Statistical inference under market equilibrium effects has attracted increasing attention recently. In this paper we focus on the specific case of linear Fisher markets. They have been widely use in fair resource allocation of food/blood donations and budget management in large-scale Internet ad auctions. In resource allocation, it is crucial to quantify the variability of the resource received by the agents (such as blood banks and food banks) in addition to fairness and efficiency properties of the systems. For ad auction markets, it is important to establish statistical properties of the platform's revenues in addition to their expected values. To this end, we propose a statistical framework based on the concept of infinite-dimensional Fisher markets. In our framework, we observe a market formed by a finite number of items sampled from an underlying distribution (the "observed market") and aim to infer several important equilibrium quantities of the underlying long-run market. These equilibrium quantities include individual utilities, social welfare, and pacing multipliers. Through the lens of sample average approximation (SSA), we derive a collection of statistical results and show that the observed market provides useful statistical information of the long-run market. In other words, the equilibrium quantities of the observed market converge to the true ones of the long-run market with strong statistical guarantees. These include consistency, finite sample bounds, asymptotics, and confidence. As an extension, we discuss revenue inference in quasilinear Fisher markets.
翻译:市场平衡效应下的统计推断最近引起越来越多的关注。在本文件中,我们侧重于线性渔业市场的具体案例,在粮食/血液捐赠的公平资源分配和大规模互联网拍卖的预算管理中广泛使用;在资源分配方面,除了系统的公平和效率特性外,还必须量化代理人(如血库和粮食银行)收到的资源的变异性;对于拍卖市场来说,除了预期价值外,还必须确定平台收入的统计属性;为此,我们提议了一个基于无限规模渔业市场概念的统计框架;在我们的框架内,我们观察一个市场,由从基本分配(“观察市场”)抽样的有限数量的项目组成,目的是推算长期市场的若干重要均衡数量;这些均衡数量包括个别公用事业、社会福利和速率乘数;通过抽样平均近似(SSA),我们收集了统计结果,并表明所观察的市场提供了长期市场有用的统计信息;在我们的框架中,所观察到的市场均衡数量是从基本分配(“观察的市场”)的市场与长期稳定水平的市场。我们观察到的市场,这些稳定性水平的市场包括:我们所观察到的市场与稳定的市场之间的稳定程度。