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Bootstrapping Fisher Market Equilibrium and First-Price Pacing Equilibrium

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  • Luofeng Liao
  • Christian Kroer

Abstract

The linear Fisher market (LFM) is a basic equilibrium model from economics, which also has applications in fair and efficient resource allocation. First-price pacing equilibrium (FPPE) is a model capturing budget-management mechanisms in first-price auctions. In certain practical settings such as advertising auctions, there is an interest in performing statistical inference over these models. A popular methodology for general statistical inference is the bootstrap procedure. Yet, for LFM and FPPE there is no existing theory for the valid application of bootstrap procedures. In this paper, we introduce and devise several statistically valid bootstrap inference procedures for LFM and FPPE. The most challenging part is to bootstrap general FPPE, which reduces to bootstrapping constrained M-estimators, a largely unexplored problem. We devise a bootstrap procedure for FPPE under mild degeneracy conditions by using the powerful tool of epi-convergence theory. Experiments with synthetic and semi-real data verify our theory.

Suggested Citation

  • Luofeng Liao & Christian Kroer, 2024. "Bootstrapping Fisher Market Equilibrium and First-Price Pacing Equilibrium," Papers 2402.02303, arXiv.org, revised Mar 2025.
    • Handle: RePEc:arx:papers:2402.02303
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    References listed on IDEAS

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    Cited by:

    1. Luofeng Liao & Christian Kroer, 2024. "Statistical Inference and A/B Testing in Fisher Markets and Paced Auctions," Papers 2406.15522, arXiv.org, revised Mar 2025.

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