THE COMPROMISE SOLUTIONS OF CLASSICAL COOPERATIVE GAME
The subject of paper’s investigation is the one-point solutions for transferable utility game that balance, in some sense, opposite principles of distribution of profit among the partners. First we describe known compromise solutions: the consensus value being the average of the Shapley value and the equal surplus division solution; the t-value that balances the upper vector and the lower vector of a game; s-values that equal the average of pairs of extreme points, one of which belongs to the imputation set whereas the other belongs to the dual imputation set. Axiomatic approach was used for the comparisons of solution concepts. Among the non-uniquely determined sets of characterizing axioms we chose the Shapley axioms and similar ones. The main result of the paper is an introducing the new solution for cooperative transferable utility game being an average of two most popular one-point solutions: the Shapley value and the nucleolus. It is proved that for some games new solution, called NS-core, possesses more desirable properties than main one-point solutions and other compromise solutions. It is given the example of game in which NS-core does not coincide with the considered one-point solutions and is the most preferred outcome with respect to standard dominance relation. The application domains of the NS-core are the games that model economic, social and political situations where the Shapley value does not satisfy an individual rationality condition or it is not an element of a nonempty core, while the nucleolus gives a contrary-intuitive (paradoxical, tyrannous) sharing the joint profit.