Banzhaf Value for Games with Restriction

This paper belongs to the value theory research for cooperative game. A ldquorestrictionrdquo is a monotonic projection assigning to each coalition of a finite player set a sub-coalition. Those games that are associated with ´restriction´ are called games with restriction. In fact, this kind of games considers those cooperative games in which the cooperation among players is constrained. Applying a certain rule of allocation to the games with restriction, we get the imputation value for games with restriction. Banzhaf value for games with restriction is given in this paper and is characterized by method of axiom. Moreover the Multilinear Extension for games with restriction is given, which provides a calculation method of the value. An example of the games with restriction-games with permission structure is given at last. The calculation results show that it is easier to calculate Bazhaf value under the meaning of ldquorestrictionrdquo than in the usual meaning.