Reduced Game Property of Linear Values with Equal Treatment Property
A transferable utility game deals with problems of how to allocate the total benefit among players by considering contributions of various coalitions of players to the total benefit. A value for games is an allocation of the total benefit among them. Many values such as the Shapley value and the prenucleolus are introduced by their own equity consideration. Thus a consistency in terms of a reduced game is a useful tool to compare various solutions in a unified way, because it expresses the differences in solutions as those in associated reduced games. This paper axiomatizes linear values with Equal Treatment Property by the consistency in terms of a reduced game.
KeywordsTU-game consistency reduced game Shapley value Solidarity value.
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