Information Percolation in Large Markets

Abstract

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 over time 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. Hayek (1945) argues that markets allow information that is dispersed in a population to be revealed through prices. Grossman’s (1981) notion of a rational-expectations equilibrium formalizes this idea in a setting with price-taking agents. Milgrom (1981), Pesendorfer and Swinkels (1997), and Reny and 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. Wolinsky (1990) and Blouin and Serrano (2002) study information transmission in decentralized markets. In contrast to these two papers, equilibrium behavior in our market example leads to full revelation of information We happily acknowledge conversations with Manuel Amador, Frank Kelly, Jeremy Stein, and Pierre-Olivier Weill, and research assistance from Sergey Lobanov. Rubinstein and Wolinsky (1985) and Gale (1986a, 1986b) study decentralized markets without asymmetric information. Satterthwaite and Shneyerov (2003) study decentralized market with private-value asymmetric information. Amador and Weill (2006) study a more abstract setting regarding transmission of common and private i nformation.