In joint work with Paulo Barelli and Hari Govindan, we study an exchange economy in which each trader observes a signal about an unobserved state parameter. With standard assumptions, and assuming countably many traders divided into a finite set of types of payoff and signal distribution, there is a unique fully revealing rational expectations Walrasian equilibrium (REE). The REE is totally monotone (TM) if each type’s cutoff signal for who gets to trade is increasing in the state. TM determines whether the REE is feasible for anonymous mechanisms in a class that includes auctions. If and only if the REE is feasible, it is approximated by equilibria of auctions with sufficiently many traders of each type. TM limits heterogeneity across types of traders. A sufficient condition is an average crossing property of the model’s primitives.