Abstract
Michael Dummett andRobin Farquharson [1961] provided a sufficient condition for ann-person simple majority game with ordinal preferences to have a nonempty core. In the present paper we generalize this result to an arbitrary proper simple game. It is proved that their condition is also sufficient for this game to have a nonempty core. Our proof of this theorem is much simpler than the proof given byDummett andFarquharson. Finally some applications of the theorem are presented.
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Nakamura, K. The core of a simple game with ordinal preferences. Int J Game Theory 4, 95–104 (1975). https://doi.org/10.1007/BF01766188
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DOI: https://doi.org/10.1007/BF01766188