Cesa-Bianchi, Nicolo, Tommaso, Cesari, Colomboni, Roberto, Fusco, Federico and Leonardi, Stefano (2024) Bilateral trade: a regret minimization perspective. Mathematics of Operations Research, vol. 49 (n° 1). pp. 1-651.

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:

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.