Pyramid scheme model for consumption rebate frauds

Shi Yong^{1, 2, 3}, Li Bo^{1, 2, 3}, Long Wen^{1, 2, 3, †}

(a) The analytical result and the simulative result of maximum generation G_SW when the possible participants ϕ changes. We take the parameters N = 1000, K = 3, r₀ = 0.2, r₁ = 0.2. (b) The analytical result and the simulative result of maximum generation G_SW when the number of possible participants N changes. We take the parameters K = 3, ϕ=0.1, r₀ = 0.2, r₁ = 0.2. The simulative results are averaged after 100 simulations.