A Regret Analysis of Bilateral Trade
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866913236528398336 |
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| author | Cesa-Bianchi, Nicolò Cesari, Tommaso Colomboni, Roberto Fusco, Federico Leonardi, Stefano |
| author_facet | Cesa-Bianchi, Nicolò Cesari, Tommaso Colomboni, Roberto Fusco, Federico Leonardi, Stefano |
| contents | 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:
$\bullet$ $\widetildeΘ(\sqrt{T})$ for full-feedback (i.e., direct revelation mechanisms);
$\bullet$ $\widetildeΘ(T^{2/3})$ for realistic feedback (i.e., posted-price mechanisms) and independent seller/buyer valuations with bounded densities;
$\bullet$ $Θ(T)$ for realistic feedback and seller/buyer valuations with bounded densities;
$\bullet$ $Θ(T)$ for realistic feedback and independent seller/buyer valuations;
$\bullet$ $Θ(T)$ for the adversarial setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_08754 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A Regret Analysis of Bilateral Trade Cesa-Bianchi, Nicolò Cesari, Tommaso Colomboni, Roberto Fusco, Federico Leonardi, Stefano Machine Learning Theoretical Economics 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: $\bullet$ $\widetildeΘ(\sqrt{T})$ for full-feedback (i.e., direct revelation mechanisms); $\bullet$ $\widetildeΘ(T^{2/3})$ for realistic feedback (i.e., posted-price mechanisms) and independent seller/buyer valuations with bounded densities; $\bullet$ $Θ(T)$ for realistic feedback and seller/buyer valuations with bounded densities; $\bullet$ $Θ(T)$ for realistic feedback and independent seller/buyer valuations; $\bullet$ $Θ(T)$ for the adversarial setting. |
| title | A Regret Analysis of Bilateral Trade |
| topic | Machine Learning Theoretical Economics |
| url | https://arxiv.org/abs/2102.08754 |