{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T21:03:50Z","timestamp":1784667830084,"version":"3.55.0"},"reference-count":54,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100012456","name":"National Social Science Fund of China","doi-asserted-by":"publisher","award":["ZD136"],"award-info":[{"award-number":["ZD136"]}],"id":[{"id":"10.13039\/501100012456","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100018529","name":"Major Project of Philosophy and Social Science Research in Colleges and Universities of Jiangsu Province","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100018529","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Applied Mathematics and Computation"],"published-print":{"date-parts":[[2026,12]]},"DOI":"10.1016\/j.amc.2026.130221","type":"journal-article","created":{"date-parts":[[2026,6,26]],"date-time":"2026-06-26T12:57:18Z","timestamp":1782478638000},"page":"130221","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Evolution of cooperation through dynamic probabilistic punishment under individual camouflage"],"prefix":"10.1016","volume":"531","author":[{"given":"Jingyi","family":"Wang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-0026-390X","authenticated-orcid":false,"given":"Hangkun","family":"Hu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Minggang","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lixin","family":"Tian","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"5427","key":"10.1016\/j.amc.2026.130221_bib0001","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1038\/246015a0","article-title":"The logic of animal conflict","volume":"246","author":"Maynard Smith","year":"1973","journal-title":"Nature"},{"key":"10.1016\/j.amc.2026.130221_bib0002","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2017.05.004","article-title":"Statistical physics of human cooperation","volume":"687","author":"Perc","year":"2017","journal-title":"Phys. Rep."},{"issue":"12","key":"10.1016\/j.amc.2026.130221_bib0003","doi-asserted-by":"crossref","DOI":"10.1063\/5.0242606","article-title":"Evolution of cooperation with early social influence for explaining collective action","volume":"34","author":"He","year":"2024","journal-title":"Chaos: Interdiscip. J. Nonlinear Sci."},{"issue":"5","key":"10.1016\/j.amc.2026.130221_bib0004","doi-asserted-by":"crossref","first-page":"1733","DOI":"10.1007\/s13235-025-00619-5","article-title":"Public goods games in disease evolution and spread","volume":"15","author":"Morison","year":"2025","journal-title":"Dyn. Games Appl."},{"key":"10.1016\/j.amc.2026.130221_bib0005","series-title":"Evolutionary games and population dynamics","author":"Hofbauer","year":"1998"},{"issue":"11","key":"10.1016\/j.amc.2026.130221_bib0006","doi-asserted-by":"crossref","first-page":"4643","DOI":"10.1007\/s11538-018-00545-1","article-title":"Generalized social dilemmas: the evolution of cooperation in populations with variable group size","volume":"81","author":"Broom","year":"2019","journal-title":"Bull. Math. Biol."},{"issue":"1876","key":"10.1016\/j.amc.2026.130221_bib0007","doi-asserted-by":"crossref","DOI":"10.1098\/rstb.2021.0502","article-title":"Evolutionary game theory and the adaptive dynamics approach: adaptation where individuals interact","volume":"378","author":"Avila","year":"2023","journal-title":"Philos. Trans. R. Soc. B."},{"issue":"2","key":"10.1016\/j.amc.2026.130221_bib0008","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1007\/s40305-021-00350-z","article-title":"Game theory and the evolution of cooperation","volume":"10","author":"Zhang","year":"2022","journal-title":"J. Oper. Res. Soc. China"},{"issue":"5659","key":"10.1016\/j.amc.2026.130221_bib0009","doi-asserted-by":"crossref","first-page":"793","DOI":"10.1126\/science.1093411","article-title":"Evolutionary dynamics of biological games","volume":"303","author":"Nowak","year":"2004","journal-title":"Science"},{"issue":"5805","key":"10.1016\/j.amc.2026.130221_bib0010","doi-asserted-by":"crossref","first-page":"1560","DOI":"10.1126\/science.1133755","article-title":"Five rules for the evolution of cooperation","volume":"314","author":"Nowak","year":"2006","journal-title":"Science"},{"key":"10.1016\/j.amc.2026.130221_bib0011","doi-asserted-by":"crossref","DOI":"10.1016\/j.eswa.2023.121579","article-title":"Coevolutionary dynamics of population and institutional rewards in public goods games","volume":"237","author":"Hua","year":"2024","journal-title":"Expert Syst. Appl."