In a repeated market for short-lived assets, we investigate long run wealth-driven selection on the general class of investment rules that depend on endogenously determined current and past prices. We study the random dynamical system that describes the price and wealth dynamics and characterize local stability of long-run market equilibria. Instability, leading to asset mis-pricing and informational inefficiencies, turns out to be a common phenomenon generated by two different mechanisms. Firstly, conditioning investment decisions on asset prices implies that dominance of an investment rule on others, as measured by the relative entropy, can be different at different prevailing prices thus reducing the global selective capability of the market. Secondly, the feedback existing between past realized prices and current investment decisions can lead to a form of deterministic overshooting.