We introduce a simple model of the “percolation” of information of common interest through a large market, as agents encounter each other over time and reveal information to each other, some of which they may have received earlier from other agents. We are particularly interested in the evolution of the cross-sectional distribution in the population of the posterior probability assignments of the various agents. We provide a market example based on privately held auctions, and obtain a relatively explicit solution for the cross-sectional distribution of posterior beliefs at each time.
Our results contribute to the literature on information transmission in markets. Friedrich A. Hayek (1945) argues that markets allow information that is dispersed in a population to be revealed through prices. Sanford J. Grossman’s (1981) notion of a rational-expectations equilibrium formalizes this idea in a setting with price-taking agents. Paul R. Milgrom (1981), Wolfgang Pesendorfer and Jeroen M. Swinkels (1997), and Philip J. Reny and Motty Perry (2006) provide strategic foundations for the rational expectations equilibrium concept in centralized markets. A number of important markets, however, are decentralized. These include over-the-counter markets and private-auction markets. Asher Wolinsky (1990) and Max R. Blouin and Roberto Serrano (2001) study information transmission in decentralized markets. In contrast to these two papers, equilibrium behavior in our market example leads to full revelation of information through trading. We also explicitly characterize the percolation of this information through the market.
Our paper is also related to the literature on social learning. For example, our objectives are similar to those of Abhijit Banerjee and Drew Fudenberg (2004), who provide a brief survey of the literature. Like us, Banerjee and Fudenberg (2004) exploit the law of large numbers for random matching among a large population, provide a dynamic rule for updating, and show conditions for convergence. Our model allows a relatively explicit solution for the cross-sectional distribution of posterior beliefs at each time.