IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v525y2019icp535-547.html
   My bibliography  Save this article

Mean field model of a game for power

Author

Listed:
  • Karataieva, Tatiana
  • Koshmanenko, Volodymyr
  • Krawczyk, Małgorzata J.
  • Kułakowski, Krzysztof

Abstract

Our aim is to model a game for power (equivalent to total energy) as a dynamical process, where an excess of power possessed by a player allows him to gain even more power. Such a positive feedback is often termed as the Matthew effect. Analytical and numerical methods allow to identify a set of stationary states, i.e. fixed points of the model dynamics. The positions of the unstable fixed points give an insight on the basins of attraction of the stable fixed points. The results are interpreted in terms of modeling of coercive power.

Suggested Citation

  • Karataieva, Tatiana & Koshmanenko, Volodymyr & Krawczyk, Małgorzata J. & Kułakowski, Krzysztof, 2019. "Mean field model of a game for power," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 535-547.
    • Handle: RePEc:eee:phsmap:v:525:y:2019:i:c:p:535-547
    DOI: 10.1016/j.physa.2019.03.110
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119303450
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2019.03.110?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Dietrich Stauffer, 2016. "Income inequality in the 21st century — A biased summary of Piketty’s capital in the twenty-first century," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 27(02), pages 1-6, February.
    2. Jousseph, C.A.C. & de S. Pinto, S.E. & Martins, L.C. & Beims, M.W., 2003. "Influence of impurities on the dynamics and synchronization of coupled map lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 317(3), pages 401-410.
    3. Martins, Luciano C & Brunnet, Leonardo G, 2001. "Multi-state coupled map lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(1), pages 119-130.
    4. Weisbuch, Gerard, 2000. "Environment and institutions: a complex dynamical systems approach," Ecological Economics, Elsevier, vol. 35(3), pages 381-391, December.
    5. Rainer Hegselmann & Ulrich Krause, 2002. "Opinion Dynamics and Bounded Confidence Models, Analysis and Simulation," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 5(3), pages 1-2.
    6. Lacasa, Lucas & Luque, Bartolo, 2006. "Bonabeau hierarchy models revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 472-484.
    7. de Pontes, José C.A. & Batista, Antônio M. & Viana, Ricardo L. & Lopes, Sérgio R., 2006. "Self-organized memories in coupled map lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(2), pages 387-398.
    8. Tao, Yong, 2018. "Swarm intelligence in humans: A perspective of emergent evolution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 436-446.
    9. Bonabeau, Eric & Theraulaz, Guy & Deneubourg, Jean-Louis, 1995. "Phase diagram of a model of self-organizing hierarchies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 217(3), pages 373-392.
    10. Katarzyna Sznajd-Weron & Józef Sznajd, 2000. "Opinion Evolution In Closed Community," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 11(06), pages 1157-1165.
    11. Hristopulos, Dionissios T. & Muradova, Aliki, 2016. "Kinetic model of mass exchange with dynamic Arrhenius transition rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 95-109.
    12. Kaniadakis, G., 2001. "Non-linear kinetics underlying generalized statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(3), pages 405-425.
    13. Atmanspacher, Harald & Scheingraber, Herbert, 2005. "Stabilization of causally and non-causally coupled map lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 345(3), pages 435-447.
    14. K. Malarz & D. Stauffer & K. Kułakowski, 2006. "Bonabeau model on a fully connected graph," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 50(1), pages 195-198, March.
    15. Guillaume Deffuant & David Neau & Frederic Amblard & Gérard Weisbuch, 2000. "Mixing beliefs among interacting agents," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 3(01n04), pages 87-98.
    16. Volodymyr Koshmanenko, 2004. "Theorem of conflicts for a pair of probability measures," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(2), pages 303-313, June.
    17. Nagatani, Takashi, 2001. "Phase diagrams in unidirectionally coupled map lattice for open traffic flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 289(1), pages 267-277.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Miszczak, Jarosław Adam, 2022. "Constructing games on networks for controlling the inequalities in the capital distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 594(C).

