We study a novel class of noisy rational expectations equilibria in markets with large number of agents. We show that, as long as noise increases with the number of agents in the economy, the limiting competitive equilibrium is well-defined and leads to non-trivial information acquisition, perfect information aggregation, and partially revealing prices, even if per capita noise tends to zero. We find that in such equilibrium risk sharing and price revelation play dierent roles than in the standard limiting economy in which per capita noise is not negligible. We apply our model to study information sales by a monopolist, information acquisition in multi-asset markets, and derivatives trading. The limiting equilibria are shown to be perfectly competitive, even when a strategic solution concept is used.