The core
The set of divisions that no group of players could beat by walking away and keeping what they could make on their own.
Often misread asExpecting the core to pick out one sensible division, when in practice it is usually a whole region and in many games there is nothing in it at all.
How to see it
No group could walk out and do better
A division is in the core if no set of players could leave, keep what they can make on their own, and do better for every one of their members. It is a stability test applied to every possible breakaway group at once, which is why it is often large and quite often empty.
The checkThe core is a region defined by inequalities. Nothing guarantees it is small and nothing guarantees it is non empty.
Try itThree people. Any two of them can secure a hundred pounds together, and all three together can also secure only a hundred. Try to split that hundred so that every pair holds at least a hundred between them. Fail, and you have met an empty core.
Know these first
Leads on to
Easily confused with
Sources
- Osborne, M. & Rubinstein, A. (1994). MIT Press.
- Maschler, M., Solan, E. and Zamir, S. (2013). Game Theory. Cambridge University Press.
- Myerson, R. (1991). Harvard University Press.