    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. Shang, Lihui & Zhao, Mingming & Ai, Jun & Su, Zhan, 2021. "Opinion evolution in the Sznajd model on interdependent chains," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    2. Lu, Xi & Mo, Hongming & Deng, Yong, 2015. "An evidential opinion dynamics model based on heterogeneous social influential power," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 98-107.
    3. María Cecilia Gimenez & Luis Reinaudi & Ana Pamela Paz-García & Paulo Marcelo Centres & Antonio José Ramirez-Pastor, 2021. "Opinion evolution in the presence of constant propaganda: homogeneous and localized cases," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(1), pages 1-11, January.
    4. Toth, Gabor & Galam, Serge, 2022. "Deviations from the majority: A local flip model," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    5. Tiwari, Mukesh & Yang, Xiguang & Sen, Surajit, 2021. "Modeling the nonlinear effects of opinion kinematics in elections: A simple Ising model with random field based study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
    6. Deffuant, Guillaume & Roubin, Thibaut, 2022. "Do interactions among unequal agents undermine those of low status?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 592(C).
    7. Agnieszka Kowalska-Styczeń & Krzysztof Malarz, 2020. "Noise induced unanimity and disorder in opinion formation," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-22, July.
    8. Wang, Chaoqian, 2021. "Opinion dynamics with bilateral propaganda and unilateral information blockade," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    9. Muslim, Roni & Wella, Sasfan A. & Nugraha, Ahmad R.T., 2022. "Phase transition in the majority rule model with the nonconformist agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P2).
    10. Quanbo Zha & Gang Kou & Hengjie Zhang & Haiming Liang & Xia Chen & Cong-Cong Li & Yucheng Dong, 2020. "Opinion dynamics in finance and business: a literature review and research opportunities," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-22, December.
    11. Benjamin Cabrera & Björn Ross & Daniel Röchert & Felix Brünker & Stefan Stieglitz, 2021. "The influence of community structure on opinion expression: an agent-based model," Journal of Business Economics, Springer, vol. 91(9), pages 1331-1355, November.
    12. Shane T. Mueller & Yin-Yin Sarah Tan, 2018. "Cognitive perspectives on opinion dynamics: the role of knowledge in consensus formation, opinion divergence, and group polarization," Journal of Computational Social Science, Springer, vol. 1(1), pages 15-48, January.
    13. Castro, Luis E. & Shaikh, Nazrul I., 2018. "A particle-learning-based approach to estimate the influence matrix of online social networks," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 1-18.
    14. Calvelli, Matheus & Crokidakis, Nuno & Penna, Thadeu J.P., 2019. "Phase transitions and universality in the Sznajd model with anticonformity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 518-523.
    15. Yaofeng Zhang & Renbin Xiao, 2015. "Modeling and Simulation of Polarization in Internet Group Opinions Based on Cellular Automata," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-15, August.
    16. Han, Wenchen & Gao, Shun & Huang, Changwei & Yang, Junzhong, 2022. "Non-consensus states in circular opinion model with repulsive interaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    17. Li, Tingyu & Zhu, Hengmin, 2020. "Effect of the media on the opinion dynamics in online social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    18. Zhu, Jiefan & Yao, Yiping & Tang, Wenjie & Zhang, Haoming, 2022. "An agent-based model of opinion dynamics with attitude-hiding behaviors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    19. Ni, Xuelian & Xiong, Fei & Pan, Shirui & Chen, Hongshu & Wu, Jia & Wang, Liang, 2023. "How heterogeneous social influence acts on human decision-making in online social networks," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    20. Huang, Changwei & Dai, Qionglin & Han, Wenchen & Feng, Yuee & Cheng, Hongyan & Li, Haihong, 2018. "Effects of heterogeneous convergence rate on consensus in opinion dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 428-435.

    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:phsmap:v:525:y:2019:i:c:p:535-547. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.