On core stability, vital coalitions, and extendability |
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| Authors: | Evan Shellshear Peter Sudhlter |
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| Institution: | aInstitute of Mathematical Economics (IMW), University of Bielefeld, Germany;bDepartment of Business and Economics, University of Southern Denmark at Odense, Campusvej 55, Odense, Denmark |
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| Abstract: | If a TU game is extendable, then its core is a stable set. However, there are many TU games with a stable core that are not extendable. A coalition is vital if there exists some core element x such that none of the proper subcoalitions is effective for x. It is exact if it is effective for some core element. If all coalitions that are vital and exact are extendable, then the game has a stable core. It is shown that the contrary is also valid for matching games, for simple flow games, and for minimum coloring games. |
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| Keywords: | TU game Core Stable set Extendability Vital coalition |
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