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**:** k- n-

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**:** 2009
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**:** 26.1
**:** . ., . . k- n- / . 26.1. .: , 2009. .32-54.

**. :** 04200900023/0038

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** :** , k-, n-,

** (.):** TU game, prekernel, prenucleolus, consistency

**:** , k- n-. , -. - k, , k, k n-, , k, , .. k- . .

** (.):** A collection of TU games solutions intermediate between the prekernel and the prenucleolus is considered. All these solutions are Davis-Maschler consistent, symmetric and covariant. Each solution from the collection is parametrized by a positive integer k such that for all games with the number of players not greater than k the solution for parameter k coincides with the prenucleolus, and for the games with more than k players it is maximal, i.e. satisfies the "k-converse consistency". The properties of solutions are described and their characterization in terms of balancedness is given.

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