It is well known that if agents update their beliefs according to Bayes’ Law, then their beliefs will eventually converge to the true data generating process (“weak merging”). A great deal of experimental evidence (by Camerer and Rabin, among others) suggests that people are not Bayesians: they sometimes undervalue new information (bias toward previous beliefs) and sometimes overvalue new information (the “hot hand fallacy” in sports, for instance). What implication does that have for learning? It turns out that underreaction does not affect the limit of the learning process (intuitively, it only slows down the rate of convergence), but that overreaction can lead an agent to converge on an untrue belief. Indeed, underreaction can also lead to convergence to an untrue belief if the agent is allowed to condition his “Bayesianness” – the extent to which she is a standard Bayesian updater or is an undervaluer of new information – on the current information.
http://www.bepress.com/bejte/vol10/iss1/art3/ (BE Press articles are free to download, but you must first register your email)
A Fine Theorem 