Multidimensional Mechanism Design: Theory and Applications

9410747斯塔切蒂机制设计问题在许多经济情况下自然出现，包括对垄断者的监管、拍卖、政府采购、非线性定价和公共产品的提供。到目前为止，在这些主要应用领域中的每一个领域都有大量的文献，但在大多数情况下，分析已经被简化为不确定性由单个参数建模的情况，并且商品的数量被限制在两个(两个商品中的一个通常是货币)。更高维度的案例带来的技术困难阻碍了进展，并推迟了我们对经济应用的理解。该项目开发了多维机构设计理论中的新技术，并将这些技术应用于几个重要的经济问题。更具体地说，该项目开发的多维机构设计技术是基于Rochet和Armstrong的工作。对于具有一定线性结构的问题(包括具有外部性的拍卖和多产品垄断中的定价)，共轭对偶导致了激励相容机制的包络条件和完全刻画。散度定理代替了一维情况下的分部积分，简化了主体的目标函数。在具有外部性的对称拍卖中，这些技术允许人们识别参与约束约束于最优解的唯一买家类型。迈尔森的“正则性”概念在一维问题中是如此关键，但在更高的维度上有一个更复杂但有用的类比。对Jehiel、摩尔多瓦和Stacchetti的具有外部性的对称拍卖模型进行了扩展，放松了对称性假设，并考虑了买家即使在卖方保留物品的情况下也会经历外部性的情况。动态博弈的研究是在存在购买目标的战略动机的情况下进行的，即稍后转售。上面提到的广义规律性分析将把阿姆斯特朗关于定价和监管的结果扩展到更广泛的经济环境中，适用于多种产品垄断。

9410747 Stacchetti Mechanism design problems arise naturally in numerous economic situations, including the regulation of a monopolist, auctions, government procurement, nonlinear pricing, and the provision of public goods. There is a vast literature in each one of these major fields of application by now, but for the most part, the analysis has been reduced to the case in which uncertainty is modelled by a single parameter, and the number of goods is restricted to two (one of the two goods is typically money). The technical difficulties presented by higher dimensional cases have impeded progress, and delayed our understanding of economic applications. The project develops new techniques in the theory of multidimensional mechanism design, and applies these techniques to several important economic problems. More specifically, the techniques for multidimensional mechanism design developed by this project are based on the work of Rochet and Armstrong. For problems with a certain linear structure (including auctions with externalities and pricing in multiproduct monopolies) conjugate duality leads to an envelope condition and a full characterization of incentive compatible mechanisms. The divergence theorem takes the place of integration by parts, which is used in the one-dimensional case to simplify the objective function of the principal. In a symmetric auction with externalities, these techniques allow one to identify the only buyer type whose participation constraint binds at the optimal solution. Myerson's notion of "regularity", which is so crucial in one-dimensional problems, has a more complicated but useful analog in higher dimensions. The symmetric auction model with externalities of Jehiel, Moldovanu and Stacchetti is extended by relaxing the assumption of symmetry and considering the case where buyers experience externalities even when the seller keeps the object. Dynamic games are investigated where there is a strategic motive for buying t he objective, namely, to resell it later. The generalized regularity analysis alluded to above would extend Armstrong's results on pricing and regulation to multiproduct monopolies to a much wider range of economic environments.