Bilateral Trade: A Regret Minimization Perspective

TL;DR

This paper analyzes bilateral trade as a regret minimization problem over multiple rounds, providing tight bounds for different feedback models and valuation assumptions, advancing understanding of dynamic trading mechanisms.

Contribution

It offers a complete characterization of regret regimes for fixed-price mechanisms under various feedback and valuation scenarios, filling a key gap in economic mechanism design.

Findings

Regret is $ ilde{O}( oot{T}{} )$ for full-feedback.

Regret is $ ilde{O}(T^{2/3})$ for realistic feedback with independent valuations.

Regret is linear in $T$ for certain valuation and feedback settings.

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.