Illusions and Perceived Wealth: an Agent-based model of Madoff’s Ponzi scheme

We describe an Agent-Based Model of a Ponzi scheme following the Madoff’s case. Agents have an initial propensity to invest in the scam, as the wealth is perceived to grow, whereas it is not invested in any way, and is dissipated by the fraudster. We emphasize that the widening gap between the perceived wealth and the true total money in the hands of the impostor is the key feature of such schemes. If trust evaporates due to the absorption of bad news on the economy, the propensity gradually reverses and an increasing number of agents withdraw their capital (and made up profits). We examine the time needed to reveal the scam and reach a bankruptcy, as a function of the amount of news that hits the market. We also investigate how a special agent named Markopolos (inspired to a real personage) affects the time to bankruptcy, due to his ability to abruptly “convince” to dis-invest the agents he run across. The Markopolos effect appears to be statistically significant, but is quite weak with respect to the outcome generated by a flow of news and the ensuing widespread loss of trust and redemptions.