Abstract
This paper investigates the networked evolutionary model based on snow-drift game with the strategy of rewards and penalty. Firstly, by using the semi-tensor product of matrices approach, the mathematical model of the networked evolutionary game is built. Secondly, combined with the matrix expression of logic, the mathematical model is expressed as a dynamic logical system and next converted into its evolutionary dynamic algebraic form. Thirdly, the dynamic evolution process is analyzed and the final level of cooperation is discussed. Finally, the effects of the changes in the rewarding and penalty factors on the level of cooperation in the model are studied separately, and the conclusions are verified by examples.
Highlights
Cooperation widely exists in various complex systems from biological to economic and social networks
This paper investigates the networked evolutionary model based on snow-drift game with the strategy of rewards and penalty
Combined with the matrix expression of logic, the mathematical model is expressed as a dynamic logical system and converted into its evolutionary dynamic algebraic form
Summary
Cooperation widely exists in various complex systems from biological to economic and social networks. A useful tool, called the semi-tensor product of matrices emerged as the times require It was proposed by professor Cheng [1] [2], and provides an effective mathematical tool for systematically analyzing the dynamic process of networked evolutionary games. The semi-tensor product of matrices has been applied to Boolean network control [3], which has been widely used in many fields, such as graph theory, fuzzy control, Boolean function distribution, fault detection and so on [4] By using this method, Professor Cheng and his team have studied the dynamic behavior of the networked evolutionary games and the strategy optimization problem, and have achieved certain achievements.
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