From zero-intelligence to Bayesian learning: the effect of rationality on market efficiency

Abstract

In this paper, we investigate the relationship between individual rationality and price informative efficiency studying a prediction market model where agents repeatedly bet on the occurrence of a binary event following their subjective beliefs. We define individual rationality in terms of the amount of past observations used to update beliefs. In this way, a wide spectrum of rationality levels emerges, ranging from zero-intelligence to Bayesian learning. We show that the relationship between individual rationality and price informative efficiency is nonlinear and U-shaped. We argue that the results emerge from the particular interaction of two evolutionary forces operating at different levels: the market selection mechanism that moves wealth toward more accurate agents and the individual learning process that moves posterior probabilities over models depending on observed realizations.