# A Pyramid Scheme Model Based on "Consumption Rebate" Frauds

## TL;DR

This paper models pyramid schemes using network theory, analyzing their lifespan across different network structures and applying the model to real-world data to understand participant connections.

## Contribution

It introduces a network-based pyramid scheme model incorporating common features and analyzes its dynamics across various network topologies.

## Key findings

- Pyramid schemes can last longer in scale-free networks.
- Real-world pyramid schemes may form small-world networks.
- Analytical results vary with network structure.

## Abstract

There are various types of pyramid schemes which 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 appeared in recent years: promising high returns, rewarding the participants recruiting the next generation of participants, and the organizer will take all the money away when he finds the money from the new participants is not enough to pay the previous participants interest and rewards. We assume the pyramid scheme carries on in the tree network, ER random network, SW small-world network or BA scale-free network respectively, then give the analytical results of how many generations the pyramid scheme can last in these cases. We also use our model to analyse a pyramid scheme in the real world and we find the connections between participants in the pyramid scheme may constitute a SW small-world network.