Introduction

Many economic problems concern the need to match members of one group of agents with one or more members of a second group. For example, workers need to be matched with firms, graduate students with graduate schools, authors with publishers, landlords with tenants, and men with women, to name just a few.

Matching problems pose three central issues:

• Is there a stable matching – one that cannot be upset by individual negotiations?

• What procedures or institutions accomplish stable matchings?

• Are these procedures manipulable?

This chapter gives a brief introduction to the economics of two-sided matching. To keep matters as simple as possible, we focus on one particular class of matching problems: the matching of two distinct groups (two-sided matching).

Notation and Basic Assumptions

Consider the problem of matching two distinct groups, say W := {w1, …, wn} and M := {m1, …, mn}, metaphorically referred to as the marriage problem. Keeping the particular application of marriage in mind, W may be remembered as the group of women and M as the group of men.

Each man is assumed to have a complete and transitive strict preference defined on W, and each woman has such a preference defined on M. These are conveniently described by a preference matrix, as in the following example.

Example 7.1 The preference matrix below gives the rankings of three men and three women.