A characterization of those n-person games that can be solved by excluding one or more players from a share of the proceeds and then solving the ensuing "fraction" of the original game. It is shown that a discriminatory solution exists if, and only if, there is one group of players strong enough to enforce all possible distributions of proceeds in the original game that exclude the "out" players. Some previously known results that follow as special cases of this general condition are given.
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