IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v201y2025ip1s0960077925012172.html

The establishment of norms in the multivariate Illegal Strategy Metanorm Game model

Author

Listed:
  • Jin, Xing
  • Zhang, Wenhao
  • Fan, Ziyou
  • Wang, Chao
  • Wang, Zhen

Abstract

Social norms (collective solutions to social dilemmas) in the real world regulate degrees of wrongdoing, yet classical metanorm games treat violations as binary. We propose the Multivariate Illegal Strategy Metanorm (MISM) model, extending Axelrod’s framework to an n-level offense scale with matching gradient punishments, and introduce a reinforcement-learning updater, Multivariate Boldness-Vengefulness Learning (MBVL), that blends Q-learning and evolutionary imitation. Large-scale Monte Carlo simulations on lattice, Watts–Strogatz, and Barabási–Albert networks reveal that (i) finer-grained violation levels accelerate the eradication of severe offenders; (ii) larger neighborhood amplify cascading peer punishment; and (iii) graded sanctions achieve higher collective welfare than uniform ones. MISM thus bridges binary-norm models and graded real-world governance, providing a scalable test-bed for studying multilevel norm emergence and compliance. The source code for the MISM model and MBVL algorithm is publicly available at: https://github.com/DAISec-Lab/MISM.

Suggested Citation

  • Jin, Xing & Zhang, Wenhao & Fan, Ziyou & Wang, Chao & Wang, Zhen, 2025. "The establishment of norms in the multivariate Illegal Strategy Metanorm Game model," Chaos, Solitons & Fractals, Elsevier, vol. 201(P1).
    • Handle: RePEc:eee:chsofr:v:201:y:2025:i:p1:s0960077925012172
    DOI: 10.1016/j.chaos.2025.117204
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077925012172
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2025.117204?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Catherine Molho & Joshua M. Tybur & Paul A. M. Van Lange & Daniel Balliet, 2020. "Direct and indirect punishment of norm violations in daily life," Nature Communications, Nature, vol. 11(1), pages 1-9, December.
    2. Axelrod, Robert, 1986. "An Evolutionary Approach to Norms," American Political Science Review, Cambridge University Press, vol. 80(4), pages 1095-1111, December.
    3. José Manuel Galán & Luis R. Izquierdo, 2005. "Appearances Can Be Deceiving: Lessons Learned Re-Implementing Axelrod's 'Evolutionary Approach to Norms'," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 8(3), pages 1-2.
    4. Eriksson, Kimmo & Strimling, Pontus & Coultas, Julie C., 2015. "Bidirectional associations between descriptive and injunctive norms," Organizational Behavior and Human Decision Processes, Elsevier, vol. 129(C), pages 59-69.
    5. Frémeaux, Sandrine & Mercier, Guillaume & Grevin, Anouk, 2025. "The Free-Riding Issue in Contemporary Organizations: Lessons from the Common Good Perspective," Business Ethics Quarterly, Cambridge University Press, vol. 35(1), pages 28-53, January.
    6. Wang, Jingrui & Zhang, Huizhen & An, Tianbo & Jin, Xing & Wang, Chao & Zhao, Jian & Wang, Zhen, 2024. "Effect of vaccine efficacy on vaccination behavior with adaptive perception," Applied Mathematics and Computation, Elsevier, vol. 469(C).
    7. Lucas Molleman & Felix Kölle & Chris Starmer & Simon Gächter, 2019. "People prefer coordinated punishment in cooperative interactions," Nature Human Behaviour, Nature, vol. 3(11), pages 1145-1153, November.
    8. Catherine Molho & Joshua Tybur & Paul A.M. van Lange & Daniel Balliet, 2020. "Direct and indirect punishment of norm violations in daily life," Post-Print hal-02909831, HAL.
    9. Li, Yipeng & Hu, Xiangyue & Jin, Xing & Zhang, Huizhen & Yang, Jiajia & Wang, Zhen, 2025. "Environmental information perception enhances cooperation in stochastic public goods games via Q-learning," Applied Mathematics and Computation, Elsevier, vol. 504(C).
    10. Bryan C. McCannon, 2018. "Leadership and motivation for public goods contributions," Scottish Journal of Political Economy, Scottish Economic Society, vol. 65(1), pages 68-96, February.
    11. Karl Sigmund & Hannelore De Silva & Arne Traulsen & Christoph Hauert, 2010. "Social learning promotes institutions for governing the commons," Nature, Nature, vol. 466(7308), pages 861-863, August.
    12. Ding, Rui & Wang, Xianjia & Zhao, Jinhua & Gu, Cuiling, 2025. "Effects of punishment driven by inequity aversion on promoting cooperation in public goods games," Chaos, Solitons & Fractals, Elsevier, vol. 190(C).
    13. Zhang, Wei & Zhao, Dongkai & Jin, Xing & Zhang, Huizhen & An, Tianbo & Cui, Guanghai & Wang, Zhen, 2025. "Q-learning facilitates norm emergence in metanorm game model with topological structures," Chaos, Solitons & Fractals, Elsevier, vol. 195(C).
