May 15 (10:00-11:00) room C.510
Zsófia Dornai (HUN-REN Centre for Economic and Regional Studies, Institute of Economics, Game Theory Research Group)
TU-games with utility functions: dually u-essential coalitions and other characterization sets for the u-prenucleolus
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. Generalizations of some important theorems about the prenucleolus to the u-prenucleolus stand, such as Kohlberg’s theorem, the theorem of Katsev and Yanovskaya about a sufficient and necessary condition on the unicity of the u-prenucleolus and a generalization of Huberman’s theorem, which claims that the u-essential 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, if the game is u-balanced. Using these results, we get that in the primal game the dually u-essential coalitions – which generalize the dually essential coalitions defined by Solymosi and Sziklai – characterize the u-prenucleolus of u-balanced games. In addition, we show, that in case of games where the u-least-core is a proper subset of the u-core the intersection of u-essential and dually u-essential coalitions also characterize the u-prenucleolus. To prove this latter theorem, we also give a generalization of a theorem by Granot, Granot and Zhu about a sufficient condition of a set of coalitions characterizing the u-prenucleolus, which also extends this result to games with restricted cooperation.
The talk is based on joint work with Miklós Pintér.