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Bilateral trade: a regret minimization perspective

Author

Listed:
  • Nicolo Cesa-Bianchi

    (UNIMI - Università degli Studi di Milano = University of Milan)

  • Cesari Tommaso

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Roberto Colomboni

    (UNIMI - Università degli Studi di Milano = University of Milan, IIT - Istituto Italiano di Tecnologia)

  • Federico Fusco

    (UNIROMA - Università degli Studi di Roma "La Sapienza" = Sapienza University [Rome])

  • Stefano Leonardi

    (UNIROMA - Università degli Studi di Roma "La Sapienza" = Sapienza University [Rome])

Abstract

Bilateral trade, a fundamental topic in economics, models the problem of intermediating between two strategic agents, a seller and a buyer, willing to trade a good for which they hold private valuations. In this paper, we cast the bilateral trade problem in a regret minimization framework over T rounds of seller/buyer interactions, with no prior knowledge on their private valuations. Our main contribution is a complete characterization of the regret regimes for fixed-price mechanisms with different feedback models and private valuations, using as a benchmark the best fixed price in hindsight. More precisely, we prove the following tight bounds on the regret: Θ(T−−√) for full-feedback (i.e., direct revelation mechanisms). Θ(T2/3) for realistic feedback (i.e., posted-price mechanisms) and independent seller/buyer valuations with bounded densities. Θ(T) for realistic feedback and seller/buyer valuations with bounded densities. Θ(T) for realistic feedback and independent seller/buyer valuations. Θ(T) for the adversarial setting.

Suggested Citation

  • Nicolo Cesa-Bianchi & Cesari Tommaso & Roberto Colomboni & Federico Fusco & Stefano Leonardi, 2024. "Bilateral trade: a regret minimization perspective," Post-Print hal-04475574, HAL.
    • Handle: RePEc:hal:journl:hal-04475574
    DOI: 10.1287/moor.2023.1351
    as

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    Citations

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    Cited by:

    1. Nicolo Cesa-Bianchi & Roberto Colomboni & Maximilian Kasy, 2023. "Adaptive maximization of social welfare," Papers 2310.09597, arXiv.org, revised Jul 2024.
    2. Tommaso Cesari & Roberto Colomboni, 2024. "Trading Volume Maximization with Online Learning," Papers 2405.13102, arXiv.org.
    3. Franc{c}ois Bachoc & Tommaso Cesari & Roberto Colomboni, 2024. "A Contextual Online Learning Theory of Brokerage," Papers 2407.01566, arXiv.org.

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