A note on a generalization of the nucleolus to games without sidepayments

We present a generalization of the nucleolus to games without sidepayments. By allowing the interpersonal utility comparison such that payoffs are determined proportionally to given weights, we define an excess of a coalition as a number depending on this vector of weights. The existence and the inclusion in nonempty cores are proved, but the uniqueness is not preserved. It is also remarked that the excess defined here is not the same as that ofKalai 1975]