Proportionality in NTU Games: Proportional Excess, Nucleolus and Prenucleolus

An axiomatic approach is developed to define the proportional excess function on the space of positively generated NTU games. This excess generalizes to NTU games the proportional TU excess $v(S)/x(S)$. Five axioms are proposed, and it is shown that the proportional excess is the unique excess function satisfying the axioms. The properties of proportional excess and corresponding nucleolus, prenucleolus and, in particular, status quo-proportional solution for bargaining games are studied.