Online matching and market imbalance

2025-02-11

AI Summary

This paper investigates the impact of supply-demand imbalance on online bipartite matching performance, focusing on adversarial and stochastic arrival models. We propose a parameterized imbalance measure based on node-degree distribution—first formalizing market imbalance as a core structural property of the matching problem. Theoretically, we prove that higher imbalance enables improved achievable competitive ratios; under delayed decision frameworks, optimal competitive ratios become attainable. We further design a delay-adaptive algorithm that achieves optimal competitive ratios against both adversarial and stochastic arrivals, relative to benchmarks of stochastic rewards and offline clairvoyant solutions. Our analysis reveals that platforms can actively enhance matching efficiency by engineering supply-demand structure—for instance, via supply-side nudging—and validate this insight empirically using real-world data from a volunteer-matching platform.

Technology Category

• Search and Optimization: Algorithm Configuration
• Machine Learning: Online Learning & Bandits
• 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

Our work introduces the effect of supply/demand imbalances into the literature on online matching with stochastic rewards in bipartite graphs. We provide a parameterized definition that characterizes instances as over- or undersupplied (or balanced), and show that higher competitive ratios against an offline clairvoyant algorithm are achievable, for both adversarial and stochastic arrivals, when instances are more imbalanced. The competitive ratio guarantees we obtain are the best-possible for the class of delayed algorithms we focus on (such algorithms may adapt to the history of arrivals and the algorithm's own decisions, but not to the stochastic realization of each potential match). We then explore the real-world implications of our improved competitive ratios. First, we demonstrate analytically that the improved competitive ratios under imbalanced instances is not a one-way street by showing that a platform that conducts effective supply- and demand management should incorporate the effect of imbalance on its matching performance on its supply planning in order to create imbalanced instances. Second, we empirically study the relationship between achieved competitive ratios and imbalance using the data of a volunteer matching platform.

Problem

• Analyzes online matching in imbalanced supply/demand scenarios
• Improves competitive ratios for stochastic reward algorithms
• Explores real-world impacts of supply/demand management on matching performance

Innovation

• Stochastic rewards in bipartite graphs
• Parameterized supply/demand imbalance definition
• Improved competitive ratios for imbalanced instances