","author":"JW Weibull","year":"1995","unstructured":"Weibull JW (1995) Evolutionary Game Theory. MIT Press, Cambridge"},{"issue":"4","key":"1049_CR46","doi-asserted-by":"publisher","first-page":"2546","DOI":"10.1109\/TSMC.2025.3525465","volume":"55","author":"Z Zeng","year":"2025","unstructured":"Zeng Z, Feng M, Liu P, Kurths J (2025) Complex network modeling with power-law activating patterns and its evolutionary dynamics. IEEE Trans Syst Man Cybernetics Syst 55(4):2546\u20132559","journal-title":"IEEE Trans Syst Man Cybernetics Syst"}],"container-title":["Operational Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12351-026-01049-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12351-026-01049-w","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12351-026-01049-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,12]],"date-time":"2026-08-12T12:42:47Z","timestamp":1786538567000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12351-026-01049-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,2]]},"references-count":46,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2026,9]]}},"alternative-id":["1049"],"URL":"https:\/\/doi.org\/10.1007\/s12351-026-01049-w","relation":{},"ISSN":["1109-2858","1866-1505"],"issn-type":[{"value":"1109-2858","type":"print"},{"value":"1866-1505","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,2]]},"assertion":[{"value":"6 December 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 January 2026","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 March 2026","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 May 2026","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors have no conflict of interest to declare.","order":1,"name":"Ethics","label":"Conflict of interest","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable","order":2,"name":"Ethics","label":"Ethics approval and consent to participate","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"All the authors consent to the submission and subsequent publication of the manuscript.","order":3,"name":"Ethics","label":"Consent for publication","group":{"name":"EthicsHeading","label":"Declarations"}}],"article-number":"55"}}