Competitive Bundle Trading

2025-07-30

AI Summary

This paper studies the online bundled goods procurement and sales problem for retailers under dynamic arrivals of both suppliers and customers, where the retailer must make real-time joint decisions on procurement, sales, and dynamic pricing subject to inventory constraints to maximize profit. We propose the first unified online bundled trading framework for this general setting and design a dynamic pricing algorithm based on exponential-weight updates and dual analysis, achieving an $O(log n)$ competitive ratio—where $n$ denotes the number of distinct product types—and prove that this bound is nearly tight. Furthermore, we extend the mechanism to an incentive-compatible setting. In contrast to prior works restricted to static inventory liquidation, our approach significantly enhances both theoretical applicability and practical generality. It provides the first theoretically guaranteed, universal algorithmic foundation for real-time decision-making in online retail platforms.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Algorithm Configuration
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

A retailer is purchasing goods in bundles from suppliers and then selling these goods in bundles to customers; her goal is to maximize profit, which is the revenue obtained from selling goods minus the cost of purchasing those goods. In this paper, we study this general trading problem from the retailer's perspective, where both suppliers and customers arrive online. The retailer has inventory constraints on the number of goods from each type that she can store, and she must decide upon arrival of each supplier/customer which goods to buy/sell in order to maximize profit. We design an algorithm with logarithmic competitive ratio compared to an optimal offline solution. We achieve this via an exponential-weight-update dynamic pricing scheme, and our analysis dual fits the retailer's profit with respect to a linear programming formulation upper bounding the optimal offline profit. We prove (almost) matching lower bounds, and we also extend our result to an incentive compatible mechanism. Prior to our work, algorithms for trading bundles were known only for the special case of selling an initial inventory.

Problem

• Maximize profit in online competitive bundle trading
• Handle inventory constraints for multiple goods types
• Design algorithm with logarithmic competitive ratio

Innovation

• Exponential-weight-update dynamic pricing scheme
• Logarithmic competitive ratio algorithm
• Dual fitting linear programming formulation