Abstract
We introduce in this note the consistent organizational structure (COS) problem, which can be viewed as a generalization of the college admission and room-mates problems. Both the room-mates problem and the COS problem may have no stable solution. When side payments are allowed, the COS problem, but not the room-mates problem, always has a nonempty core. We further study some nucleoli of the COS problem with side payments.
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