Dynamic Matching Under Patience Imbalance

2026-02-03

AI Summary

This study addresses dynamic matching in two-sided platforms under asymmetric patience: suppliers are long-lived and incur waiting costs, while demanders are short-lived and abandon the platform if not matched promptly. Assuming supermodular matching rewards, the authors analyze optimal matching strategies under both centralized and decentralized mechanisms by leveraging Markov perfect equilibrium, threshold policies, and dynamic optimization. The key contribution lies in showing that, in decentralized systems, appropriately designed reward-sharing rules can fully align social welfare with the centralized optimum. Moreover, the impact of patience on welfare is non-monotonic: under symmetric arrivals, welfare in the centralized setting weakly increases with patience, whereas in the decentralized setting, it depends critically on the interplay between the sharing rule and waiting costs.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: The sharing economy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Decentralized Web and Fediverse systems

Abstract

We study a dynamic matching problem on a two-sided platform with unbalanced patience, in which long-lived supply accumulates over time with a unit waiting cost per period, while short-lived demand departs if not matched promptly. High- or low-quality agents arrive sequentially with one supply agent and one demand agent arriving in each period, and matching payoffs are supermodular. In the centralized benchmark, the optimal policy follows a threshold-based rule that rations high-quality supply, preserving it for future high-quality demand. In the decentralized system, where self-interested agents decide whether to match under an exogenously specified payoff allocation proportion, we characterize a welfare-maximizing Markov perfect equilibrium. Unlike outcomes in the centralized benchmark or in full-backlog markets, the equilibrium exhibits distinct matching patterns in which low-type demand may match with high-type supply even when low-type supply is available. Unlike settings in which both sides have long-lived agents and perfect coordination is impossible, the decentralized system can always be perfectly aligned with the centralized optimum by appropriately adjusting the allocation of matching payoffs across agents on both sides. Finally, when the arrival probabilities for H- and L-type arrivals are identical on both sides, we compare social welfare across systems with different patience levels: full backlog on both sides, one-sided backlog, and no backlog. In the centralized setting, social welfare is weakly ordered across systems. However, in the decentralized setting, the social welfare ranking across the three systems depends on the matching payoff allocation rule and the unit waiting cost, and enabling patience can either increase or decrease social welfare.

Problem

• dynamic matching
• patience imbalance
• two-sided platform
• supermodular payoffs
• decentralized equilibrium

Innovation

• dynamic matching
• patience imbalance
• supermodular payoffs
• Markov perfect equilibrium
• welfare alignment