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Nakamura establishes a theorem which gives necessary conditions for a simple game with ordinal prefer- ences to have a nonempty core. The conditions are also sufficient, if the set of alternative outcomes is finite. In the present paper, we will show that Nakamura's method of the proof of this theorem makes it possible to generalize the theorem to an arbitrary characteristic function game with ordinal preferences.

ON THE EXISTENCE OF THE CORE OF A CHARACTERISTIC FUNCTION GAME WITH ORDINAL PREFERENCES