Tight Regret Bounds for Fixed-Price Bilateral Trade

2025-04-06

AI Summary

This paper investigates the theoretical limits of fixed-price mechanisms with global budget balance in bilateral trade under regret minimization. For independent valuations, we propose the “fractal elimination” algorithmic paradigm, coupled with one-bit feedback, to establish a tight regret bound of $widetilde{Theta}(T^{2/3})$. For correlated or adversarial valuations, we develop a novel lower-bound construction and analysis technique, yielding the first rigorous $Omega(T^{3/4})$ lower bound—optimal up to logarithmic factors. Our core contributions are threefold: (i) breaking classical feedback constraints to enable unified treatment of independent, strongly correlated, and adversarial environments; (ii) achieving the first tight characterization of regret under global budget balance; and (iii) providing foundational theoretical support for the co-design of learning and incentive compatibility in mechanism design.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Machine Learning: Online Learning & Bandits

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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 $ extsf{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 $ extsf{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 $ extit{{fractal elimination}}$, to address one-bit feedback and independent values. (ii) A new $ extit{lower-bound construction}$ with novel proof techniques, to address the $ extsf{Global Budget Balance}$ constraint and correlated values.

Problem

• Analyzes regret minimization in fixed-price bilateral trade mechanisms
• Establishes tight bounds for independent and correlated/adversarial values
• Introduces novel techniques for one-bit feedback and budget balance

Innovation

• Fractal elimination for one-bit feedback
• Novel lower-bound construction for correlated values
• Tight regret bounds for fixed-price mechanisms