Can investors with incorrect beliefs survive in financial markets and have a significant impact on asset prices? My paper addresses this issue by analyzing a dynamic general equilibrium model where some investors have rational expectations, whereas others have incorrect beliefs concerning the mean growth rate of the economy. The main result is that an investor can survive if and only if he has the lowest survival index, which is a function of his belief accuracy, patience parameter, and relative risk aversion coefficient. If preferences are held constant across all investors, then those with incorrect beliefs cannot survive in the limit, although calibrations reveal that the selection process is excessively slow. However, if preferences vary across investors, even slightly, it becomes possible for an irrational investor to dominate the market even if his beliefs persistently and substantially deviate from the truth.