IDEAS home Printed from https://ideas.repec.org/a/spr/dyngam/v8y2018i2d10.1007_s13235-017-0228-4.html
   My bibliography  Save this article

Algebraic Formulation and Nash Equilibrium of Competitive Diffusion Games

Author

Listed:
  • Haitao Li

    (Shandong Normal University
    Shandong Normal University)

  • Xueying Ding

    (Shandong Normal University)

  • Qiqi Yang

    (Shandong Normal University)

  • Yingrui Zhou

    (Shandong Normal University)

Abstract

This paper investigates the algebraic formulation and Nash equilibrium of competitive diffusion games by using semi-tensor product method, and gives some new results. Firstly, an algebraic formulation of competitive diffusion games is established via the semi-tensor product of matrices, based on which all the fixed points (the end of the diffusion process) are obtained. Secondly, using the algebraic formulation, a necessary and sufficient condition is presented for the verification of pure-strategy Nash equilibrium. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained new results.

Suggested Citation

  • Haitao Li & Xueying Ding & Qiqi Yang & Yingrui Zhou, 2018. "Algebraic Formulation and Nash Equilibrium of Competitive Diffusion Games," Dynamic Games and Applications, Springer, vol. 8(2), pages 423-433, June.
    • Handle: RePEc:spr:dyngam:v:8:y:2018:i:2:d:10.1007_s13235-017-0228-4
    DOI: 10.1007/s13235-017-0228-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13235-017-0228-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13235-017-0228-4?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. H Peyton Young, 2000. "The Diffusion of Innovations in Social Networks," Economics Working Paper Archive 437, The Johns Hopkins University,Department of Economics.
    2. Wang, Xiao Fan & Chen, Guanrong, 2002. "Pinning control of scale-free dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 310(3), pages 521-531.
    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. Tang, Yu & Li, Lulu & Lu, Jianquan, 2022. "Modeling and optimization for networked evolutionary games with player exit mechanism: Semi-tensor product of matrices method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 590(C).
    2. Guo, Peilian & Han, Changda, 2021. "Nash equilibrium and group strategy consensus of networked evolutionary game with coupled social groups," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    3. Liu, Yansheng & Song, Mengjin & Li, Haitao & Li, Yalu & Hou, Wenying, 2021. "Containment problem of finite-field networks with fixed and switching topology," Applied Mathematics and Computation, Elsevier, vol. 411(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. Pi, Xiaochen & Tang, Longkun & Chen, Xiangzhong, 2021. "A directed weighted scale-free network model with an adaptive evolution mechanism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    2. Huanxiu GUO & Mary-Françoise RENARD, 2013. "Social activity and collective action for agricultural innovation: a case study of New Rural Reconstruction in China," Working Papers 201306, CERDI.
    3. T. Botmart & N. Yotha & P. Niamsup & W. Weera, 2017. "Hybrid Adaptive Pinning Control for Function Projective Synchronization of Delayed Neural Networks with Mixed Uncertain Couplings," Complexity, Hindawi, vol. 2017, pages 1-18, August.
    4. Wenle Zhang & Jianchang Liu, 2016. "Ultra-fast consensus of discrete-time multi-agent systems with multi-step predictive output feedback," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(6), pages 1465-1479, April.
    5. Miao, Qingying & Rong, Zhihai & Tang, Yang & Fang, Jianan, 2008. "Effects of degree correlation on the controllability of networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(24), pages 6225-6230.
    6. Wang, Fei & Yang, Yongqing & Hu, Manfeng & Xu, Xianyun, 2015. "Projective cluster synchronization of fractional-order coupled-delay complex network via adaptive pinning control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 434(C), pages 134-143.
    7. Yunlong Wu & Qian Zhao & Hui Li, 2018. "Synchronization of directed complex networks with uncertainty and time-delay," International Journal of Distributed Sensor Networks, , vol. 14(5), pages 15501477187, May.
    8. Yan, Jiaye & Zhou, Jiaying & Wu, Zhaoyan, 2019. "Structure identification of unknown complex-variable dynamical networks with complex coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 256-265.
    9. Li, Chunguang & Chen, Guanrong, 2004. "Synchronization in general complex dynamical networks with coupling delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 263-278.
    10. Yi, Chengbo & Feng, Jianwen & Wang, Jingyi & Xu, Chen & Zhao, Yi, 2017. "Synchronization of delayed neural networks with hybrid coupling via partial mixed pinning impulsive control," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 78-90.
    11. Floortje Alkemade & Carolina Castaldi, 2005. "Strategies for the Diffusion of Innovations on Social Networks," Computational Economics, Springer;Society for Computational Economics, vol. 25(1), pages 3-23, February.
    12. Chan, Felix T.S. & Wang, Zheng & Zhang, Jie, 2007. "A two-level hedging point policy for controlling a manufacturing system with time-delay, demand uncertainty and extra capacity," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1528-1558, February.
    13. Noah J Cowan & Erick J Chastain & Daril A Vilhena & James S Freudenberg & Carl T Bergstrom, 2012. "Nodal Dynamics, Not Degree Distributions, Determine the Structural Controllability of Complex Networks," PLOS ONE, Public Library of Science, vol. 7(6), pages 1-5, June.
    14. Yang-Yu Liu & Jean-Jacques Slotine & Albert-László Barabási, 2012. "Control Centrality and Hierarchical Structure in Complex Networks," PLOS ONE, Public Library of Science, vol. 7(9), pages 1-7, September.
    15. Liu, Z.X. & Chen, Z.Q. & Yuan, Z.Z., 2007. "Pinning control of weighted general complex dynamical networks with time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(1), pages 345-354.
    16. Liu, Xinzhi & Zhang, Kexue & Xie, Wei-Chau, 2016. "Stabilization of time-delay neural networks via delayed pinning impulses," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 223-234.
    17. Xiang, L.Y. & Liu, Z.X. & Chen, Z.Q. & Chen, F. & Yuan, Z.Z., 2007. "Pinning control of complex dynamical networks with general topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(1), pages 298-306.
    18. Li, Sheng & Liu, Wenwen & Wu, Ruizi & Li, Junli, 2023. "An adaptive attack model to network controllability," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    19. Liu, Xian & Wang, Jinzhi & Huang, Lin, 2007. "Stabilization of a class of dynamical complex networks based on decentralized control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(2), pages 733-744.
    20. Flores Díaz, Ramón Jesús & Koster, Maurice & Lindner, Ines & Molina, Elisenda, 2010. "Networks and collective action," DES - Working Papers. Statistics and Econometrics. WS ws104830, Universidad Carlos III de Madrid. Departamento de Estadística.

    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:spr:dyngam:v:8:y:2018:i:2:d:10.1007_s13235-017-0228-4. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.