Nonlinear Self Dual Solutions for TU-Games∗)

For cooperative transferable utility games solution concepts are presented which resemble the core-like solution concepts prenucleolus and prekernel. 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. Sudhölter’s recent results on the modified nucleolus are surveyed. Moreover, an axiomatization of the modified kernel is presented.