For each cooperative n-person game v and each , let be the average worth of coalitions of size and the average worth of coalitions of size h which do not contain player The paper introduces the notion of a proportional average worth game (or PAW-game), i.e., the zero-normalized game v for which there exist numbers such that for all , and . The notion of average worth is used to prove a formula for the Shapley value of a PAW-game. It is shown that the Shapley value, the value representing the center of the imputation set, the egalitarian non-separable contribution value and the egalitarian non-separable contribution value and the egalitarian non-average contribution value of a PAW-game are collinear. The class of PAW-games contains strictly the class of k-coalitional games possessing the collinearity property discussed by Driessen and Funaki. Finally, it is illustrated that the unanimity games and the landlord games are PAW-games.
