Ponzi Pyramid Model

P.I.V.O.T. Protocol

Wealth Distribution

Box Plot

Statistical Data

Code

rankMax = 15;
n = 2*2^rankMax - 1;
a = Flatten[
   Table[
    Table[2^rank, 2^(rankMax - rank)]
    ,
    {rank, 0, rankMax}
    ]
   ];
a = a/Total[a];
a = N[a*n];
medianA = N[Median[a]]
Histogram[a, PlotLabel -> "wealth distribution of Ponzi model"]
BoxWhiskerChart[a, "Outliers", 
 PlotLabel -> "BoxWhisker of Ponzi model"]

b = Table[Sum[N[1/rank], {rank, x, n}], {x, 1, n}];
b = b/Total[b];
b = N[b*n];
medianB = N[Median[b]]
Histogram[b, PlotLabel -> "wealth distribution of 囧 model"]
BoxWhiskerChart[b, "Outliers", PlotLabel -> "BoxWhisker of 囧 model"]

Conclusion

The above examples compare two models with 65,535 participants. In the Ponzi model, nearly everyone incurs losses, and most people's returns are approximately 0, while those at the top can have returns of about 4096 times. However, in the P.I.V.O.T. protocol, about 37% (1/e ≈ 37%) of people have positive returns, and even the top participants have a more reasonable return of 11.66 times.