Fisher市场均衡的统计推断
Statistical Inference for Fisher Market Equilibrium
AI总结：
本文针对线性Fisher市场提出基于无限维市场与SSA的统计推断框架，证明观察市场的个体效用、社会福利和 pacing 乘子等均衡量可强保证地收敛至长期市场真值。
摘要：
市场均衡效应下的统计推断近来受到越来越多的关注。本文聚焦于线性Fisher市场这一具体情形。它们已被广泛用于食品/血液捐赠的公平资源配置，以及大规模互联网广告拍卖中的预算管理。在资源配置中，除了系统的公平性和效率性质外，量化代理人（如血库和食品银行）所获得资源的变异性也至关重要。对于广告拍卖市场，除平台收入的期望值外，建立其统计性质也很重要。为此，我们提出了一个基于无限维Fisher市场概念的统计框架。在该框架中，我们观察到一个由从潜在分布中抽样的有限数量物品构成的市场（即“观察到的市场”），并旨在推断潜在长期市场的若干重要均衡量。这些均衡量包括个体效用、社会福利和 pacing multipliers（ pacing 乘子）。借助样本平均近似（SSA）的视角，我们推导了一系列统计结果，并表明观察到的市场提供了关于长期市场的有用统计信息。换言之，观察到的市场的均衡量会在强统计保证下收敛至长期市场的真实均衡量。这些保证包括一致性、有限样本界、渐近性和置信性。作为扩展，我们讨论了拟线性Fisher市场中的收入推断。
英文摘要：
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.
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