Dynamic Games and Applications

, Volume 8, Issue 2, pp 423–433 | Cite as

Algebraic Formulation and Nash Equilibrium of Competitive Diffusion Games



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.


Competitive diffusion game Pure-strategy Nash equilibrium Algebraic formulation Semi-tensor product of matrices 



The authors would like to thank the anonymous reviewers for their constructive comments and suggestions which improved the quality of this paper.


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Haitao Li
    • 1
    • 2
  • Xueying Ding
    • 1
  • Qiqi Yang
    • 1
  • Yingrui Zhou
    • 1
  1. 1.School of Mathematics and StatisticsShandong Normal UniversityJinanPeople’s Republic of China
  2. 2.Institute of Data Science and TechnologyShandong Normal UniversityJinanPeople’s Republic of China

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