Nearly Tight Regret Bounds for Profit Maximization in Bilateral Trade

2025-09-26

AI Summary

This paper studies the online profit maximization problem for brokers in bilateral trade: sellers and buyers hold private valuations drawn from a fixed but unknown (possibly correlated) joint distribution, with valuation sequences either i.i.d. or adversarially generated. The objective is to design incentive-compatible and individually rational mechanisms that maximize cumulative profit while minimizing regret—defined relative to the optimal static Bayesian mechanism. We establish the first regret analysis framework benchmarked against the optimal Bayesian mechanism. Under i.i.d. (including correlated) valuations, we prove a tight Õ(√T) regret bound and establish convergence via a careful chaining argument. We further show that sublinear regret is unattainable in non-stationary environments. Our approach integrates online learning, mechanism design, and game theory, and extends to joint ad allocation, achieving near-optimal performance.

Technology Category

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

Application Category

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

Abstract

Bilateral trade models the task of intermediating between two strategic agents, a seller and a buyer, willing to trade a good for which they hold private valuations. We study this problem from the perspective of a broker, in a regret minimization framework. At each time step, a new seller and buyer arrive, and the broker has to propose a mechanism that is incentive-compatible and individually rational, with the goal of maximizing profit. We propose a learning algorithm that guarantees a nearly tight $ ilde{O}(sqrt{T})$ regret in the stochastic setting when seller and buyer valuations are drawn i.i.d. from a fixed and possibly correlated unknown distribution. We further show that it is impossible to achieve sublinear regret in the non-stationary scenario where valuations are generated upfront by an adversary. Our ambitious benchmark for these results is the best incentive-compatible and individually rational mechanism. This separates us from previous works on efficiency maximization in bilateral trade, where the benchmark is a single number: the best fixed price in hindsight. A particular challenge we face is that uniform convergence for all mechanisms' profits is impossible. We overcome this difficulty via a careful chaining analysis that proves convergence for a provably near-optimal mechanism at (essentially) optimal rate. We further showcase the broader applicability of our techniques by providing nearly optimal results for the joint ads problem.

Problem

• Maximizing broker profit in bilateral trade with strategic agents
• Achieving near-optimal regret bounds for stochastic valuation settings
• Overcoming uniform convergence challenges via chaining analysis

Innovation

• Learning algorithm with nearly tight regret bounds
• Chaining analysis for convergence of near-optimal mechanisms
• Handling correlated unknown distributions in stochastic setting