In economics, assignment valuation is a kind of a utility function on sets of items.
It was introduced by Shapley[1] and further studied by Lehmann, Lehmann and Nisan,[2] who use the term OXS valuation (not to be confused with XOS valuation).
Fair item allocation in this setting was studied by Benabbou, Chakraborty, Elkind, Zick and Igarashi.
[3][4] Assignment valuations correspond to preferences of groups.
Suppose there are three items and two agents who value the items as follows: Then the assignment-valuation v corresponding to the group {Alice,George} assigns the following values: