Matching and Allocation Problems: An Axiomatic Approach with Applications

该奖项为各种新兴领域的应用程序的匹配和分配问题的研究提供资金，包括互联网和电子商务增长所推动的应用程序，以及非标准应用程序，如肾脏移植交换的设计，学生到有学校选择的地区学校的分配，将特别注意设计一种机制，使参与者不会因误报与所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化的框架中进行研究，该框架旨在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，将设计具有令人信服的效率和公平特性的新机制，并将评价其在实践中的使用情况。几个经典的流量和匹配模型-传统上在运筹学文献中从计算效率的角度进行研究-将被研究，考虑到激励约束和公平目标。如果成功，该项目将导致几个现实生活中的匹配和分配问题的新机制。它还将导致新的理论工具和技术的发展，可能广泛适用于理解公平目标和（经济和计算）效率目标之间的相互作用，在激励约束的存在。该奖项将支持博士课程的开发，重点是实践中的匹配和分配问题的应用，以及重新设计涵盖O.R.的课程。公共部门的方法。该奖项还将支持研究生和外联活动，如撰写临时文章。

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.