Fundamentals of Matching Theory

Abstract

Matching theory, in economics, is a mathematical framework that allows analyzing the formation of mutually beneficial relationships over time. Prior to the seminal work of Gale and Shapley on the stable marriage and college admission problems in 1962, many matching problems were solved by the “free for all market”. The “free for all market” term refers to the period before matching theory was conceived as a discipline, as well as the way in which matching problems were dealt with during the period. Economists have identified several issues such as unraveling, congestion, and exploding offers in the “free for all market”. Since then, with decades of efforts devoted to developing matching algorithms (i.e., there arises a trusted third party, which collects information, runs a matching algorithm, and broadcasts the matching results), these challenges were overcome. As a result, there has been a surge in the development of matching frameworks that have become widely used in many areas, such as the national resident matching program in the United States, the college admission in Hungary, the incompatible kidney exchange market, and the partnership formation in peer-to-peer (P2P) network, among others.