Modeling values for TU-games using generalized versions of consistency, standardness and the null player property

In the paper we discuss three general properties of values of TU-games: $$\uplambda $$λ-standardness, general probabilistic consistency and some modifications of the null player property. Necessary and sufficient conditions for different families of efficient, linear and symmetric values are given in terms of these properties. It is shown that the results obtained can be used to get new axiomatizations of several classical values of TU-games.

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