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Substitutability, equilibrium transport, and matching models

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  • Alfred Galichon
  • Antoine Jacquet

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.

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  • Alfred Galichon & Antoine Jacquet, 2024. "Substitutability, equilibrium transport, and matching models," Papers 2405.07628, arXiv.org.
    • Handle: RePEc:arx:papers:2405.07628
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    1. Alfred Galichon & Yu-Wei Hsieh & Maxime Sylvestre, 2023. "Monotone comparative statics for submodular functions, with an application to aggregated deferred acceptance," Papers 2304.12171, arXiv.org, revised Aug 2024.
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