in partition function form. Whether or not the core exists depends crucially on the expectations of each coalition … regarding the coalition formation of the outsiders. If each coalition has pessimistic expectations, then the core always exists …, while if it has optimistic expectations, the core may be empty. …

We show that neither Peleg's nor Tadenuma's well-known axiomatizations of the core by non-emptiness, individual … balanced TU games are considered, even if anonymity is required in addition. Moreover, we show that the core and its relative …