A Learning-Based Hybrid Decision Framework for Matching Systems with User Departure Detection
Authors: Ruiqi Zhou, Donghao Zhu, Houcai Shen
Organizations: School of Management and Engineering, Nanjing University, China · The Institute of Statistical Mathematics, Tokyo, Japan · The University of Tokyo Market Design Center, Tokyo, Japan.
In matching markets such as kidney exchanges and freight exchanges, delayed matching has been shown to improve overall market efficiency. The benefits of delay are highly sensitive to participants' sojourn times and departure behavior, and delaying matches can impose significant costs, including longer waiting times and increased market congestion. These competing effects make fixed matching policies inherently inflexible in dynamic environments. We propose a learning-based Hybrid framework that adaptively combines immediate and delayed matching. The framework continuously collects data on user departures over time, estimates the underlying departure distribution via regression, and determines whether to delay matching in the subsequent period based on a decision threshold that governs the system's tolerance for matching efficiency loss. The proposed framework can substantially reduce waiting times and congestion while sacrificing only a limited amount of matching efficiency. By dynamically adjusting its matching strategy, the Hybrid framework enables system performance to flexibly interpolate between purely greedy and purely patient policies, offering a robust and adaptive alternative to static matching mechanisms.
Figures & tables
Figure 1: Decision framework: a kidney exchange example.
Figure 2: A data-driven adaptive matching system.
Figure 3: Heatmap of Greedy vs. Patient policy gap across Log-normal parameters ( μ , σ ). Solid lines trace actual contours for loss tolerance threshold τ∈{1%,10%,15%} .; dashed lines show framework-fitted decision thresholds.
Figure 4: Performance of the Hybrid framework (under varying thresholds τ ) versus static policies as d varies. Fixed parameters include w=0.3 , λ=100 , T0=50 , and T=100 . Results are averaged over k=10 independent runs.
Figure 5: Performance of the Hybrid framework (under varying window sizes w ) versus static policies as d varies. Fixed parameters include τ=10% , λ=100 , T0=50 , T=100 , and k=10 .
Figure 6: Dynamic policy selection under the Hybrid framework with τ=10% , w=0.3 , over the interval T∈[95,100] .
Figure 7: Policy frequency under the Hybrid framework as window size varies, τ=10% and k=10 , over the interval T∈[80,100] .
Department of Economics, University of Washington, Seattle, United States · Paul G. Allen School of Computer Science & Engineering, University of Washington, Seattle, United States