Matching under Transferable Utility: Theory

This chapter considers the theory of matching under transferable utility (TU). It first introduces a formal definition of the TU property: a group satisfies TU if there exists monotone transformations of individual utilities such that the Pareto frontier is a hyperplane. It then examines the cornerstone of the theory of nontransferable utility (NTU) matching, namely, the Gale-Shapley algorithm, before turning to a discussion of a crucial property of matching models under TU: their intrinsic relationship with optimal transportation. It also describes the notions of supermodularity and assortativeness, along with individual utilities and intrahousehold allocation. Finally, it looks at hedonic models, taking into account hedonic equilibrium and stable matching, and presents two examples that illustrate the relationship between matching and hedonic models: a competitive IO model and randomized matching.