The economy has six agents: three men (m1, m2, m3) and three women (w1,w2, w3). A match is every feasible pair of men and women. So every match has to be between a man and a woman (like the marriage problem we studied in Chapter 3).

Their preferences are described as follows (where “P” means that he/she strictly prefers one alternative over the other):

**m1**: w2 P w1 P w3 **w1**: m1 P m3 P m2

**m2**: w1 P w3 P w2 **w2**: m3 P m1 P m2

**m3**: w1 P w2 P w3 **w3**: m1 P m3 P m2

In this economy, matches are randomly assigned, so there are six different assignations possible. Suppose every assignation is equally probable.

For example, one assignation possible is:

{m1, w1}

{m2, w3}

{m3, w2}

A match is stable if and only if there exists no pair {m, w} such that both agents strictly prefer marrying between them than the match they where assigned.

**Question**: Which assignations are stable?

This exercise is from the Roth&Sotomayor book on matching.