Abstract
Under-reaction is a robust response to model misspecification rewarded by financial markets, rather than an “irrational” attitude that leads to extinction. I show that under-reacting rules guarantee predictions as accurate as Bayes’ in well-specified learn- ing problems and beat Bayes’ in many misspecified learning environments. Therefore, when a Bayesian agent trades with an under-reacting agent with the same information, there are no paths on which the under-reacting agent loses all his wealth against the Bayesian, while there is a large class of misspecified learning settings in which the Bayesian agent loses all his wealth against the under-reacting agent.