Self-Fulfilling Prophecies, Quasi Non-Ergodicity & Wealth Inequality

Jean-Philippe Bouchaud and Roger E.A. Farmer

4 March, 2021

Abstract

We construct a model where people trade assets contingent on an observable signal that reflects public opinion. The agents in our model are replaced occasionally and each person updates beliefs in response to observed outcomes. We show that the distribution of the observed signal is described by a quasi non-ergodic process and that people continue to disagree with each other forever. Our model generates large wealth inequalities that arise from the multiplicative nature of wealth dynamics which makes successful bold bets highly profitable. The flip side of this statement is that unsuccessful bold bets are ruinous and lead the person who makes such bets into poverty. People who agree with the market belief have a low expected subjective gain from trading. People who disagree may either become spectacularly rich, or spectacularly poor.