In
economics
Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services.
Economics focuses on the behaviour and interac ...
, assignment valuation is a kind of a
utility function
In economics, utility is a measure of a certain person's satisfaction from a certain state of the world. Over time, the term has been used with at least two meanings.
* In a Normative economics, normative context, utility refers to a goal or ob ...
on sets of items. It was introduced by
Shapley and further studied by Lehmann, Lehmann and Nisan, who use the term OXS valuation (not to be confused with
XOS valuation).
Fair item allocation
Fair item allocation is a kind of the fair division problem in which the items to divide are ''discrete'' rather than continuous. The items have to be divided among several partners who potentially value them differently, and each item has to be gi ...
in this setting was studied by Benabbou, Chakraborty, Elkind, Zick and Igarashi.
Assignment valuations correspond to preferences of groups. In each group, there are several individuals; each individual attributes a certain numeric value to each item. The assignment-valuation of the group to a set of items ''S'' is the value of the
maximum weight matching of the items in ''S'' to the individuals in the group.
The assignment valuations are a subset of the
submodular valuations.
Example
Suppose there are three items and two agents who value the items as follows:
Then the assignment-valuation ''v'' corresponding to the group assigns the following values:
*
- since the maximum-weight matching assigns x to George.
*
- since the maximum-weight matching assigns y to Alice.
*
- since the maximum-weight matching assigns z to George.
*
- since the maximum-weight matching assigns x to George and y to Alice.
*
- since the maximum-weight matching assigns z to George and x to Alice.
*
- since the maximum-weight matching assigns z to George and y to Alice.
*
- since the maximum-weight matching assigns z to George and x to Alice.
References
Utility function types