中国物理B ›› 2019, Vol. 28 ›› Issue (7): 78901-078901.doi: 10.1088/1674-1056/28/7/078901

• INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY • 上一篇    

Pyramid scheme model for consumption rebate frauds

Yong Shi(石勇), Bo Li(李博), Wen Long(龙文)   

  1. 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
  • 收稿日期:2019-03-15 修回日期:2019-04-17 出版日期:2019-07-05 发布日期:2019-07-05
  • 通讯作者: Wen Long E-mail:longwen@ucas.edu.cn
  • 基金资助:

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

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. 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
  • Received:2019-03-15 Revised:2019-04-17 Online:2019-07-05 Published:2019-07-05
  • Contact: Wen Long E-mail:longwen@ucas.edu.cn
  • Supported by:

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

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摘要：

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.

关键词: pyramid scheme, complex networks, small-world networks

Abstract:

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.

Key words: pyramid scheme, complex networks, small-world networks

中图分类号:  (Economics; econophysics, financial markets, business and management)

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64.60.aq (Networks)