I could use some help with this: Assume that Arthur, Bruce, Clark and Diana are looking for jobs. The jobs available are dolphin-rider, detective, radiologist and cattle roper.
Arthur's preferences: dolphin-rider, detective, radiologist, cattle roper. Bruce's preferences: dolphin-rider, detective, radiologist, cattle roper. Clark's preferences: dolphin-rider, cattle roper, radiologist, detective. Diana's preferences: detective, radiologist, cattle roper, dolphin-rider.
Their preferences aren't the only criteria, though. There is the question of skills:
Arthur's skills: dolphin-rider, radiologist, cattle roper, detective. Bruce's skills detective, cattle roper, dolphin-rider, radiologist. Clark's skills: radiologist, dolphin-rider, cattle roper, detective. Diana's skills: cattle roper, detective, dolphin-rider, radiologist.
It is clear that a matching will be an assignment of each person to a unique job. (a) Give a nice intuitive definition of a "stable matching" in this context. (b) Find a stable matching. Here is what I was thinking: (a). A stable matching in this context would be the four people will be assigned to a job they have the highest skill in and one they will prefer in order to keep them happy and productive. (b). Arthur is a Dolphin-rider, Bruce is a detective, Clark is a radiologist, and Diane is a cattle-roper.
Not sure if that would be a suitable definition, or if my answer for b would work for my definition.