Abstract
For cooperative transferable utility games solution concepts are presented which resemble the core-like solution concepts prenucleolus and prekernei These modified solutions take into account both, the ‘power’, i.e. the worth, and the ‘blocking power’ of a coalition, i.e. the amount which the coalition cannot be prevented from by the complement coalition, in a totally symmetric way. As a direct consequence of the corresponding definitions they are self dual, i.e. the solutions of the game and its dual coincide. Sudhælter’s recent results on the modified nucleolus are surveyed. Moreover, an axiomatization of the modified kernel is presented.
I am grateful to an anonymous referee for insightful remarks and comments.
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Sudhölter, P. (1997). Nonlinear Self Dual Solutions for TU-Games. In: Parthasarathy, T., Dutta, B., Potters, J.A.M., Raghavan, T.E.S., Ray, D., Sen, A. (eds) Game Theoretical Applications to Economics and Operations Research. Theory and Decision Library, vol 18. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2640-4_5
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DOI: https://doi.org/10.1007/978-1-4757-2640-4_5
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