A regret analysis of bilateral trade

Nicolo Cesa-Bianchi, Cesari Tommaso, Roberto Colomboni, Federico Fusco and Stefano Leonardi
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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
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]

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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. Despite the simplicity of this problem, a classical result by Myerson and Satterthwaite (1983) affirms the impossibility of designing a mechanism which is simultaneously efficient, incentive compatible, individually rational, and budget balanced. This impossibility result fostered an intense investigation of meaningful trade-offs between these desired properties. Much work has focused on approximately efficient fixed-price mechanisms, i.e., Blumrosen and Dobzinski (2014; 2016), Colini-Baldeschi et al. (2016), which have been shown to fully characterize strong budget balanced and ex-post individually rational direct revelation mechanisms. All these results, however, either assume some knowledge on the priors of the seller/buyer valuations, or a black box access to some samples of the distributions, as in D{ü}tting et al. (2021). In this paper, we cast for the first time the bilateral trade problem in a regret minimization framework over rounds of seller/buyer interactions, with no prior knowledge on the private seller/buyer valuations. Our main contribution is a complete characterization of the regret regimes for fixed-price mechanisms with different models of feedback and private valuations, using as benchmark the best fixed price in hindsight. More precisely, we prove the following 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.

Date: 2021
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Published in EC '21: Proceedings of the 22nd ACM Conference on Economics and Computation, 2021, pp.289-309. ⟨10.1145/3465456.3467645⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03881144

DOI: 10.1145/3465456.3467645

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