Pyramid scheme model for consumption rebate frauds

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, Erdos-Reney (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.