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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
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    References listed on IDEAS

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    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.
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    Cited by:

    1. 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).
    2. 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).
    3. 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).

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