The paper analyzes a finite time economy with a single risky asset which pays a one-shot payoff (dividend). The payoff is random and its distribution is not known a priori. Agents observe public signals (random draws from the same distribution) and update their beliefs about the payoff. They trade in order to reshuffle their portfolios according to new beliefs. Agents may use various updating rules and are considered to be of two types: sophisticated who are aware of their future beliefs and prices, and naive who are not. Drawing on the methodology by Sandroni (2000), it is shown that among sophisticated agents, those with less accurate beliefs are driven out, in the sense that their wealth becomes arbitrarily small when the number of signals is sufficiently large. On the other hand, it is shown that this statement may not hold in economies with naive agents only, where even agents with inaccurate beliefs may survive.