Equilibrium Existence Issues

均衡存在问题

• 批准号: 0617884
• 负责人: Philip Reny
• 金额: $ 11.78万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2009-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0617884&HistoricalAwards=false
• 关键词: Equilibrium; Existence; Issues

Auctions with multi-dimensional signals are recognized to be important, yet, unless private information is independent, there are no general existence results in such situations. A new single-crossing result is expected to establish the existence of a monotone pure strategy equilibrium in an m+1st price auction with interdependent values and multi-dimensional private information. In particular, this result will supply the missing existence result in the information aggregation result in Pesendorfer and Swinkels (2000). It will also mark an important first step in the theory of auctions with multi-dimensional signals.A more basic issue is the existence of Nash equilibria in games with discontinuous payoffs (auctions are one class of such games). Reny (1999) contains the most general result of this kind to date. Even so, the main result there does not cover some important games from political science (e.g., Downsian electoral competition models). This current study will develop generalization of the pure strategy existence result. Relating these new results to the Downsian model of electoral competition is not at all straightforward and thus will be a significant contribution of this research.Finally, the classic question of the existence of a rational expectations equilibrium in an exchange economy with differential information is analyzed. The new insight will permit a general existence result centers around the use of demand correspondences. Since Kreps (1977) it was thought that restricting attention to strictly concave utilities avoids the need to permit consumers from submitting demand correspondences. The lack of indifference, it was thought, meant that consumers would only want to submit demand functions. This is not the case and permitting consumers to submit correspondences resolves the existence problem in the classic counter examples. The existence problem is similarly resolved much more generally in this study.

具有多维信号的拍卖被认为是重要的，然而，除非私人信息是独立的，否则在这种情况下没有一般的存在结果。 一个新的单交叉结果被期望建立一个单调的纯策略均衡的存在性在m+1价格拍卖相互依赖的价值和多维私人信息。 特别地，该结果将提供Pesendorfer和Swinkels（2000）中的信息聚合结果中缺失的存在结果。 这也标志着多维信号拍卖理论的重要的第一步。一个更基本的问题是具有不连续支付的博弈中纳什均衡的存在性（拍卖是这类博弈的一类）。 Reny（1999）包含了迄今为止这类最一般的结果。 即便如此，那里的主要结果并没有涵盖政治学中的一些重要博弈（例如，Downsian选举竞争模型）。 本研究将推广纯策略存在性结果。 将这些新结果与选举竞争的Downsian模型联系起来并不简单，因此将是本研究的一个重大贡献。最后，分析了具有差异信息的交换经济中理性预期均衡的存在性这一经典问题。 新的洞察力将允许一个一般的存在结果围绕使用需求对应。 自Kreps（1977）以来，人们认为限制对严格凹效用的关注可以避免允许消费者提交需求对应的需要。 人们认为，缺乏无差别意味着消费者只想提交需求函数。 但事实并非如此，允许消费者提交通信解决了经典反例中的存在性问题。 在本研究中，存在性问题同样得到了更普遍的解决。