One axiomatization of generalized Owen extension

New approach to generalized Owen extension's construction for some classes of polynomial games is considered. It is proved that this extension coincides with Aumann-Shapley extension for one class of nonatomic games. The explicit formula for multiplicative Aumann-Shapley extension is obtained. The axiomatization of classical Owen extension for the class of discrete-time cooperative games is obtained and it differs from Aumann-Shapley axiomatization only by weak multiplicative axiom.