Statistical Inference for Fisher Market Equilibrium
费希尔市场均衡的统计推断AI 解读 ↓
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费希尔市场均衡的统计推断
- 研究问题
- 如何利用从潜在物品分布抽样形成的有限市场，推断长期费希尔市场的个体效用、社会福利、预算节奏乘子等均衡量？
- 方法与思路
- 作者以无限维线性费希尔市场定义长期目标，借助样本平均近似研究有限观测市场的均衡，并扩展讨论准线性市场收入。
- 材料陈述的贡献
- 摘要称建立均衡量的一致性、有限样本界、渐近结果和置信推断，说明有限观测市场能够提供关于长期市场的统计信息。
- 阅读关注点
- 应核对物品抽样机制、长期均衡的定义与唯一性要求，以及不同均衡量的收敛、置信推断和收入扩展分别需要哪些条件。
- 阅读边界
- 这是 arXiv 预印本，同行评审与期刊接收未核验。摘要未说明统计保证的具体条件，也未提供真实市场中的验证结果。
原文摘要
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.