Information aggregation in smooth markets

Recent years have seen extensive investigation of the information aggregation properties of prediction markets. However, relatively little is known about conditions under which a market will aggregate the private information of rational risk averse traders who optimize their portfolios over time; in particular, what features of a market encourage traders to ultimately reveal their private information through trades? We consider a market model involving finitely many informed risk-averse traders interacting with a market maker. Our main result identifies a basic asymptotic smoothness condition on the price in the market that ensures information will be aggregated under a portfolio convergence assumption. Asymptotic smoothness is fairly mild: it requires that, eventually, infinitesimal purchases or sales should see the same per unit price. Notably, we demonstrate that, under some mild conditions, cost function market makers (or, equivalently, market makers based on market scoring rules) satisfy the asymptotic smoothness requirement.