Markets play the role of re-distributing resources. Which type of behaviors are rewarded by the exchange? Under which conditions are market capable of rewarding rational better informed agents or profit maximizing firms? Is agents and firms heterogeneity a persistent or transient property? Ultimately, what is the role of market selection in shaping aggregate economic outcomes?Despite little is known on the issue, most of economic models rely on the Market Selection Hypothesis stating that non maximizing economic actors persistently loose wealth in favors of the maximizing ones. In the long-run the former are driven out of the market so that only the latter have an impact on the economy. However, a formal general proof of the selective capability of markets is still missing.Aim of this project is to build upon the recent market selection literature, in particular, preliminary results about its possible failure, and recent techniques for the analysis of random dynamical systems in order to provide a definite check of the Market Selection Hypothesis, both in exchange and production economies. Moreover, we shall use the market selection approach to tackle some specific economic questions, such as the effect of financial innovations on financial markets stability, and the ensuing possible misallocations of resources in financing productive activities.Our research has thus a positive content, namely the characterization of the outcome of market selection under the most general assumptions about agents behavior, and a normative one, namely how to use this knowledge to improve the effect of economic policies.