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

For the class of cooperative games with transferable utilities an excess function e is defined as a function of two variables increasing in the first variable and decreasing in the first one such that given a TU game (N,v) , a coalition S, and a payoff vector x, the value e(v(S), x(S)) is a relative dissatisfaction of coalition S by its payoff x(S) equal the sum of coordinates of x corresponding to the players from S. A TU game solution is called an excess value if for every games (N,v) and (N,w) from the equalities e(v(S),x(S))=e(w(S),y(S)) for all coalitions S and for some payoff vectors x and y it follows that either both vector x,y belong to the solution or both do not belong to it.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 sufficient conditions on the excess functions under which both definitions of consistency - for the allocation methods and for TU game solutions - coincide on the class of surplus sharing problems are given