Shapley value
The unique way of dividing the spoils that gives each player their average contribution to the group, taken over every order in which the group could have assembled.
Often misread asExpecting the Shapley value to be stable, so it is assumed to lie inside the core whenever the core is not empty.
How to see it
Your average contribution over every order of arrival
Imagine the group assembling one person at a time in a random order, each arrival handed exactly what they add to whoever is already there. Average that over every possible order and you have each player's share. It always exists, it always divides the whole amount, and it is the only rule meeting a short list of fairness conditions.
The checkIt is a fairness rule, not a stability rule. It averages over orderings without ever asking whether some coalition would object, so it can land outside a perfectly good core, and it still returns an answer when the core is empty.
Try itThree players, each worth nothing alone, the three pairs worth twenty, thirty and forty, and all three together worth fifty. The core is not empty. Compute the first player's Shapley value, which comes to just under twelve, then check the constraint that the other two can secure forty between them. It fails.
Know these first
Easily confused with
Sources
- 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.
- Myerson, R. (1991). Harvard University Press.
- Maschler, M., Solan, E. and Zamir, S. (2013). Game Theory. Cambridge University Press.