Information Aggregation with Costly Information Acquisition

Abstract

We study information aggregation in a dynamic trading model with partially informed traders. Ostrovsky [2012] showed that ‘separable’ securities aggregate information in all equilibria, however, separability is not robust to small changes in the traders’ private information. To remedy this problem, we allow traders to acquire signals with cost κ, in every period. We show that ‘κ separable securities’ characterize information aggregation and, as the cost decreases, nearly all securities become κ separable, irrespective of the traders’ initial private information. Moreover, the switch to κ separability happens not gradually but discontinuously, hence even a small decrease in costs can result in a security aggregating information. We provide a complete classification of securities in terms of how well they aggregate information, which surprisingly depends only on their payoff structure. Finally, even with myopic traders, cheaper information may accelerate or decelerate information aggregation for all but Arrow-Debreu securities.

Keywords: C91, D82, D83, D84, G14, G41 Information Aggregation, Information Acquisition, Financial Markets, Prediction Markets

JEL Classification: C91, D82, D83, D84, G14, G41