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. We consider a market model involving finitely many informed risk-averse traders interacting with a market maker. Our main result identifies a basic smoothness condition on the price in the market that ensures information will be aggregated. We give conditions under which cost function market makers (or, equivalently, market makers based on market scoring rules) satisfy the smoothness requirement. We further show that regardless of the level of risk aversion of the traders, the final allocation and prices together constitute a competitive equilibrium; thus, in particular, the final portfolios of the traders are ex post Pareto efficient.
Iyer, Kris, Ramesh Johari, and Ciamac Moallemi. "Information aggregation in smooth markets." In EC '10 Proceedings of the 11th ACM Conference on Electronic Commerce, 199-206. New York, NY: ACM, June 2010.
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