18 Stable Matching for allocations within one group

Consider the following example with four people $A,B,C$ and $D$

• Preferences of $A$ are $B>C>D$
• Preferences of $B$ are $C>A>D$
• Preferences of $C$ are $A>B>D$
• Preferences of $D$ are $A>B>C$

There are three possible matchings:

• $(A,B)$ and $(C,D)$
  • $B$ and $C$ form an unstable pair
• $(A,C)$ and $(B,D)$
  • $A$ and $B$ form an unstable pair
• $(A,D)$ and $(B,C)$
  • $A$ and $C$ form an unstable pair

No stable matching