},{"issue":"4","key":"10.1016\/j.amc.2026.130221_bib0012","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/j.plrev.2009.08.001","article-title":"Evolutionary game theory: temporal and spatial effects beyond replicator dynamics","volume":"6","author":"Roca","year":"2009","journal-title":"Phys. Life Rev."},{"issue":"12","key":"10.1016\/j.amc.2026.130221_bib0013","doi-asserted-by":"crossref","DOI":"10.1088\/1367-2630\/aca995","article-title":"Evolution dynamics with the switching strategy of punishment and expulsion in the spatial public goods game","volume":"24","author":"Zhuo","year":"2022","journal-title":"New J. Phys."},{"issue":"1","key":"10.1016\/j.amc.2026.130221_bib0014","doi-asserted-by":"crossref","DOI":"10.1073\/pnas.2113468118","article-title":"Evolution of cooperation with asymmetric social interactions","volume":"119","author":"Su","year":"2022","journal-title":"Proc. Natl. Acad. Sci."},{"key":"10.1016\/j.amc.2026.130221_bib0015","article-title":"Reinforcement learning in evolutionary game theory: a brief review of recent developments","volume":"510","author":"Xie","year":"2026","journal-title":"Appl. Math. Comput."},{"issue":"3","key":"10.1016\/j.amc.2026.130221_bib0016","doi-asserted-by":"crossref","first-page":"2133","DOI":"10.1109\/TSMC.2024.3519510","article-title":"A trust incentive driven feedback mechanism with risk attitude for group consensus in social networks","volume":"55","author":"Ji","year":"2025","journal-title":"IEEE Trans. Syst. Man Cybern.: Syst."},{"issue":"5","key":"10.1016\/j.amc.2026.130221_bib0017","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevE.81.057101","article-title":"Impact of critical mass on the evolution of cooperation in spatial public goods games","volume":"81","author":"Szolnoki","year":"2010","journal-title":"Phys. Rev. E\u2014Stat. Nonlinear Soft Matter Phys."},{"key":"10.1016\/j.amc.2026.130221_bib0018","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2025.116398","article-title":"Reputation in public goods cooperation under double Q-learning protocol","volume":"196","author":"Xie","year":"2025","journal-title":"Chaos Solit. Fractals"},{"key":"10.1016\/j.amc.2026.130221_bib0019","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2023.113669","article-title":"Facilitating the evolution of cooperation through altruistic punishment with adaptive feedback","volume":"173","author":"Hua","year":"2023","journal-title":"Chaos Solit. Fractals"},{"issue":"4","key":"10.1016\/j.amc.2026.130221_bib0020","doi-asserted-by":"crossref","DOI":"10.1063\/5.0268194","article-title":"Evolutionary dynamics in state-feedback public goods games with peer punishment","volume":"35","author":"Wang","year":"2025","journal-title":"Chaos: Interdiscip. J. Nonlinear Sci."},{"issue":"9","key":"10.1016\/j.amc.2026.130221_bib0021","doi-asserted-by":"crossref","DOI":"10.1088\/1367-2630\/14\/9\/093016","article-title":"Evolutionary advantages of adaptive rewarding","volume":"14","author":"Szolnoki","year":"2012","journal-title":"New J. Phys."},{"issue":"1816","key":"10.1016\/j.amc.2026.130221_bib0022","doi-asserted-by":"crossref","DOI":"10.1098\/rspb.2015.1975","article-title":"Antisocial pool rewarding does not deter public cooperation","volume":"282","author":"Szolnoki","year":"2015","journal-title":"Proc. R. Soc. B: Biol. Sci."},{"key":"10.1016\/j.amc.2026.130221_bib0023","doi-asserted-by":"crossref","DOI":"10.1016\/j.physa.2022.128165","article-title":"Reward and punishment mechanism with weighting enhances cooperation in evolutionary games","volume":"607","author":"Zu","year":"2022","journal-title":"Phys. a: Stat. Mech. Appl."},{"issue":"5","key":"10.1016\/j.amc.2026.130221_bib0024","doi-asserted-by":"crossref","DOI":"10.1088\/1367-2630\/ad3f3e","article-title":"Competition between self- and other-regarding preferences in resolving social dilemmas","volume":"26","author":"Wang","year":"2024","journal-title":"New J. Phys."},{"key":"10.1016\/j.amc.2026.130221_bib0025","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2025.116099","article-title":"Eeffects of other-regarding preferences on cooperation in networked Prisoner\u2019s dilemma game","volume":"193","author":"Chen","year":"2025","journal-title":"Chaos Solit. Fractals"},{"key":"10.1016\/j.amc.2026.130221_bib0026","article-title":"Intergroup-based public goods games in complex networks with leader-driven other-regarding preferences","volume":"508","author":"Chen","year":"2026","journal-title":"Appl. Math. Comput."