JAMP  Vol.7 No.3 , March 2019
Networked Evolutionary Model of Snow-Drift Game Based on Semi-Tensor Product
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.
Cite this paper: Chen, L. (2019) Networked Evolutionary Model of Snow-Drift Game Based on Semi-Tensor Product. Journal of Applied Mathematics and Physics, 7, 726-737. doi: 10.4236/jamp.2019.73050.

[1]   Cheng, D., Qi, H., He, F., Xu, T. and Dong, H. (2014) Semi-Tensor Product Approach to Networked Evolutionary Games. Control Theory and Technology, 12, 198-214.

[2]   Cheng, D., He, F., Qi, H. and Xu, T. (2015) Modeling, Analysis and Control of Networked Evolutionary Games. IEEE Transactions on Automatic Control, 60, 2402-2415.

[3]   Cheng, D., Qi, H. and Li, Z. (2011) Analysis and Control of Boolean Networks: A Semi-Tensor Product Approach. Springer, London.

[4]   Cheng, D., Qi, H. and Zhao, Y. (2012) An Introduction to Semi-Tensor Product of Matrices and Its Applications. World Scientific Publishing Co. Pte. Ltd., Singapore.

[5]   Wang, J., Zhao, J. and Li, Y. (2017) The Dynamic Processes of the Control Network Evolution Based on Boxed Pig Game with the Strategy of Punishment and Incentive. Mathematics in Practice and Theory, 47, 225-234.

[6]   Liu, H., Li, Y., Zhao, J. and Ge, M. (2016) Impact of Keeping Silence in the Final Cooperation Levels of Prisoner’s Dilenna Game. Mathematics in Practice and Theory, 46, 240-247.

[7]   Ge, M., Zhao, J. and Li, Y. (2016) Modeling and Analysis of Network Evolution Based on Prisoner’s Dilemma Game with Punishment Strategy. Journal of Systems Science and Mathematical Sciences, 36, 2041-2048.

[8]   Xing, H. and Zhao, J. (2016) Formulation of Networked Evolutionary Games with Variation Mechanism. Journal of Shandong University (Natural Science), 51, 103-107.

[9]   Li, H., Wang, Y. and Liu, Z. (2012) Existence and Number of Fixed Points of Boolean Transformations via the Semi-Tensor Product Method. Applied Mathematics Letters, 25, 1142-1147.