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 that 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, e.g., 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 black-box access to some samples of the distributions, as in Dutting 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 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 bounds on the regret.

A Regret Analysis of Bilateral Trade / N. Cesa Bianchi, T. Cesari, R. Colomboni, F. Fusco, S. Leonardi - In: EC '21: Proceedings / [a cura di] P. Birtò, S. Chawla, F. Echenique. - [s.l] : ACM, 2021. - ISBN 9781450385541. - pp. 289-309 (( Intervento presentato al 22. convegno ACM Conference on Economics and Computation tenutosi a Budapest nel 2021 [10.1145/3465456.3467645].

A Regret Analysis of Bilateral Trade

N. Cesa Bianchi;T. Cesari;R. Colomboni;
2021

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 that 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, e.g., 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 black-box access to some samples of the distributions, as in Dutting 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 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 bounds on the regret.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/861764
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