# An ODE Model for Dynamic Matching in Heterogeneous Networks

arXiv: https://arxiv.org/abs/2302.09757 · HTML: https://mlsanity.com/paper/2302.09757/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 39 references that are in the map.
- First posted on arXiv 20 Feb 2023.

## Builds on (most cited first, 6 of 6)

- [Learning Strategies in Decentralized Matching Markets under Uncertain Preferences](https://mlsanity.com/paper/2011.00159/) (2020)
- [Learning in Multi-Stage Decentralized Matching Markets](https://mlsanity.com/paper/2102.06988/) (2021)
- [Incentive-Aware Recommender Systems in Two-Sided Markets](https://mlsanity.com/paper/2211.15381/) (2022)
- [Two-sided Competing Matching Recommendation Markets With Quota and Complementary Preferences Constraints](https://mlsanity.com/paper/2301.10230/) (2023)
- [Kidney Exchange in Dynamic Sparse Heterogenous Pools](https://mlsanity.com/paper/1301.3509/) (2013)
- [On Matching and Thickness in Heterogeneous Dynamic Markets](https://mlsanity.com/paper/1606.03626/) (2016)

## Abstract (arXiv)

We study the problem of dynamic matching in heterogeneous networks, where agents are subject to compatibility restrictions and stochastic arrival and departure times. In particular, we consider networks with one type of easy-to-match agents and multiple types of hard-to-match agents, each subject to its own compatibility constraints. Such a setting arises in many real-world applications, including kidney exchange programs and carpooling platforms. We introduce a novel approach to modeling dynamic matching by establishing the ordinary differential equation (ODE) model, which offers a new perspective for evaluating various matching algorithms. We study two algorithms, namely the Greedy and Patient Algorithms, where both algorithms prioritize matching compatible hard-to-match agents over easy-to-match agents in heterogeneous networks. Our results demonstrate the trade-off between the conflicting goals of matching agents quickly and optimally, offering insights into the design of real-world dynamic matching systems. We provide simulations and a real-world case study using data from the Organ Procurement and Transplantation Network to validate theoretical predictions.