Matching and Allocation Problems: An Axiomatic Approach with Applications

该奖项提供资金，用于研究与各种新兴领域的申请相匹配和分配的问题，包括互联网和电子商务的发展所刺激的应用，以及非标准应用，如肾脏移植交换的设计，将学生分配到有学校选择的地区的学校等。将特别注意机制的设计，其中参与者不会因错误报告与正在考虑的分配问题有关的任何私人信息(如他们的偏好)而受益。这些问题将在一个公理框架内研究，该框架试图理解满足许多理想标准的机制，这些标准的选择是由所考虑的应用程序驱动的。将确定唯一确定常用机制的最小属性集。此外，还将设计具有令人信服的效率和公平性的新机制，并对其在实践中的使用进行评估。几个经典的流动和匹配模型-运筹学文献中传统上从计算效率的角度进行研究的模型-将在考虑激励约束和公平目标的情况下进行研究。如果成功，该项目将为几个现实生活中的匹配和分配问题带来新的机制。它还将导致开发新的理论工具和技术，这些工具和技术可广泛适用于在存在激励约束的情况下理解公平目标和(经济和计算)效率目标之间的相互作用。该奖项将支持开发一门博士课程，重点放在匹配和分配问题在实践中的应用，以及重新设计一门涵盖公共部门手术室方法的课程。该奖项还将支持一名研究生和外展活动，如撰写说明性文章。

This award provides funding for the study of matching and allocation problems with applications to a variety of emerging areas, including applications spurred by the growth of the internet and electronic commerce, as well as non-standard applications such as the design of exchanges for kidney transplants, the assignment of students to schools in districts where there is school choice, etc. Particular attention will be paid to the design of mechanisms in which participants do not benefit from misreporting any private information (such as their preferences) that is relevant to the allocation problem under consideration. These problems will be studied in an axiomatic framework, which seeks to understand mechanisms that satisfy many desirable criteria, whose choice is motivated by the application under consideration. Minimal sets of properties that uniquely determine commonly-used mechanisms will be identified. Further, new mechanisms with compelling efficiency and equity properties will be designed and their use in practice will be evaluated. Several classical flow and matching models---traditionally studied in the operations research literature from the point of view of computational efficiency---will be studied, taking into account incentive constraints and equity objectives.If successful, the project will result in new mechanisms for several real-life matching and allocation problems. It will also result in the development of new theoretical tools and techniques that may be broadly applicable in understanding the interaction between equity objectives and (both economic and computational) efficiency objectives in the presence of incentive constraints. This award will support the development of a doctoral course focusing on the applications of matching and allocation problems in practice, as well as the redesign of a course that covers O.R. methods in the public sector. The award will also support a graduate student and outreach activities such as the writing of expository articles.