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Article Dans Une Revue Mathematics of Operations Research Année : 2024

Bilateral trade: a regret minimization perspective

Résumé

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.
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Dates et versions

hal-04475574 , version 1 (23-02-2024)

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Nicolo Cesa-Bianchi, Cesari Tommaso, Roberto Colomboni, Federico Fusco, Stefano Leonardi. Bilateral trade: a regret minimization perspective. Mathematics of Operations Research, 2024, 49 (1), pp.171-203. ⟨10.1287/moor.2023.1351⟩. ⟨hal-04475574⟩
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