AF: Small: Effective Resource Allocation Mechanisms: Fairness and Incentives

这个项目将关注在相互竞争的主体之间分配有限数量的共享资源的问题，这是运筹学和经济学中的一个基本问题。这样的问题出现在许多环境中：计算机和通信网络中的调度，决定公共设施的位置，将大学与未来的学生配对，为研究生分配住房，为轮候名单上的患者分配器官，在兄弟姐妹之间分配遗产，分担公共物品的成本，等等。这个项目的中心目标是设计有效的资源分配机制，这些机制(I)有强有力的理论理由；(Ii)易于计算；(Iii)在实践中易于实施。该项目可以大致分为两个部分：第一部分讨论了基于最大遗憾最小化的均衡概念，并将探讨其对机制设计的影响。这种方法解决不完全信息讨价还价问题的初步结果似乎很有希望。该项目的第二部分涉及匹配和分配问题。在这里，公平和激励等非标准标准被纳入到一些研究得很好的优化模型中。该项目将力求确定在哪些条件下可以为一些自然模式设计既公平又符合激励的机制。其中一个目标是通过说明一个学科的研究问题、想法和工具如何为另一个学科提供信息和丰富另一个学科，促进经济学家和优化研究人员之间的更大互动。如果成功，该项目的结果将有助于更好地理解匹配和分配问题中的共谋和联盟形成等重要现象。该项目中开发的方法及其衍生的算法有可能提高几个现实生活中的系统的性能。例如，配对和分配问题的工作灵感来自于“择校”问题的应用。这项研究的结果将深入了解资源分配决策如何与激励相容和公平的目标(往往是相互冲突的)相互作用。拟议项目的教育目标包括在本科生和研究生课程中介绍机械设计领域令人振奋的最新发展。这些课程将使本科生和研究生接触到各种适用于优化方法和工具的公共决策问题。

This project will focus on the problem of allocating a limited number of shared resources among competing agents, which is a fundamental problem in operations research and economics. Such problems arise in many settings: scheduling in computer and communication networks, deciding where to locate public facilities, matching colleges to prospective students, assigning housing to graduate students, allocating organs to patients on a waiting-list, dividing an estate between siblings, sharing the cost of a public good, etc. The central aim of this project is to design effective resource allocation mechanisms that (i) have a strong theoretical justification; (ii) are easy to compute; and (iii) are simple to implement in practice. The project can be broadly classified in two parts: the first part deals with a notion of equilibrium based on minimizing maximum regret, and will explore its implications for mechanism design. Initial results of this approach to bargaining problems with incomplete information appear promising. The second part of the project deals with matching and allocation problems. Here, nonstandard criteria such as fairness and incentives are incorporated into some well-studied optimization models. The project will seek to characterize conditions under which it is possible to design mechanisms that are both fair and incentive-compatible for a number of natural models. One of the aims will be to promote a greater interaction between economists and optimization researchers by illustrating how the research questions, ideas, and tools in one discipline can inform and enrich the other. If successful, the results of the project will lead to a better understanding of important phenomena such as collusion and coalition formation in matching and allocation problems.The methods developed in this project, and the algorithms derived from them have the potential to improve the performance of several real-life systems. For example, the work on matching and allocation problems is inspired by applications to "school choice" problems. The results of this research will provide insight into how resource allocation decisions interact with the (often conflicting) goals of incentive-compatibility and fairness. The educational goals of the proposed project include the introduction of the exciting recent developments in the area of mechanism design in the undergraduate and graduate curriculum. These courses will serve to expose the undergraduate and graduate students to the large variety of public-decision making problems for which optimization methods and tools are applicable.