Equilibrium Existence Issues

具有多维信号的拍卖被认为是重要的，但除非私人信息是独立的，否则在这种情况下没有普遍存在的结果。期望得到一个新的单交结果，在具有相互依赖价值和多维私有信息的m+1价格拍卖中，建立单调纯策略均衡的存在性。特别是，该结果将弥补Pesendorfer和Swinkels（2000）的信息聚合结果中缺失的存在性结果。这也标志着多维信号拍卖理论迈出了重要的第一步。一个更基本的问题是，在具有不连续收益的博弈中存在纳什均衡（拍卖是此类博弈的一类）。Reny（1999）包含了迄今为止最普遍的这类结果。即便如此，主要结果并没有涵盖政治科学中的一些重要游戏（例如，唐氏选举竞争模型）。本研究将对纯策略存在性结果进行推广。将这些新结果与唐氏选举竞争模型联系起来并不简单，因此这将是本研究的重要贡献。最后，分析了具有差异信息的交换经济中存在理性预期均衡的经典问题。新的见解将允许以需求对应的使用为中心的普遍存在结果。自Kreps（1977）以来，人们认为将注意力限制在严格的凹效用上，避免了允许消费者提交需求对应的需要。人们认为，缺乏冷漠意味着消费者只愿意提交需求函数。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问题。存在问题同样在本研究中得到了更普遍的解决。

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.