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Chin. Phys. B, 2022, Vol. 31(8): 080204    DOI: 10.1088/1674-1056/ac4651
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Evolution of donations on scale-free networks during a COVID-19 breakout

Xian-Jia Wang(王先甲)1,2 and Lin-Lin Wang(王琳琳)1,†
1 Economics and Management School, Wuhan University, Wuhan 430072, China;
2 Institute of Systems Engineering, Wuhan University, Wuhan 430072, China
Abstract  Having a large number of timely donations during the early stages of a COVID-19 breakout would normally be considered rare. Donation is a special public goods game with zero yield for donors, and it has the characteristics of the prisoners' dilemma. This paper discusses why timely donations in the early stages of COVID-19 occurred. Based on the idea that donation is a strategy adopted by players during interconnection on account of their understanding of the environment, donation-related populations are placed on social networks and the inter-correlation structures in the population are described by scale-free networks. Players in donation-related populations are of four types: donors, illegal beneficiaries, legal beneficiaries, and inactive people. We model the evolutionary game of donation on a scale-free network. Donors, illegal beneficiaries and inactive people learn and update strategies under the Fermi update rule, whereas the conversion between legal beneficiaries and the other three types is determined by the environment surrounding the players. We study the evolution of cooperative action when the agglomeration coefficient, the parameters of the utility function, the noise intensity, the utility coefficient, the donation coefficient and the initial states of the population on the scale-free network change. For population sizes of 50, 100, 150, and 200, we give the utility functions and the agglomeration coefficients for promoting cooperation and study the corresponding steady states and structural characteristics of the population. We identify the best ranges of the noise intensity K, the donation coefficient α and the utility coefficient β for promoting cooperation at different population sizes. Furthermore, with the increase of the population size, the donor traps are found. At the same time, it is discovered that the initial states of the population have a great impact on the steady states; thus the upper and lower triangle phenomena are proposed. We also find that the population size itself is also an important factor for promoting donation, pointing out the direction of efforts to further promote donation and achieve better social homeostasis under the donation model.
Keywords:  donation      public goods game      evolutionary game      scale-free network  
Received:  12 October 2021      Revised:  13 December 2021      Accepted manuscript online:  24 December 2021
PACS:  02.50.Le (Decision theory and game theory)  
  05.45.Pq (Numerical simulations of chaotic systems)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 72031009 and 71871171) and the National Social Science Foundation of China (Grant No. 20&ZD058).
Corresponding Authors:  Lin-Lin Wang     E-mail:

Cite this article: 

Xian-Jia Wang(王先甲) and Lin-Lin Wang(王琳琳) Evolution of donations on scale-free networks during a COVID-19 breakout 2022 Chin. Phys. B 31 080204

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