Stable Matching by Optimal Transport

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Introduces a model with aligned preferences (u=v) and uses optimal transport to show concrete links: a family of transport costs c_alpha = (1/alpha)(1−e^{alpha u}) yields approximate stability for large positive alpha (epsilon ≈ log 2 / alpha) and approximate egalitarianism for large negative alpha (epsilon–delta tradeoff), proves existence of stable matchings as limits of OT solutions in infinite markets, and derives 1‑D non-crossing (cyclic monotonicity) structure relevant to organ exchange and team formation.

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" chapters (10)

1. 0:00Introduction to aligned matching
2. 2:35Infinite market dynamics
3. 6:33Stability versus fairness
4. 9:44Optimal transport framework
5. 12:29Formal definitions and stability
6. 16:44Defining egalitarian outcomes
7. 18:55Cost functions and optimization
8. 22:23Existence and structural results
9. 26:11Cyclic monotonicity
10. 30:27Ordinal preferences and conclusions