Abstract:
It is well known that, for cooperative games with transferable utility (and with crisp payoffs), the set of reasonable imputations is nonempty. It is also known for what values of $\varepsilon$ the set of reasonable imputations belongs to the $\varepsilon$-core. Then the $\varepsilon$-core is also nonempty. This result is of considerable interest, because the 0-core of a cooperative game can be empty, but if the $\varepsilon$-core is nonempty in this case for some small $\varepsilon>0$, then there exist imputations such that the difference in the properties between them and the imputations from the 0-core is small. In this paper, these results are generalized to the case of games with fuzzy payoffs.
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