Highly mutually dependent unions and new axiomatizations of the Owen value

The Owen value is an well-known allocation rule for cooperative games with coalition structure.In this paper, we introduce the concept of highly mutually dependent unions. Two unions in a cooperative game with coalition structure are said to be highly mutually dependent if any pair of players, with one from each of the two unions, are mutually dependent in the game.Based on this concept, we introduce two axioms: weak mutually dependent between unions and differential marginality of inter-mutually dependent unions. Furthermore, we also propose another two axioms: super inter-unions marginality and invariance across games, where the former one is based on the concept of the inter-unions marginal contribution. By using the axioms and combining with some standard axioms, we present three axiomatic characterizations of the Owen value.