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17 février 2024
- handle: 10670/1.kz40lj
- hal: hal-04475574
- doi: 10.1287/moor.2023.1351
- WOS: 000956117900001
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info:eu-repo/semantics/altIdentifier/doi/10.1287/moor.2023.1351
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Nicolo Cesa-Bianchi et al., « Bilateral trade: a regret minimization perspective », HAL-SHS : économie et finance, ID : 10.1287/moor.2023.1351
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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.