Abstract
The ε-core is an immediate generalization of the core, which may be nonempty even when the core is empty. In Section 7.1 we define the ε-core of a coalitional game and study some of its geometric properties. The least-core of a game is the minimum nonempty ε-core. The individual rationality and reasonableness of the least-core are investigated in Section 7.2. In Section 7.3 we prove some basic results on the set of all reasonable payoff vectors of a game. Also, we find the minimum values of ε which guarantee that the ε-core contains the set of individually rational payoff vectors, or the set of reasonable payoffs, or the intersection of these two sets.
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© 2007 Springer-Verlag Berlin Heidelberg
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(2007). Geometric Properties of the ε-Core, Kernel, and Prekernel. In: Introduction to the Theory of Cooperative Games. Theory and Decision Library, vol 34. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72945-7_7
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DOI: https://doi.org/10.1007/978-3-540-72945-7_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72944-0
Online ISBN: 978-3-540-72945-7
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