Characteristic function
The rule that assigns to every coalition the total payoff its members can guarantee themselves without help from anyone outside it.
Often misread asTaking a coalition's worth to be what it would end up with in play, rather than what it can guarantee itself regardless of how the players outside it behave.
How to see it
A number for every group, and it is a guarantee
Instead of describing moves, you describe outcomes for groups: for every possible set of players, one number saying what that set can secure by itself. The whole game becomes that list of numbers, and the solution concepts are different ways of reading it.
The checkIt is a floor computed against the worst the outsiders could do, and it is that guaranteed quality which makes it usable as a threat in a bargaining argument.
Try itThree musicians: a solo act earns a hundred, any duo three hundred, the trio five hundred. Write out all seven numbers. Then ask whether three hundred is what the duo would get or what the duo could guarantee. Only the second belongs in the function.
Know these first
Leads on to
Easily confused with
Sources
- von Neumann, J. & Morgenstern, O. (1944). Princeton UP.
- Shapley, L. S. (1953). In Kuhn, H. W. and Tucker, A. W. (eds), Contributions to the Theory of Games, Volume II, Annals of Mathematics Studies 28. Princeton University Press, 307-317.
- Maschler, M., Solan, E. and Zamir, S. (2013). Game Theory. Cambridge University Press.