    14. José M Galán & Maciej M Łatek & Seyed M Mussavi Rizi, 2011. "Axelrod's Metanorm Games on Networks," PLOS ONE, Public Library of Science, vol. 6(5), pages 1-11, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Simon Gächter & Lucas Molleman & Daniele Nosenzo, 2025. "Why people follow rules," Nature Human Behaviour, Nature, vol. 9(7), pages 1342-1354, July.
    2. Columbus, Simon & Feld, Lars P. & Kasper, Matthias & Rablen, Matthew D., 2023. "Behavioural Responses to Unfair Institutions: Experimental Evidence on Rule Compliance, Norm Polarisation, and Trust," IZA Discussion Papers 16346, IZA Network @ LISER.
    3. Zhang, Wei & Zhao, Dongkai & Jin, Xing & Zhang, Huizhen & An, Tianbo & Cui, Guanghai & Wang, Zhen, 2025. "Q-learning facilitates norm emergence in metanorm game model with topological structures," Chaos, Solitons & Fractals, Elsevier, vol. 195(C).
    4. J. Gareth Polhill & Dawn C. Parker & Daniel Brown & Volker Grimm, 2008. "Using the ODD Protocol for Describing Three Agent-Based Social Simulation Models of Land-Use Change," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 11(2), pages 1-3.
    5. Jun Qian & Tongda Zhang & Xiao Sun & Yueting Chai, 2023. "The coordination of collective and individual solutions in risk-resistant scenarios," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(2), pages 1-15, February.
    6. An, Tianbo & Zhang, Huizhen & Zhang, Zhanshuo & Liu, Guanghui & Li, Jiayu & Chen, Liangyu & Wang, Zhen, 2025. "Cooperation dynamics driven by reinforcement learning with interactive diversity in structured populations," Chaos, Solitons & Fractals, Elsevier, vol. 201(P2).
    7. Tatsuya Sasaki & Isamu Okada & Satoshi Uchida & Xiaojie Chen, 2015. "Commitment to Cooperation and Peer Punishment: Its Evolution," Games, MDPI, vol. 6(4), pages 1-14, November.
    8. Rainer Widmann & Michael E. Rose & Marina Chugunova, 2023. "Allegations of Sexual Misconduct, Accused Scientists, and Their Research," Rationality and Competition Discussion Paper Series 419, CRC TRR 190 Rationality and Competition.
    9. Dirk Helbing & Anders Johansson, 2010. "Cooperation, Norms, and Revolutions: A Unified Game-Theoretical Approach," PLOS ONE, Public Library of Science, vol. 5(10), pages 1-15, October.
    10. Luis R. Izquierdo & J. Gareth Polhill, 2006. "Is Your Model Susceptible to Floating-Point Errors?," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 9(4), pages 1-4.
    11. Jennifer A. Loughmiller-Cardinal & James Scott Cardinal, 2023. "The Behavior of Information: A Reconsideration of Social Norms," Societies, MDPI, vol. 13(5), pages 1-27, April.
    12. Christiane Reif & Dirk Rübbelke & Andreas Löschel, 2017. "Improving Voluntary Public Good Provision Through a Non-governmental, Endogenous Matching Mechanism: Experimental Evidence," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 67(3), pages 559-589, July.
    13. Uri Wilensky & William Rand, 2007. "Making Models Match: Replicating an Agent-Based Model," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 10(4), pages 1-2.
    14. Satoshi Uchida & Hitoshi Yamamoto & Isamu Okada & Tatsuya Sasaki, 2019. "Evolution of Cooperation with Peer Punishment under Prospect Theory," Games, MDPI, vol. 10(1), pages 1-13, February.
    15. Gao, Hongyu & Wang, Juan & Zhang, Fan & Li, Xiaopeng & Xia, Chengyi, 2021. "Cooperation dynamics based on reputation in the mixed population with two species of strategists," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    16. Fujio Toriumi & Hitoshi Yamamoto & Isamu Okada, 2020. "A belief in rewards accelerates cooperation on consumer-generated media," Journal of Computational Social Science, Springer, vol. 3(1), pages 19-31, April.
    17. Luis R. Izquierdo & Segismundo S. Izquierdo & José Manuel Galán & José Ignacio Santos, 2009. "Techniques to Understand Computer Simulations: Markov Chain Analysis," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 12(1), pages 1-6.
    18. Wang, Jingrui & Li, Juan & Wang, Zhen, 2025. "Impact of infectious sources on the vaccination dilemma in networked population," Chaos, Solitons & Fractals, Elsevier, vol. 200(P1).
    19. José Manuel Galán & Luis R. Izquierdo & Segismundo S. Izquierdo & José Ignacio Santos & Ricardo del Olmo & Adolfo López-Paredes & Bruce Edmonds, 2009. "Errors and Artefacts in Agent-Based Modelling," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 12(1), pages 1-1.
    20. José M Galán & Maciej M Łatek & Seyed M Mussavi Rizi, 2011. "Axelrod's Metanorm Games on Networks," PLOS ONE, Public Library of Science, vol. 6(5), pages 1-11, May.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:201:y:2025:i:p1:s0960077925012172. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.