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arXiv · 2109.12974

Bilateral Trade: A Regret Minimization Perspective

Nicolò Cesa-Bianchi·Tommaso Cesari·Roberto Colomboni·Federico Fusco·Stefano Leonardi
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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. In this paper, we cast 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 tight bounds on the regret: - $\Theta(\sqrt{T})$ for full-feedback (i.e., direct revelation mechanisms). - $\Theta(T^{2/3})$ for realistic feedback (i.e., posted-price mechanisms) and independent seller/buyer valuations with bounded densities. - $\Theta(T)$ for realistic feedback and seller/buyer valuations with bounded densities. - $\Theta(T)$ for realistic feedback and independent seller/buyer valuations. - $\Theta(T)$ for the adversarial setting.

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Nicolò Cesa-Bianchi, Tommaso Cesari, Roberto Colomboni, Federico Fusco, Stefano Leonardi. 2021-09-08. Bilateral Trade: A Regret Minimization Perspective. https://arxiv.org/abs/2109.12974

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