Question $2$

Suppose that the Gale$-$Shapley algorithm is given the following input, where for each $b$ and $g$ its list of preferences is given, in order of most preferable first, e$.$g$.$ b$1$:

$g2,g4,g3,g1$ means that b$1\text{'}$s top choice is g $2,$ the next g $4,$ the next g $3,$ and the last g $1$ :

$b1$ : $g2,g4,g3,g1$

$b2$ : $g4,g1,g2,g3$

$b3$ : $g2,g1,g3,g4$

$b4$ : $g3,g4,g1,g2$

$g1$ : $b1,b3,b4,b2$

$g2$ : $b3,b1,b4,b2$

$g3$ : $b3,b4,b1,b2$

$g4$ : $b2,b1,b3,b4$

When the first stage completes, b$1$ is matched with:

g$1$

g$3$

g$2$

g$4$