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 Dütting et al. (2021). In this paper, we cast for the first time 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 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.

A regret analysis of bilateral trade / Cesa-Bianchi, Nicolò; Cesari, Tommaso R.; Colomboni, Roberto; Fusco, Federico; Leonardi, Stefano. - (2021), pp. 289-309. (Intervento presentato al convegno ACM Conference on Economics and Computation tenutosi a Virtuale) [10.1145/3465456.3467645].

A regret analysis of bilateral trade

Federico Fusco
;
Stefano Leonardi
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 Dütting et al. (2021). In this paper, we cast for the first time 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 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.
2021
ACM Conference on Economics and Computation
Bilateral trade; online learning; posted price
04 Pubblicazione in atti di convegno::04b Atto di convegno in volume
A regret analysis of bilateral trade / Cesa-Bianchi, Nicolò; Cesari, Tommaso R.; Colomboni, Roberto; Fusco, Federico; Leonardi, Stefano. - (2021), pp. 289-309. (Intervento presentato al convegno ACM Conference on Economics and Computation tenutosi a Virtuale) [10.1145/3465456.3467645].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1563225
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