},{"key":"10.1016\/j.amc.2026.130221_bib0027","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2025.116693","article-title":"Dynamic evolution of cooperation based on adaptive reputation threshold and game transition","volume":"199","author":"Yue","year":"2025","journal-title":"Chaos Solit. Fractals"},{"key":"10.1016\/j.amc.2026.130221_bib0028","doi-asserted-by":"crossref","DOI":"10.1016\/j.physa.2025.130824","article-title":"Adaptive reputation promotes the cooperation of multiplayer snowdrift game on higher-order networks","author":"Zhu","year":"2025","journal-title":"Phys. a: Stat. Mech. Appl."},{"key":"10.1016\/j.amc.2026.130221_bib0029","doi-asserted-by":"crossref","DOI":"10.1016\/j.physleta.2024.129652","article-title":"The role of reputation to reduce punishment costs in spatial public goods game","volume":"516","author":"Kang","year":"2024","journal-title":"Phys. Lett. A."},{"key":"10.1016\/j.amc.2026.130221_bib0030","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2026.118149","article-title":"Unveiling cooperative dynamics in scale-free networks through adaptive deep Q-networks","volume":"208","author":"Yang","year":"2026","journal-title":"Chaos Solit. Fractals"},{"key":"10.1016\/j.amc.2026.130221_bib0031","article-title":"The impact of anxiety on cooperative behavior: a network evolutionary game theory approach","volume":"474","author":"Zhang","year":"2024","journal-title":"Appl. Math. Comput."},{"key":"10.1016\/j.amc.2026.130221_bib0032","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2024.115955","article-title":"The role of emotional expression in the evolution of cooperation in spatial prisoner\u2019s dilemma games","volume":"192","author":"Chen","year":"2025","journal-title":"Chaos Solit. Fractals"},{"key":"10.1016\/j.amc.2026.130221_bib0033","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2026.117986","article-title":"Shaping the learning signal in a combined Q-learning rule to improve structured cooperation","volume":"206","author":"Du","year":"2026","journal-title":"Chaos Solit. Fractals"},{"issue":"4","key":"10.1016\/j.amc.2026.130221_bib0034","doi-asserted-by":"crossref","DOI":"10.1063\/5.0201968","article-title":"Evolution of cooperation on reinforcement-learning driven-adaptive networks","volume":"34","author":"Du","year":"2024","journal-title":"Chaos: Interdiscip. J. Nonlinear Sci."},{"key":"10.1016\/j.amc.2026.130221_bib0035","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2026.118289","article-title":"Evolutionary dynamics under combined regret-based learning and random exploration","volume":"208","author":"Zhu","year":"2026","journal-title":"Chaos Solit. Fractals"},{"key":"10.1016\/j.amc.2026.130221_bib0036","article-title":"Punishment: one tool, many uses","volume":"1","author":"Raihani","year":"2019","journal-title":"Evol. Hum. Sci."},{"issue":"8","key":"10.1016\/j.amc.2026.130221_bib0037","doi-asserted-by":"crossref","DOI":"10.1088\/1367-2630\/16\/8\/083016","article-title":"Probabilistic sharing solves the problem of costly punishment","volume":"16","author":"Chen","year":"2014","journal-title":"New J. Phys."},{"issue":"11","key":"10.1016\/j.amc.2026.130221_bib0038","doi-asserted-by":"crossref","first-page":"2127","DOI":"10.1142\/S0218202519500428","article-title":"Evolutionary dynamics of cooperation in a population with probabilistic corrupt enforcers and violators","volume":"29","author":"Liu","year":"2019","journal-title":"Math. Models Methods Appl. Sci."},{"key":"10.1016\/j.amc.2026.130221_bib0039","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.chaos.2016.12.008","article-title":"Characteristics of the evolution of cooperation by the probabilistic peer-punishment based on the difference of payoff","volume":"95","author":"Ohdaira","year":"2017","journal-title":"Chaos Solit. Fractals"},{"issue":"1","key":"10.1016\/j.amc.2026.130221_bib0040","doi-asserted-by":"crossref","first-page":"6604","DOI":"10.1038\/s41598-022-10582-5","article-title":"The probabilistic pool punishment proportional to the difference of payoff outperforms previous pool and peer punishment","volume":"12","author":"Ohdaira","year":"2022","journal-title":"Sci. Rep."},{"issue":"9","key":"10.1016\/j.amc.2026.130221_bib0041","doi-asserted-by":"crossref","first-page":"8837","DOI":"10.1007\/s11071-023-08297-x","article-title":"Cooperation dynamics in spatial public goods games with graded punishment mechanism","volume":"111","author":"Quan","year":"2023","journal-title":"Nonlinear Dyn."