Coalition
A subset of the players considered as a group that can act together and is credited with whatever it can achieve on its own.
Often misread asThinking of a coalition as a group that has actually formed and agreed something, when in the theory every subset of players has a worth whether or not it ever assembles.
How to see it
Every possible group has a worth, whether or not it forms
In cooperative theory the unit of analysis is the group rather than the individual. A coalition is any set of players treated as a bloc, and the theory credits it with whatever its members could achieve by walking away from everybody else.
The checkCoalitions that never form do most of the work, because their worth is the threat that constrains how the surplus may be divided.
Try itWith three players there are seven non empty coalitions. Name them. Then ask which of them matter when you are deciding whether a proposed split is stable. The answer is all seven, and that is the point.
Know these first
Leads on to
Easily confused with
Sources
- von Neumann, J. & Morgenstern, O. (1944). Princeton UP.
- Osborne, M. & Rubinstein, A. (1994). MIT Press.
- Maschler, M., Solan, E. and Zamir, S. (2013). Game Theory. Cambridge University Press.