Information Percolation

Abstract

We study the "percolation" of information of common interest through a large market as agents encounter and reveal information to each other over time. We provide an explicit solution for the dynamics of the cross-sectional distribution of posterior beliefs. We also show that convergence of the cross-sectional distribution of beliefs to a common posterior is exponential and that the rate of convergence does not depend on the size of the groups of agents that meet. The rate of convergence is merely the mean rate at which an individual agent is matched. (JEL D83)

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

“…For cases in which there is a fixed number n of agents at each private meeting, Duffie, Giroux and Manso (2009) prove that equation (5) has a unique solution, given explicitly by an expansion in convolution powers of α 0 , in a form of summation originated by Wild (1951). We now provide a similar result for any distribution of meeting sizes.…”

“…We will later show how to compute h(m, t) by extending the results of Duffie, Giroux, and Manso (2009). Almost surely, h(µ 0 , t) has two outcomes, one on the event {X = H}, and the other on the event {X = L}.…”

“…In prior work, Duffie and Manso (2007) and Duffie, Giroux, and Manso (2009) allowed only private information sharing. Further, rather than fixing the sizes of groups sharing information privately as in prior work, we allow randomly sized groups.…”

“…The purely-private type distribution α t is calculated explicitly by Duffie, Giroux, and Manso (2009) for cases in which the number of agents sharing information at each meeting is a fixed integer. The equation (5) for α t is thus somewhat familiar from Duffie, Giroux, and Manso (2009).…”

“…The purely-private type distribution α t is calculated explicitly by Duffie, Giroux, and Manso (2009) for cases in which the number of agents sharing information at each meeting is a fixed integer. The equation (5) for α t is thus somewhat familiar from Duffie, Giroux, and Manso (2009). The equation (6) for β t , folding in the effects of public information releases, reflects the characterization given by Lemma 3.1 as well as the mean rate η at which β t gets replaced by a new public release.…”