The Relative Contributions of Private Information Sharing and Public Information Releases to Information Aggregation

Abstract

We calculate learning rates when agents are informed through both public and private observation of other agents' actions. We provide an explicit solution for the evolution of the distribution of posterior beliefs. When the private learning channel is present, we show that convergence of the distribution of beliefs to the perfect-information limit is exponential at a rate equal to the sum of the mean arrival rate of public information and the mean rate at which individual agents are randomly matched with other agents. If, however, there is no private information sharing, then convergence is exponential at a rate strictly lower than the mean arrival rate of public information. JEL Classification Numbers: D83, D82.

Some New Results on Information Percolation

“…. It also suggests that some of the results of Duffie, Malamud and Manso [6] can be extended to the case where information exchanges involve m agents (with possibly m random as they consider) even though the equation in their model does not belong to the class studied in the present paper and the techniques of tree expansions are not directly applicable. But a functional law of large numbers might be provable for their set of ODE's (4) and (5) in theorem 3.2 on page 1581.…”

Decentralized Trading With Private Information

“…In the literature on asset pricing in decentralized markets, a few recent papers deal with information transmission through bilateral meetings: Duffie and Manso (2007), Duffie, Giroux, and Manso (2010), Duffie, Malamud, andManso (2009, 2010). These papers characterize in closed form the dynamics of beliefs in models in which agents perfectly share the information of the agents they meet.…”