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.

翻译：本章探讨可替代性在经济模型中的作用，尤其聚焦于最优运输与匹配模型。在具有可替代性的均衡模型中，市场出清价格通常可通过坐标更新方法（如雅可比算法）恢复。我们通过Z函数和M函数的视角，对具有可替代性的模型进行了详细的数学分析，特别关注它们在确保雅可比算法收敛性中的作用。随后，本章利用可替代性研究匹配模型，首先关注（非完美）可转移效用模型，进而讨论非转移效用模型。针对这两种情况，本文综述了理论意义及计算方法（Sinkhorn算法、Gale-Shapley算法），并重点介绍了一个实用经济应用。