  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.
