Pyramid scheme model for consumption rebate frauds
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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, Erd?s–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.
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, Erd?s–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.
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, Erd?s–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.
引文
[1]http://tv.cctv.com/2017/06/18/VIDE8gtfpFkpiBv2QYnNuGIF170618.shtml[2019-3-15]
[2]http://www.mps.gov.cn/n2253534/n2253543/c6108362/content.html[2019-3-15]
[3]https://news.china.com/news100/11038989/20170707/30931598 all.html[2019-3-15]
[4]https://en.wikipedia.org/wiki/MMM(Ponzi scheme company)[2019-3-15]
[5]http://www.51voa.com/VOA Special English/pyramid-vs-ponzi-69196.html[2019-3-15]
[6]Gastwirth J L 1977 Am.Stat.31 79
[7]Artzrouni M 2009 Math.Soc.Sci.58 190
[8]Moore T, Han J and Clayton R 2012 Financial Cryptography and Data Security-16th International Conference, Februray 27–March 2, 2012,Kralendijk, Bonaire, p.41
[9]Zhu A, Fu P, Zhang Q and Chen Z 2017 Physica A 479 128
[10]Fu P, Zhu A, Ni H, Zhao X and Li X 2017 Physica A 490S0378437117308087
[11]Háznagy A, Fi I, London A and Nemeth T 2015 International Conference on Models and Technologies for Intelligent Transportation Systems, June 3–5, 2015, Budapest, Hungary, p.371
[12]Liu J, Xiong Q Y, Wang K and Shi W R 2015 Chin.Phys.B 24 076401
[13]Brantle T F and Fallah M 2007 PICMET’07-2007 Portland International Conference on Management of Engineering and Technology,August 5–9, 2007, Portland, OR, USA, p.540
[14]Pastor-Satorras R and Vespignani A 2001 Phys.Rev.Lett.86 3200
[15]Moreno Y, Nekovee M and Pacheco A F 2004 Phys.Rev.E 69 066130
[16]West D B 2001 Networks 30 73
[17]Erd?s P and Rényi A 2011 Trans.Am.Math.Soc.286 257
[18]Watts D J and Strogatz S H 1998 Nature 393 440
[19]Grossman J W 2002 Phys.Today 31 74
[20]Santos V M L D, Moreira F G D and Longo R L 2004 Chem.Phys.Lett.390 157
[21]Barabasi A L and Albert R 1999 Science 286 509
[22]Albert R and Barabasi A L 2001 Rev.Mod.Phys.74 12
[23]Katzav E, Nitzan M, ben-Avraham D, Krapivsky P, Khn R, Ross N and Biham O 2015 Europhys.Lett.111 26006
[24]Newman M E and Watts D J 1999 Phys.Rev.E 60 7332
[25]Barrat A and Weigt M 1999 Eur.Phys.J.B 13 547
[26]Ventrella A V, Piro G and Grieco L A 2018 IEEE Syst.J.12 3869
[27]Reuven C and Shlomo H 2003 Phys.Rev.Lett.90 058701
[28]http://www.gd.chinanews.com/2018/2018-07-24/2/397998.shtml[2019-3-15]
[2]http://www.mps.gov.cn/n2253534/n2253543/c6108362/content.html[2019-3-15]
[3]https://news.china.com/news100/11038989/20170707/30931598 all.html[2019-3-15]
[4]https://en.wikipedia.org/wiki/MMM(Ponzi scheme company)[2019-3-15]
[5]http://www.51voa.com/VOA Special English/pyramid-vs-ponzi-69196.html[2019-3-15]
[6]Gastwirth J L 1977 Am.Stat.31 79
[7]Artzrouni M 2009 Math.Soc.Sci.58 190
[8]Moore T, Han J and Clayton R 2012 Financial Cryptography and Data Security-16th International Conference, Februray 27–March 2, 2012,Kralendijk, Bonaire, p.41
[9]Zhu A, Fu P, Zhang Q and Chen Z 2017 Physica A 479 128
[10]Fu P, Zhu A, Ni H, Zhao X and Li X 2017 Physica A 490S0378437117308087
[11]Háznagy A, Fi I, London A and Nemeth T 2015 International Conference on Models and Technologies for Intelligent Transportation Systems, June 3–5, 2015, Budapest, Hungary, p.371
[12]Liu J, Xiong Q Y, Wang K and Shi W R 2015 Chin.Phys.B 24 076401
[13]Brantle T F and Fallah M 2007 PICMET’07-2007 Portland International Conference on Management of Engineering and Technology,August 5–9, 2007, Portland, OR, USA, p.540
[14]Pastor-Satorras R and Vespignani A 2001 Phys.Rev.Lett.86 3200
[15]Moreno Y, Nekovee M and Pacheco A F 2004 Phys.Rev.E 69 066130
[16]West D B 2001 Networks 30 73
[17]Erd?s P and Rényi A 2011 Trans.Am.Math.Soc.286 257
[18]Watts D J and Strogatz S H 1998 Nature 393 440
[19]Grossman J W 2002 Phys.Today 31 74
[20]Santos V M L D, Moreira F G D and Longo R L 2004 Chem.Phys.Lett.390 157
[21]Barabasi A L and Albert R 1999 Science 286 509
[22]Albert R and Barabasi A L 2001 Rev.Mod.Phys.74 12
[23]Katzav E, Nitzan M, ben-Avraham D, Krapivsky P, Khn R, Ross N and Biham O 2015 Europhys.Lett.111 26006
[24]Newman M E and Watts D J 1999 Phys.Rev.E 60 7332
[25]Barrat A and Weigt M 1999 Eur.Phys.J.B 13 547
[26]Ventrella A V, Piro G and Grieco L A 2018 IEEE Syst.J.12 3869
[27]Reuven C and Shlomo H 2003 Phys.Rev.Lett.90 058701
[28]http://www.gd.chinanews.com/2018/2018-07-24/2/397998.shtml[2019-3-15]