Algebraic formulation and Nash equilibrium of competitive diffusion games. (English) Zbl 1397.91053
Summary: 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.
MSC:
| 91A15 | Stochastic games, stochastic differential games |
| 91A43 | Games involving graphs |
| 91D30 | Social networks; opinion dynamics |
Keywords:
competitive diffusion game; pure-strategy Nash equilibrium; algebraic formulation; semi-tensor product of matricesReferences:
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