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.
Keywords
Competitive diffusion game Pure-strategy Nash equilibrium Algebraic formulation Semi-tensor product of matricesNotes
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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