Assignment valuation

In <a href="/facts/Economics/HYctA2Dn">economics</a>, assignment valuation is a kind of a <a href="/facts/Utility_function/wlMDG74L">utility function</a> on sets of items. It was introduced by <a href="/facts/Lloyd_Shapley/WoY0lyI3">Shapley</a> and further studied by Lehmann, Lehmann and Nisan, who use the term OXS valuation (not to be confused with <a href="/facts/Fractionally_subadditive_valuation/xwxjqVfv">XOS valuation</a>). <a href="/facts/Fair_item_allocation/Hvx2XrG9">Fair item allocation</a> 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 <a href="/facts/Maximum_weight_matching/5H8UBkJb">maximum weight matching</a> of the items in S to the individuals in the group.
The assignment valuations are a subset of the <a href="/facts/Submodular_valuation/YNnlKb4U">submodular valuations</a>.

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Assignment valuation