},{"key":"10.1016\/j.amc.2026.130221_bib0042","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2025.117202","article-title":"Effects of dynamic probabilistic punishment with environmental threshold on cooperation in spatial public goods games","volume":"201","author":"Li","year":"2025","journal-title":"Chaos Solit. Fractals"},{"key":"10.1016\/j.amc.2026.130221_bib0043","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2024.115693","article-title":"Fostering cooperative evolution through probabilistic punishment and environmental feedback in public goods game","volume":"189","author":"Liu","year":"2024","journal-title":"Chaos Solit. Fractals"},{"key":"10.1016\/j.amc.2026.130221_bib0044","article-title":"Reputation-based probabilistic punishment on the evolution of cooperation in the spatial public goods game","volume":"441","author":"Quan","year":"2023","journal-title":"Appl. Math. Comput."},{"key":"10.1016\/j.amc.2026.130221_bib0045","article-title":"Dynamic punishment-reputation synergy drives cooperation in spatial public goods game","volume":"506","author":"Zhang","year":"2025","journal-title":"Appl. Math. Comput."},{"issue":"1704","key":"10.1016\/j.amc.2026.130221_bib0046","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1098\/rspb.2010.1275","article-title":"The evolution of punishment through reputation","volume":"278","author":"Santos","year":"2011","journal-title":"Proc. R. Soc. B: Biol. Sci."},{"issue":"1838","key":"10.1016\/j.amc.2026.130221_bib0047","doi-asserted-by":"crossref","DOI":"10.1098\/rstb.2020.0289","article-title":"Direct punishment and indirect reputation-based tactics to intervene against offences","volume":"376","author":"Molho","year":"2021","journal-title":"Philos. Trans. R. Soc. B: Biol. Sci."},{"issue":"1838","key":"10.1016\/j.amc.2026.130221_bib0048","doi-asserted-by":"crossref","DOI":"10.1098\/rstb.2020.0293","article-title":"Reputation and punishment sustain cooperation in the optional public goods game","volume":"376","author":"Podder","year":"2021","journal-title":"Philos. Trans. R. Soc. B."},{"issue":"1","key":"10.1016\/j.amc.2026.130221_bib0049","doi-asserted-by":"crossref","DOI":"10.1063\/5.0250120","article-title":"The evolution of cooperation in spatial public goods game with tolerant punishment based on reputation threshold","volume":"35","author":"Zhang","year":"2025","journal-title":"Chaos: Interdiscip. J. Nonlinear Sci."},{"issue":"1","key":"10.1016\/j.amc.2026.130221_bib0050","doi-asserted-by":"crossref","first-page":"7453","DOI":"10.1038\/s41467-023-43048-x","article-title":"Imitation dynamics on networks with incomplete information","volume":"14","author":"Wang","year":"2023","journal-title":"Nat. Commun."},{"issue":"46","key":"10.1016\/j.amc.2026.130221_bib0051","doi-asserted-by":"crossref","DOI":"10.1126\/sciadv.adg3256","article-title":"Student of games: a unified learning algorithm for both perfect and imperfect information games","volume":"9","author":"Schmid","year":"2023","journal-title":"Sci. Adv."},{"key":"10.1016\/j.amc.2026.130221_bib0052","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2025.117757","article-title":"Emergence of cooperative behaviors in incomplete information networks: evolutionary dynamics based on higher-order interactions and adaptive strategies","volume":"204","author":"Wang","year":"2026","journal-title":"Chaos Solit. Fractals"},{"issue":"4","key":"10.1016\/j.amc.2026.130221_bib0053","doi-asserted-by":"crossref","first-page":"741","DOI":"10.1007\/s11245-022-09806-0","article-title":"Faces in disguise. masks, concealment, and deceit","volume":"41","author":"Gramigna","year":"2022","journal-title":"Topoi"},{"key":"10.1016\/j.amc.2026.130221_bib0054","doi-asserted-by":"crossref","DOI":"10.1016\/j.physa.2021.126839","article-title":"Evolutionary dynamics of cooperation in n-person snowdrift games with peer punishment and individual disguise","volume":"592","author":"Pi","year":"2022","journal-title":"Phys. A: Stat. Mech. Appl."}],"container-title":["Applied Mathematics and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0096300326002730?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0096300326002730?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T20:42:16Z","timestamp":1784666536000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0096300326002730"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,12]]},"references-count":54,"alternative-id":["S0096300326002730"],"URL":"https:\/\/doi.org\/10.1016\/j.amc.2026.130221","relation":{},"ISSN":["0096-3003"],"issn-type":[{"value":"0096-3003","type":"print"}],"subject":[],"published":{"date-parts":[[2026,12]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Evolution of cooperation through dynamic probabilistic punishment under individual camouflage","name":"articletitle","label":"Article Title"},{"value":"Applied Mathematics and Computation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.amc.2026.130221","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"130221"}}