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

Luofeng Liao, Christian Kroer

arXiv 21 Jun 2024 · cs.GT

arXiv:2406.15522 · PDF · DOI · OpenAlex · Extracted main text

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.

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appendix boundary found by appendix_titled_section at “Appendix to Linear Fisher Market” · 55% of the source is main text. Read the extracted text to check this.

Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Conitzer V, Kroer C, Panigrahi D, Schrijvers O, Stier-Moses NE, Sodo… (2022) a) Pacing equilibrium in first price auction markets1.000113100%
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3Gao Y, Kroer C (2022) Infinite-dimensional fisher markets and tractable fair division0.94118683%
4Van der Vaart AW (2000) Asymptotic statistics0.8435460%
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6Duchi JC, Ruan F (2021) Asymptotic optimality in stochastic optimization0.79412550%
7Shapiro A (1989) Asymptotic properties of statistical estimators in stochastic programming0.75414543%
8Kroer C, Sinha D, Zhang X, Cheng S, Zhou Z (2023) b) Fair notification optimization: An auction approach0.73732100%
9Kim J, Pollard D (1990) Cube root asymptotics0.73732100%
10Liao H, Peng L, Liu Z, Shen X (2014) ipinyou global rtb bidding algorithm competition dataset0.73732100%

Showing the top 10 of 116 scored citations.