An axiomatization of generalized Owen extension

To introduce a generalized Owen extension we propose a new approach based on the nonadditive integration. Besides, we pay strong attention to the axiomatization problem for the extension introduced. One of the main results of the paper demonstrates that the axiomatization in question can be chosen similar to that elaborated by R. J. Aumann and L. S. Shapley for the multiplicative extension of nonatomic cooperative games.