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A last section makes a comparison with the core defined by van den Nouweland et al. Yuk sticker has the national toll-free phone number for poison centersso the number is handy when an exposure to the product occurs. We show that the classical properties of inclusion of the (pre)core into the (pre)-Weber set as well as their equality remain valid. We study its properties, introducing balancedness and marginal worth vectors, and defining the Weber set and the pre-Weber set. A second definition is proposed, imposing normalization at each level, causing the core to be a convex closed set.

show that the precore coincides with the definition proposed by Faigle, and that it contains unbounded imputations, which makes its application questionable.

We propose two definitions for the core of a multichoice game, the first one is called the precore and is a direct generalization of the classical definition. An important notion in cooperative game theory is the core of the game, as it contains the rational imputations for players.

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