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A Regret Analysis of Bilateral Trade

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 Dütting 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:
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https://hal.archives-ouvertes.fr/hal-03141589
Contributor : Tommaso Cesari <>
Submitted on : Monday, February 15, 2021 - 1:36:21 PM
Last modification on : Saturday, February 20, 2021 - 3:30:22 AM

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  • HAL Id : hal-03141589, version 1
  • ARXIV : 2102.08754

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Nicolò Cesa-Bianchi, Tommaso Cesari, Roberto Colomboni, Federico Fusco, Stefano Leonardi. A Regret Analysis of Bilateral Trade. 2021. ⟨hal-03141589⟩

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