Matching Theory and Its Applications

Abstract

Matching theory (e.g., Lovatz and Plummer 1986, Roth and Sotomayor 1990) is a mathematical tool that has wide-ranging applications in economics. By means of complex production functions, it is capable of proposing new solutions to long- standing, unresolved, important issues. For example, it can reconcile the Marxian theory of exploitation and the neoclassical marginal productivity theory. In international trade, it can reconcile the conflicting views regarding international factor prices between two Nobel laureates: Paul A. Samuelson and Bertile Ohlin. And it can implement Tatonnement dynamics in a clean manner and in a framework with boundedly rational agents. More-over, it suggests the usefulness of certain economic concepts, e.g., demand and supply, in graph theory, illustrating the reciprocal relationship between economics and mathematics. This talk makes use of one basic model to conduct a broad survey over a variety of issues, theoretical and applied, in economics. References Matching Theory, by L. Lavasz and M. Plummer, Annals of Discrete Mathematics 29, North Holland, 1986. Two-Sided Matching Theory: a Study in Game-Theoretic modeling and Analysis, by A. Roth and M. Sotomayor, Econometric Society Monographs No. 18, Cambridge University Press, 1990.