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Optimal and Equilibrium Transport: Theory and Applications to Economics and Data Science

最优和平衡运输：理论及其在经济学和数据科学中的应用

基本信息

批准号：
1716489
负责人：
Alfred Galichon
金额：
$ 30万
依托单位：
New York University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-07-01 至 2020-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1716489&HistoricalAwards=false
关键词：
Optimal Equilibrium Transport Theory Applications

项目摘要

This project is about developing some of the novel mathematical tools that are required for the new peer-to-peer economy. Recent years have witnessed the astonishing emergence of online matching platforms (such as Uber, Odesk, Airbnb, OkCupid), where agents seek to team up with each other to exchange various goods and services or form various partnerships. These platforms are provided with massive data on the populations of users, and need to take real-time decisions regarding market clearing, such as imposing surge prices, or suggesting assignments. The goal of this project is to expand the boundaries of a central tool: optimal transport theory, which was initiated in the 18th century but experienced a surge of research activity over the last decade, and which is very relevant for problems in matching, pricing, and data analysis. The project is divided into three separate projects; the first two are related, and the third one is further apart. The first project will define the framework of equilibrium transportation, which extends optimal transport to equilibrium situations. It will focus on the semi-discrete case, where one of the distributions is continuous and the other one is discrete. In this setting, it will derive analytical properties of the solution such as existence, uniqueness, monotonicity, and lattice structure. This framework is applied to the solution of a problem on the labor market. In another application, it is extended to the case of equilibrium flows on networks. The second project will demonstrate the usefulness of the equilibrium transportation framework for computing equilibrium in markets such as the taxi market, which cannot be modeled as an optimal transport problem since prices are fixed; in this type of markets, demand and supply are balanced by a congestion cost induced by limited availability. The project will derive the properties of the equilibrium, and use the framework to study the surge pricing problem: when demand and supply are uncertain, which price should be set to minimize the expected market inefficiency? The third project will focus on computational challenges brought by the introduction (due to the PI and collaborators) of the notion of vector quantile regression in the statistical literature. The project will focus on iterated projection methods (which have been very successfully applied to classical optimal transport problems) for this new class of problems.

这个项目是关于开发一些新的数学工具，这是新的P2P经济所需的。近年来，在线配对平台(如Uber、ODesk、Airbnb、OkCupid)惊人地出现，代理商寻求相互合作，交换各种商品和服务，或建立各种合作伙伴关系。这些平台拥有关于用户群体的海量数据，需要对市场清算做出实时决策，例如设定飙升的价格，或建议分配。这个项目的目标是扩展一个核心工具的边界：最优运输理论，该理论始创于18世纪，但在过去十年中经历了研究活动的激增，它与匹配、定价和数据分析问题非常相关。该项目分为三个独立的项目；前两个项目是相关的，第三个项目相距较远。第一个项目将定义均衡运输的框架，该框架将最优运输扩展到均衡情况。它将集中在半离散的情况下，其中一个分布是连续的，另一个是离散的。在这种情况下，它将得到解的存在、唯一性、单调性和格子结构等解析性质。这一框架被应用于一个劳动力市场问题的解决。在另一个应用中，它被推广到网络上的平衡流的情况。第二个项目将展示均衡运输框架在计算出租车市场等市场的均衡时的有效性，由于价格是固定的，因此不能将其建模为最优运输问题；在这种类型的市场中，需求和供应由有限的可获得性引起的拥堵成本来平衡。该项目将推导出均衡的性质，并利用该框架来研究电涌定价问题：当需求和供给不确定时，应该设定哪个价格来最小化预期的市场无效率？第三个项目将侧重于(由于PI和合作者)在统计文献中引入向量分位数回归概念所带来的计算挑战。该项目将专注于迭代投影方法(已经非常成功地应用于经典的最优运输问题)来解决这类新问题。