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Algebraic Formulation and Nash Equilibrium of Competitive Diffusion Games

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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.

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Notes

  1. The reason why we choose this kind of diffusion process is that it captures the simple fact that being closer to player’s initial seeds will result in adopting that specific player’s type.

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Acknowledgements

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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Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People’s Republic of China

    Haitao Li, Xueying Ding, Qiqi Yang & Yingrui Zhou

  2. Institute of Data Science and Technology, Shandong Normal University, Jinan, 250014, People’s Republic of China

    Haitao Li

Authors
  1. Haitao Li
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  2. Xueying Ding
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  3. Qiqi Yang
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  4. Yingrui Zhou
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Corresponding author

Correspondence to Haitao Li.

Additional information

The research was supported by the National Natural Science Foundation of China under Grants 61374065 and 61503225, the Natural Science Foundation of Shandong Province under Grant ZR2015FQ003, and the Natural Science Fund for Distinguished Young Scholars of Shandong Province under Grant JQ201613.

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Li, H., Ding, X., Yang, Q. et al. Algebraic Formulation and Nash Equilibrium of Competitive Diffusion Games. Dyn Games Appl 8, 423–433 (2018). https://doi.org/10.1007/s13235-017-0228-4

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