Evolution and market behavior with endogenous investment rules

In a repeated market for short-lived assets, we investigate wealth-driven selection among investment rules that depend on endogenous market variables, such as current and past prices. We study the random dynamical system describing prices and wealth dynamics and characterize local stability of the long-run equilibria in which one or a group of traders dominate. Multiplicity of stable and unstable equilibria, leading to path dependency and persistent heterogeneity, turns out to be a common phenomenon generated by two different mechanisms. Firstly, conditioning investment decisions on endogenous market variables implies that the relative performance of investment rules, in terms of average growth rates, may be different for different prevailing prices, so that the market may fail to select a global winner. Secondly, the feedback existing between past asset prices and current investment decisions can lead to a form of deterministic overshooting.