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 widetildeTheta(T2/3) tight bound for textsfGlobal Budget Balance fixed-price mechanisms with two-bit/one-bit feedback. (ii) For correlated/adversarial values, a near-optimal Omega(T3/4) lower bound for textsfGlobal Budget Balance fixed-price mechanisms with two-bit/one-bit feedback, which improves the best known Omega(T5/7) lower bound obtained in the work [BCCF24] and, up to polylogarithmic factors, matches the widetildeO(T3 / 4) upper bound obtained in the same work. Our work in combination with the previous works [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 textitfractal elimination, to address one-bit feedback and independent values. (ii) A new textitlower-bound construction with novel proof techniques, to address the textsfGlobal Budget Balance constraint and correlated values.