Information Aggregation in Bayesian Games with many Players

项目摘要在这个项目中，首席研究员对市场机构(以拍卖和双向拍卖为例)、选举和相关机构的福利和信息聚集特性进行了理论研究。这些机构的一个共同特点是，它们涉及大量代理人的互动。大型市场是否有效地聚合了分散的私人信息，这是经济理论的核心问题之一。这个项目分析了拍卖、双向拍卖和相关环境中的这个问题。拍卖设置的优势在于，它提供了一个明确的模型，说明个人行为和信息如何转化为价格。这与竞争性市场的定价模型不同，竞争性市场的定价模型以价格均衡条件为特征，但没有解释满足这些条件的价格是如何得出的。调查结果界定了导致“完全信息等价性”的市场结构的条件(必要和充分)。如果均衡价格相同，则完全信息等价被满足，无论买方或卖方是否拥有关于待售物品质量的私人信息。选举是否有效地汇集了私人信息，这一问题是政治理论的核心。支持选举的一个强有力的理由是，社会可能比任何个人都更了解一系列替代方案的相对质量。选举提供了一种汇总私人信息的机制，确保做出更好的集体决定。这一想法启发了一些最早的选举投票数学模型，至少可以追溯到孔多塞。选举可能有效地收集关于一对替代方案的相对质量的私人信息的环境远远超出了孔多塞工作的重点--陪审团设置。在大多数选举中，选民都有关于替代方案的相对质量的私人信息。该项目描述了导致完全信息对等的投票环境，即，无论选民关于备选方案质量的私人信息是否在选举前公布，当选的备选方案都是相同的。最后，该项目制定了一个分析框架，将选举和拍卖都作为特例包括在内。分析这一更抽象的设置有望提供对导致机构具有良好信息聚合属性的潜在特征的更深入理解。

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.