On Simple Outcomes and Cores

For a general coalitional game with non-transferable utility (NTU game) and a finite set of players, (N, V), Scarf (1967) proved that every balanced game has a non-empty core. Billera (1970) showed, through an example, that this condition is not always necessary when V(N) has a supremum. By using the concepts of simple outcome and Pareto simple outcome, the present paper provides a weaker conditio…