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2021, Proceedings of the 22nd {ACM} Conference on Economics and Computation, Pages 289-309

A Regret Analysis of Bilateral Trade (04b Atto di convegno in volume)

Cesa-Bianchi Nicol(`(o)), Cesari Tommaso R., Colomboni Roberto, Fusco Federico, Leonardi Stefano

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.
ISBN: 9781450385541
Gruppo di ricerca: Algorithms and Data Science
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