Support-Dependent Regret Rates for Profit Maximization in Multilateral Trade

2026-10-06

AI Summary

This study addresses the problem of online profit maximization in multi-party trade settings where valuation distributions are unknown and agents' marginal valuations have bounded support. To overcome the limitations inherent in multidimensional formulations, this work proposes a normalized scaling technique that prevents excessive refinement over flat regions. By integrating online learning with probabilistic modeling, an adaptive algorithm is designed to jointly optimize pricing and payment strategies. The primary contribution lies in establishing a regret bound of $\widetilde{O}(\sqrt{K^dT})$ under constant-dimensional assumptions, thereby extending the optimal theoretical guarantees for this class of problems.

Abstract

We study online profit maximization in multilateral trade, a setting that generalizes both dynamic pricing and bilateral trade. At each round, an intermediary posts prices to buyers and offers payments to sellers; trade occurs only if every agent accepts. We consider valuations drawn from an unknown joint distribution, allowing arbitrary correlation across agents, under the assumption that each agent's marginal valuation distribution has unknown support of size at most $K$. For constant dimension $d$, we design an algorithm with regret $\widetilde O(\sqrt{K^dT})$. This extends optimal support-dependent guarantees for one-dimensional dynamic pricing to the multidimensional setting of multilateral trade. At the core of our approach is a normalized zooming procedure that adapts to the local probability of trade, avoiding the excessive refinement of nearly flat regions that can arise with standard zooming.

Problem

• online profit maximization
• multilateral trade
• support-dependent regret
• dynamic pricing

Innovation

• multilateral trade
• online profit maximization
• support-dependent regret
• normalized zooming
• dynamic pricing