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In the classical approach of von Neumann and Morgenstern to cooperative games, it was assumed that the worth of all coalitions must be given. However, in real-world problems, the worth of some coalitions may be unknown. Therefore, in this study, we consider the Shapley value for convex partially defined games using two approaches. Firstly, we introduce a polytope that includes the set of Shapley values that can be obtained from a given convex partially defined game and select one rational value in some sense from the set. The elements of this polytope are said to be the Shapley payoff vectors. Secondly, we obtain the set of Shapley values that can be obtained from a given convex partially defined game and select one rational value in some sense from the set. Moreover, we axiomatize the proposed two values. [ABSTRACT FROM AUTHOR]

This paper considers a cooperative fuzzy game withnplayers andralternatives called a multi-alternative fuzzy game. Considering the non-homogeneity among players, we pro-pose a new value function on a class of these games, which means evaluation values for the game by players. Furthermore an axiom system is proposed on which the new value function is based. Finally we give a numerical example in which the new value is compared with traditional values. [ABSTRACT FROM PUBLISHER]