The Computation of Nash Equilibrium in Fashion Games via Semi-Tensor Product Method

GUO Peilian,WANG Yuzhen

系统科学与复杂性(英文) ›› 2016, Vol. 29 ›› Issue (4) : 881-896.

PDF(262 KB)
PDF(262 KB)
系统科学与复杂性(英文) ›› 2016, Vol. 29 ›› Issue (4) : 881-896. DOI: 10.1007/s11424-016-5057-9

The Computation of Nash Equilibrium in Fashion Games via Semi-Tensor Product Method

    GUO Peilian1 , WANG Yuzhen2
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The Computation of Nash Equilibrium in Fashion Games via Semi-Tensor Product Method

    GUO Peilian1 , WANG Yuzhen2
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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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GUO Peilian,WANG Yuzhen. The Computation of Nash Equilibrium in Fashion Games via Semi-Tensor Product Method. 系统科学与复杂性(英文), 2016, 29(4): 881-896 https://doi.org/10.1007/s11424-016-5057-9
GUO Peilian , WANG Yuzhen. The Computation of Nash Equilibrium in Fashion Games via Semi-Tensor Product Method. Journal of Systems Science and Complexity, 2016, 29(4): 881-896 https://doi.org/10.1007/s11424-016-5057-9
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