How to Use Prices for Efficient Online Matching
TLDR
This paper introduces the Sequential Equilibrium Mechanism (SEM), an online matching algorithm that achieves asymptotically efficient, fair, and strategy-proof assignments.
Key contributions
- Introduces the Sequential Equilibrium Mechanism (SEM), an online algorithm for dynamic matching.
- Approximates large market equilibria to efficiently match arriving agents to objects.
- Demonstrates asymptotic efficiency, fairness, and strategy-proofness with high probability.
- Provides simulation evidence of welfare improvement and plans real-world deployment.
Why it matters
Many critical matching markets, like assigning children to foster homes, face dynamic arrivals. This paper offers a novel, provably efficient, and fair algorithm (SEM) to address these challenges. Its real-world application could significantly improve welfare in vulnerable populations.
Original Abstract
Many matching markets feature unknown, dynamic arrivals of agents that must match immediately. A caseworker must match an abused child to a foster home, a hospital must assign a patient in critical condition to a room, or a city must place a homeless individual into a shelter. We design an online matching algorithm -- the Sequential Equilibrium Mechanism (SEM) -- that approximates large market equilibria to match arriving agents to objects. SEM is asymptotically efficient, fair, and strategy-proof with probability one. Our application plans to deploy a lab-in-the-field experiment where real caseworkers match vulnerable children to host homes, and we provide simulation evidence that SEM can substantially improve welfare.
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