This paper links matching markets with aligned preferences to optimal transport theory. We show that stability, efficiency, and fairness emerge as solutions to a parametric family of optimal transport problems. The parameter indexes a planner's attitude towards inequality. This link offers insights into structural properties of matchings and trade-offs between objectives, showing how stability can lead to welfare inequalities, even among similar agents. Our model captures supply-demand imbalances in contexts like spatial markets, school choice, and ride-sharing. We also show that large markets with idiosyncratic preferences can be well approximated by aligned preferences, expanding the applicability of our results.

翻译：本文将具有一致偏好的匹配市场与最优运输理论联系起来。我们证明稳定性、效率和公平性作为参数化最优运输问题族中的解出现。该参数反映了规划者对不平等的态度。这种联系揭示了匹配的结构性质与目标之间的权衡，表明即使是在相似主体之间，稳定性也可能导致福利不平等。我们的模型捕捉了空间市场、择校和拼车等情境中的供需失衡。我们还证明，具有异质性偏好的大规模市场可以通过一致偏好进行良好近似，从而扩展了研究结果的适用性。