Information Percolation in OTC Markets
This chapter describes a simple model of the [percolation] of information of common interest through an OTC market with many agents. Agents encounter each other at random over time and reveal information to each other through bids and offers. We are particularly interested in the evolution over time of the cross-sectional distribution of the posterior probability assignments of the various agents. This chapter is based mainly on results from Duffie and Manso (2007), Duffie, Giroux, and Manso (2010), and Duffie, Malamud, and Manso (2010b).
Hayek (1945) argued that markets allow information that is dispersed in a population to be revealed through prices. The notion of Grossman (1976) of a rational-expectations equilibrium formalizes this idea in a model of a centralized market with price-taking agents. Milgrom (1981), Glosten and Milgrom (1985), Kyle (1985), Pesendorfer and Swinkels (1997), and Reny and Perry (2006) provide alternative strategic foundations for the rationalexpectations equilibrium concept in centralized markets. A number of important markets, however, are decentralized. These include OTC markets and private auction markets. Wolinsky (1990), Blouin and Serrano (2001), Duffle and Manso (2007), Golosov, Lorenzoni, and Tsy vinski (2008), Duffle, Giroux, and Manso (2010), and Duffie, Malamud, and Manso (2009, 2010b) study information transmission in decentralized markets.
Models of information percolation are useful in more general settings for social learning. For example, Banerjee and Fudenberg (2004) exploit the exact law of large numbers for random matching among a large population, provide a dynamic rule for updating beliefs, and show conditions for convergence.
The approach taken in this chapter allows a relatively explicit solution for the cross-sectional distribution of posterior beliefs at each time. We begin in the next two sections with the basic information structure for the economy