Stability in Matching Markets with Complex Constraints

We develop a model of many-to-one matching markets in which agents with multiunit demand aim to maximize cardinal linear objective subject multidimensional knapsack constraints. The choice functions are therefore not substitutable. As result, pairwise stable matchings may exist and even when they do, be highly inefficient. provide an algorithm that finds group-stable approximately satisfies all the novel ingredient our is combination contracts Scarf’s Lemma. show degree constraint violation under proportional sparsity matrix. algorithm, therefore, provides practical bounds for applications contexts, such as refugee resettlement, day care allocation, college admissions diversity requirements. Simulations using resettlement data approach produces outcomes only more stable, but also efficient than Deferred Acceptance algorithm. Moreover, simulations suggest practice, violations would smaller theoretical bounds. This paper was accepted by Gabriel Weintraub, revenue management market analytics.