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)

In this paper, we develop a new approach to obtain the compactness of the fluctuation processes for Boltzmann dynamics. Our method is applicable to Kac's model, already studied by Uchiyama, but it covers many other cases. A novelty worth mentioning is the use of the weak topology of a Hilbert space.

We describe the random meeting motion of a finite number of investors in markets with friction as a Markov pure-jump process with interactions. Using a sequence of these, we prove a functional law of large numbers relating the large motions with the finite market of the so-called continuum of agents.

We study the dynamics of a large number, N , of investors which have meetings by groups of m. We obtain an explicit formula for the solution of the associated non-linear system of differential equations. This formula is tractable and it enables us to show the asymptotic stability of a large class of models. One of those models can be thought of as an interacting portfolio market.

No abstract