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Chin. Phys. B, 2019, Vol. 28(7): 078901    DOI: 10.1088/1674-1056/28/7/078901

Pyramid scheme model for consumption rebate frauds

Yong Shi(石勇)1,2,3, Bo Li(李博)1,2,3, Wen Long(龙文)1,2,3
1 School of Economics and Management, University of Chinese Academy of Sciences, Beijing 100190, China;
2 Research Center on Fictitious Economy and Data Science, Chinese Academy of Sciences, Beijing 100190, China;
3 Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences, Beijing 100190, China

There are various types of pyramid schemes that have inflicted or are inflicting losses on many people in the world. We propose a pyramid scheme model which has the principal characters of many pyramid schemes that have appeared in recent years:promising high returns, rewarding the participants for recruiting the next generation of participants, and the organizer takes all of the money away when they find that the money from the new participants is not enough to pay the previous participants interest and rewards. We assume that the pyramid scheme is carried out in the tree network, Erdös-Réney (ER) random network, Strogatz-Watts (SW) small-world network, or Barabasi-Albert (BA) scale-free network. We then give the analytical results of the generations that the pyramid scheme can last in these cases. We also use our model to analyze a pyramid scheme in the real world and we find that the connections between participants in the pyramid scheme may constitute a SW small-world network.

Keywords:  pyramid scheme      complex networks      small-world networks  
Received:  15 March 2019      Revised:  17 April 2019      Published:  05 July 2019
PACS:  89.65.Gh (Economics; econophysics, financial markets, business and management) (Networks)  

Project supported by the National Natural Science Foundation of China (Grant Nos. 71771204 and 91546201).

Corresponding Authors:  Wen Long     E-mail:

Cite this article: 

Yong Shi(石勇), Bo Li(李博), Wen Long(龙文) Pyramid scheme model for consumption rebate frauds 2019 Chin. Phys. B 28 078901

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