Bilateral Trade: A Regret Minimization Perspective

• URL: http://arxiv.org/abs/2109.12974v1
• Date: Wed, 8 Sep 2021 22:11:48 GMT
• Title: Bilateral Trade: A Regret Minimization Perspective
• Authors: Nicol\`o Cesa-Bianchi, Tommaso Cesari, Roberto Colomboni, Federico Fusco, Stefano Leonardi
• Abstract summary: We cast the bilateral trade problem in a regret minimization framework over $T$ rounds of seller/buyer interactions. Our main contribution is a complete characterization of the regret regimes for fixed-price mechanisms with different feedback models and private valuations.
• Score: 5.031063690574698
• License: http://creativecommons.org/licenses/by/4.0/
• 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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