• We propose a basis for the linear vector space of constant-sum games. The Shapley value in liability games satisfies order preservation. Liability monotonicity, asset and super-modularity also holds. Calculating is non-deterministic polynomial-time hard. In problem, an insolvent firm must be distributed among creditors itself, when has some freedom negotiating with creditors. model negotiatio...

Data envelopment analysis (DEA) is an effective tool for supporting decision-makers to assess bankruptcy, uncertainty concepts including intervals, and game theory. The bankruptcy problem with the qualitative parameters is an economic problem under uncertainty. Accordingly, we combine the concepts of the DEA game theory and uncertain models as interval linear programming (ILP), which can be app...

One of the long-debated issues in coalitional game theory is how to extend the Shapley value to games with externalities (partition-function games). When externalities are present, not only can a player’s marginal contribution—a central notion to the Shapley value—be defined in a variety of ways, but it is also not obvious which axiomatization should be used. Consequently, a number of authors e...

In this paper a new model of multichoice games with a coalition structure is proposed, which can be seen as an extension of the Owen coalition structure. A coalitional value on the given model is defined, which can be seen as an extension of the Owen value. Three axiomatic systems are studied. The first one is enlightened by Owen’s characterization for the Owen value and Faigle and Kern’s chara...

The Shapley value is arguably the most central normative solution concept in cooperative game theory. It specifies a unique way in which the reward from cooperation can be “fairly” divided among players. While it has a wide range of real world applications, its use is in many cases hampered by the hardness of its computation. A number of researchers have tackled this problem by (i) focusing on ...

Marginanism and egalitarianism are two main standpoints in economics. The Shapley value has been characterized in many ways from the view of marginalism. In this paper, we characterize the Solidarity value with respect to the egalitarianism by three approaches applied to the Shapley value. We introduce a revised potential function and deduce the recursive formula of the Solidarity value. It is ...

We consider Young (1985)'s characterization of the Shapley value, and give a new proof of this axiomatization. Moreover, as applications of the new proof, we show that Young (1985)'s axiomatization of the Shapley value works on various well-known subclasses of TU games.

Graph-restricted games, first introduced by Myerson [20], model naturally-occurring scenarios where coordination between any two agents within a coalition is only possible if there is a communication channel(a path) between them. Two fundamental solution concepts that were proposed for such a game are the Shapley value and the Myerson value. While an algorithm has been proposed to compute the S...