Information Aggregation in Bayesian Games with many Players

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Project Abstract In this project the principal investigator conducts theoretical research on the welfare and information aggregation properties of market institutions (exemplified by auctions and double auctions), elections, and related institutions. A common feature of these institutions is that they involve the interaction of a large number of agents. Whether large markets effectively aggregate decentralized private information is one of the central questions in economic theory. This project analyzes this question for auctions, double auctions and related environments. The advantage of the auction setting is that it provides an explicit model of how individual actions and information translate into prices. This is in contrast to the price-taking model of a competitive market that is characterized by equilibrium conditions on prices, but provides no explanation of how prices satisfying those conditions are arrived at. The findings define conditions (necessary and sufficient) on the structure of the market that lead to `full information equivalence` . Full information equivalence is satisfied if the equilibrium price is the same whether or not buyers or sellers have private information about the quality of the objects for sale. The question of whether elections effectively aggregate private information is central to political theory. A strong argument for elections is that society may be collectively better informed about the relative quality of a set of alternatives than any individual. Elections provide a mechanism for aggregating private information, ensuring a better collective decision. This idea inspired some of the earliest mathematical models of voting in elections and dates back at least to Condorcet. The set of environments in which elections might usefully aggregate private information about the relative quality of a pair of alternatives goes well beyond the Jury setting that was the focus of Condorcet's work. In most elections voters have private information about the relative quality of the alternatives. This project characterizes the voting environments that lead to full information equivalence, i.e., situations in which the alternative elected is the same whether or not the private information of voters about the quality of the alternatives is made public before the election. Finally, this project develops an analytical framework that includes both elections and auctions as special cases. Analyzing this more abstract setting promises to provide a deeper understanding of the underlying characteristics that lead to institutions to have good information aggregation properties.