Publication Date
8-1-2024
Abstract
In the 1950s, the future Nobelist Lloyd Shapley solved the problem of how to fairly divide the common gain. Namely, he showed that some reasonable requirements determine a unique division -- which is now known as the Shapley value. The main limitation of Shapley's solution is that it assumes that for each subgroup of the original group of participants, we know exactly how much this group could gain if it acted by itself, without involving others. In practice, we rarely know these exact values. At best, we know the bounds on each such value -- i.e., in other words, an interval that contains this value -- or even have no information about some of these values at all. In this paper, we show that a natural modification of Shapley's conditions enables us to extend Shapley's formulas to this realistic case, when we have interval uncertainty and partial information.
Comments
Technical Report: UTEP-CS-24-41