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The computation of Nash equilibrium in fashion games via semi-tensor product method

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Abstract

Using the semi-tensor product of matrices, this paper investigates the computation of purestrategy Nash equilibrium (PNE) for fashion games, and presents several new results. First, a formal fashion game model on a social network is given. Second, the utility function of each player is converted into an algebraic form via the semi-tensor product of matrices, based on which the case of two-strategy fashion game is studied and two methods are obtained for the case to verify the existence of PNE. Third, the multi-strategy fashion game model is investigated and an algorithm is established to find all the PNEs for the general case. Finally, two kinds of optimization problems, that is, the so-called social welfare and normalized satisfaction degree optimization problems are investigated and two useful results are given. The study of several illustrative examples shows that the new results obtained in this paper are effective.

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Authors and Affiliations

  1. School of Information Science and Engineering, Shandong Normal University, Jinan, 250014, China

    Peilian Guo

  2. School of Control Science and Engineering, Shandong University, Jinan, 250061, China

    Yuzhen Wang

Authors
  1. Peilian Guo
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  2. Yuzhen Wang
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Corresponding author

Correspondence to Peilian Guo.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 61374065, and the Research Fund for the Taishan Scholar Project of Shandong Province.

This paper was recommended for publication by Editor XIE Lihua.

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Guo, P., Wang, Y. The computation of Nash equilibrium in fashion games via semi-tensor product method. J Syst Sci Complex 29, 881–896 (2016). https://doi.org/10.1007/s11424-016-5057-9

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  • DOI: https://doi.org/10.1007/s11424-016-5057-9

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