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Given a number of participants(parties), each with their own objective or utility function, we want to find a solution to a sharing problem so that the smallest find a solution to a shared problem so that the smallest utility is maximized. utility is maximized, given that, the third etc...
The specific sharing problem is to allocate a number of discrete items from an inheritance to the heirs, with each heir having her own set of values for each of the items to be allocated;