Department of Industrial Engineering & Decision Analytics [Joint IEDA/CSE] seminar - Tight Regret Bounds for Fixed-Price Bilateral Trade

We examine fixed-price mechanisms in bilateral trade through the lens of regret minimization. Our main results are twofold.

(i) For independent values, a near-optimal $\widetilde{\Theta}(T^{2/3})$ tight bound for {\sf Global Budget Balance} fixed-price mechanisms with two-bit/one-bit feedback.

(ii) For correlated/adversarial values, a near-optimal $\Omega(T^{3/4})$ lower bound for {\sf Global Budget Balance} fixed-price mechanisms with two-bit/one-bit feedback, which improves the best known $\Omega(T^{5/7})$ lower bound obtained in the work \cite{BCCF24} and, up to polylogarithmic factors, matches the $\widetilde{\mathcal{O}}(T^{3 / 4})$ upper bound obtained in the same work.

Our work in combination with the previous works \cite{CCCFL24mor, CCCFL24jmlr, AFF24, BCCF24} (essentially) gives a thorough understanding of regret minimization for fixed-price bilateral trade.

En route, we have developed two technical ingredients that might be of independent interest:

(i) A novel algorithmic paradigm, called {\em fractal elimination}, to address one-bit feedback and independent values.

(ii) A new {\em lower-bound construction} with novel proof techniques, to address the {\sf Global Budget Balance} constraint and correlated values.