The Consistent Shapley Value for Games without Side Payments

In (Maschler and Owen, 1989), a new generalization of the Shapley value for a class of NTU games was introduced. The motivation was a desire to preserve as much as possible the consistency property of the Shapley value for TU games, in the sense of (Hart and Mas-Colell, 1989). It turned out that the new value resulted from an intuitive dynamic process which was interesting also for the class of TU games. Unfortunately, the class of NTU games was quite narrow; namely, the class of hyperplane games. The purpose of this paper is to extend the definition to the general class of NTU games, whose coalition functions satisfy (essentially) the usual requirements.