Information Aggregation and Allocative Efficiency in Smooth Markets

Recent years have seen extensive investigation of the information aggregation properties of 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 prices in the market that ensures information is aggregated as long as portfolios converge; further, under this assumption, the allocation achieved is ex post Pareto efficient. 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, algorithmic markets based on cost functions (or, equivalently, markets based on market scoring rules) aggregate the information of traders.