Evolution and market behavior with endogenous investment rules

In a complete market for short-lived assets, we investigate long run wealth-driven selection on a general class of investment rules that depend on endogenously determined current and past prices. We find that market instability, leading to asset mis-pricing and informational efficiencies, is a common phenomenon and is due to two different mechanisms. First, 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. Second, the feedback existing between past realized prices and current investment decisions can lead to a form of deterministic overshooting. By investigating the random dynamical system that describes the price and wealth dynamics, we are able to derive general conditions for the occurrence of each type of market instability and the emergence of informational inefficiencies.