Noise and aggregation of information in large markets

We study the relation between noise (liquidity traders, endowment shocks) and the aggregation of information in financial markets with large number of agents. We show that as long as noise increases with the number of agents, the limiting equilibrium is well-defined and leads to non-trivial information acquisition, even when per-capita noise tends to zero. In such equilibrium risk sharing and price revelation play different roles than in the standard limiting economy in which per-capita noise is finite. We apply our model to study information sales by a monopolist, and information acquisition in multi-asset markets, showing that it leads to qualitatively different results with respect to those in the existing literature. Our conditions on noise are shown to be necessary and sufficient to have limiting economies with perfectly competitive behavior consistent with endogenous information acquisition.