Dynamic Stochastic Matching Under Limited Time
66 Pages Posted: 27 Dec 2019 Last revised: 25 Oct 2021
Date Written: December 3, 2019
In centralized matching markets such as car-pooling platforms and kidney exchange schemes, new participants constantly enter the market and remain available for potential matches during a limited period of time. To reach an efficient allocation, the "timing'' of the matching decisions is a critical aspect of the platform's operations. There is a fundamental trade-off between increasing market thickness and mitigating the risk that participants abandon the market. Nonetheless, the dynamic properties of matching markets have been mostly overlooked in the algorithmic literature.
In this paper, we introduce a general dynamic matching model over edge-weighted graphs, where the agents' arrivals and abandonments are stochastic and heterogeneous. Our main contribution is to design simple matching algorithms that admit strong worst-case performance guarantees for a broad class of networks. By contrast, we show that the performance of widely used batching algorithms can be arbitrarily bad on certain graph-theoretic structures that are motivated by car-pooling settings. Our approach involves the development of a host of new techniques, including linear programming benchmarks, value function approximations, and proxies for continuous-time Markov chains, which could be of broader interest. In extensive experiments, we simulate the matching operations of a car-pooling platform using real-world taxi demand data. The newly developed algorithms have the potential to significantly improve cost efficiency against widely used batching algorithms.
Keywords: Dynamic Matching, Approximation Algorithms, Markov Decision Processes
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