Abstract
In this paper, we investigate some problems about division problems given by transferable utility cooperative games with a variable population of players. First, we set up a unified model format and introduce some new concepts . In theorem 1, we obtain a sufficient and necessary condition for judging core allocation principles in all allocation principles; In theorem 2, we obtain another sufficient condition for distinguishing core allocation principles from the given allocation principles; The conditions given in theorem 3 are easily examined, and theorem 2 is a very usful result for distingushing core allocation principles from the given allocation principles. As an example, we obtain that the Shapley value for certain kind of nonconvex games is a core allocation principle.
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