The lattice of envy-free many-to-many matchings with contracts

Agustín Bonifacio, Nadia Guiñazu, Noelia Juarez, Pablo Neme and Jorge Oviedo

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Abstract: We study envy-free allocations in a many-to-many matching model with contracts in which agents on one side of the market (doctors) are endowed with substitutable choice functions and agents on the other side of the market (hospitals) are endowed with responsive preferences. Envy-freeness is a weakening of stability that allows blocking contracts involving a hospital with a vacant position and a doctor that does not envy any of the doctors that the hospital currently employs. We show that the set of envy-free allocations has a lattice structure. Furthermore, we define a Tarski operator on this lattice and use it to model a vacancy chain dynamic process by which, starting from any envy-free allocation, a stable one is reached.

Date: 2022-06
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Related works:
Journal Article: The lattice of envy-free many-to-many matchings with contracts (2024)
Working Paper: The Lattice of Envy-Free Many-to-Many Matchings with Contracts (2022)
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