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4330. TU-games with utility: characterization sets for the u-prenucleolus
Invited abstract in session MA-36: Game Theory, Solutions and Structures I, stream Game Theory, Solutions and Structures.
Monday, 8:30-10:00Room: 32 (building: 306)
Authors (first author is the speaker)
| 1. | Zsófia Dornai
|
| Budapest University of Technology and Economics, Institute of Mathematics | |
| 2. | Miklós Pintér
|
| Corvinus Center for Operational Research, Corvinus University of Budapest |
Abstract
The u-prenucleolus is a generalization of the prenucleolus using utility functions. The u-prenucleolus can also be considered as a generalization of the per-capita prenucleolus. We prove the generalizations of some important theorems about the prenucleolus to the u-prenucleolus, such as Kohlberg’s theorem and the theorem of Katsev and Yanovskaya about a sufficient and necessary condition on the unicity of the u-prenucleolus. We also prove a generalization of Huberman’s theorem by defining the u-essential coalitions and showing that these coalitions characterize the u-prenucleolus of u-balanced games. Considering the dual of the game, we define the u-anti-prenucleolus, and show that the u-anti-essential coalitions characterize it. Using these results, we get that in the primal game the u-dually-essential coalitions – which generalize the dually essential coalitions defined by Solymosi and Sziklai - characterize the u-prenucleolus. This way, we get a characterization set for the u-prenucleolus that differs from the set of u-essential coalitions.
Keywords
- Game Theory
Status: accepted
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