Substitutability, equilibrium transport, and matching models

Alfred Galichon and Antoine Jacquet

Papers from arXiv.org

Abstract: This chapter explores the role of substitutability in economic models, particularly in the context of optimal transport and matching models. In equilibrium models with substitutability, market-clearing prices can often be recovered using coordinate update methods such as Jacobi's algorithm. We provide a detailed mathematical analysis of models with substitutability through the lens of Z- and M-functions, in particular regarding their role in ensuring the convergence of Jacobi's algorithm. The chapter proceeds by studying matching models using substitutability, first focusing on models with (imperfectly) transferable utility, and then on models with non-transferable utility. In both cases, the text reviews theoretical implications as well as computational approaches (Sinkhorn, Gale--Shapley), and highlights a practical economic application.

Date: 2024-05
New Economics Papers: this item is included in nep-des and nep-upt
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2405.07628

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