Statistical Inference and A/B Testing in Fisher Markets and Paced Auctions

Luofeng Liao and Christian Kroer

Papers from arXiv.org

Abstract: We initiate the study of statistical inference and A/B testing for two market equilibrium models: linear Fisher market (LFM) equilibrium and first-price pacing equilibrium (FPPE). LFM arises from fair resource allocation systems such as allocation of food to food banks and notification opportunities to different types of notifications. For LFM, we assume that the data observed is captured by the classical finite-dimensional Fisher market equilibrium, and its steady-state behavior is modeled by a continuous limit Fisher market. The second type of equilibrium we study, FPPE, arises from internet advertising where advertisers are constrained by budgets and advertising opportunities are sold via first-price auctions. For platforms that use pacing-based methods to smooth out the spending of advertisers, FPPE provides a hindsight-optimal configuration of the pacing method. We propose a statistical framework for the FPPE model, in which a continuous limit FPPE models the steady-state behavior of the auction platform, and a finite FPPE provides the data to estimate primitives of the limit FPPE. Both LFM and FPPE have an Eisenberg-Gale convex program characterization, the pillar upon which we derive our statistical theory. We start by deriving basic convergence results for the finite market to the limit market. We then derive asymptotic distributions, and construct confidence intervals. Furthermore, we establish the asymptotic local minimax optimality of estimation based on finite markets. We then show that the theory can be used for conducting statistically valid A/B testing on auction platforms. Synthetic and semi-synthetic experiments verify the validity and practicality of our theory.

Date: 2024-06, Revised 2025-03
New Economics Papers: this item is included in nep-des and nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2406.15522 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2406.15522

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().