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- Page number: 396
- Section number:12.2.3
- Date:30/10/2012
- Name:Felix Fischer
- Email:ff271(at)cam
- Content: In Definition 12.2.18, ``the optimal solution to O_{i−1}'' is ambiguous. There can be more than one optimal solution, and to obtain the nucleolus one in fact has to fix only those constraints that are tight in every optimal solution. Consider the game where v({1})=4, v({2})=3, v({3})=2, v({1,2})=10, v({1,3})=11, v({2,3})=5, v({1,2,3})=12. Both (8,2,2) and (15/2,2,5/2) are optimal solutions of O_1 for this game, only the latter is in the nucleolus. Fixing the constraint for {2,3}, which is tight for the former solution, does not lead to the nucleolus.
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