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; furthermore, 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.