Excess Values for Cooperative Games with Transferable Utilities and Double Consistent Allocation Methods

For cooperative games with transferable utilities (TU games) excess functions e : R2 ! R1 whose values e(x(S); v(S)); S N are relative negative utilities of coalitions S with respect to their payos x(S) = Pi2S xi are dened. The excess values for the class of two-person games are dened as those giving to both players equal excess values. An extension of this denition to the class of all TU games is given. For surplus sharing problems as a particular class of TU games, the excess values turned out to be parametric methods which are allocation-consistent. However, allocation consistency may not coincide with game theoretic consistency on the class of surplus sharing problems. Necessary and sucient conditions on the excess functions under which both denitions of consistency { for the allocation methods and for TU game solutions { coincide on the class of surplus sharing problems are given.