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Liquid Welfare Guarantees for No-Regret Learning in Sequential Budgeted Auctions

Author

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  • Giannis Fikioris

    (Cornell University, Ithaca, New York 14850)

  • Éva Tardos

    (Cornell University, Ithaca, New York 14850)

Abstract

We study the liquid welfare in sequential first-price auctions with budgeted buyers. We use a behavioral model for the buyers, assuming a learning style guarantee: the utility of each buyer is within a γ factor ( γ ≥ 1 ) of the utility achievable by shading their value with the same factor at each iteration. We show a γ + 1 / 2 + O ( 1 / γ ) price of anarchy for liquid welfare when valuations are additive. This is in stark contrast to sequential second-price auctions, where the resulting liquid welfare can be arbitrarily smaller than the maximum liquid welfare, even when γ = 1 . We prove a lower bound of γ on the liquid welfare loss under the given assumption in first-price auctions. Our liquid welfare results extend when buyers have submodular valuations over the set of items they win across iterations with a slightly worse price of anarchy bound of γ + 1 + O ( 1 / γ ) compared with the guarantee for the additive case.

Suggested Citation

  • Giannis Fikioris & Éva Tardos, 2025. "Liquid Welfare Guarantees for No-Regret Learning in Sequential Budgeted Auctions," Mathematics of Operations Research, INFORMS, vol. 50(2), pages 1233-1249, May.
    • Handle: RePEc:inm:ormoor:v:50:y:2025:i:2:p:1233-1249
    DOI: 10.1287/moor.2023.0274
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