Imputation
A way of dividing the worth of the grand coalition that leaves nothing on the table and gives every player at least what they could get alone.
Often misread asTreating imputation as a fairness notion, when all it rules out is splits that waste surplus or pay somebody less than going it alone would have done.
How to see it
The shortlist, not the answer
An imputation is a division of the whole group's winnings that clears two very low bars: nothing is left unallocated, and nobody gets less than they could have made entirely alone. It is the set of candidate answers rather than an answer.
The checkEvery reasonable division is an imputation, and so are plenty of grossly unfair ones. The fairness work is done entirely by whatever concept you apply next.
Try itThree partners create five hundred pounds together and each could make a hundred alone. Check that giving one of them three hundred and the others a hundred each is an imputation. It is. Now ask whether you would call it fair. The gap between those two answers is the concept.
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.