Cesa-Bianchi, Nicolo, Tommaso, Cesari
, Colomboni, Roberto, Fusco, Federico and Leonardi, Stefano
(2021)
A regret analysis of bilateral trade.
EC '21: Proceedings of the 22nd ACM Conference on Economics and Computation.
pp. 289-309.
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.
Item Type: | Article |
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Language: | English |
Date: | 2021 |
Refereed: | Yes |
Subjects: | B- ECONOMIE ET FINANCE |
Divisions: | TSE-R (Toulouse) |
Site: | UT1 |
Date Deposited: | 01 Dec 2022 14:37 |
Last Modified: | 01 Dec 2022 14:37 |
OAI Identifier: | oai:tse-fr.eu:126474 |
URI: | https://publications.ut-capitole.fr/id/eprint/44214 |