Consistency of the Owen value for TU-games with coalition and graph structures

Consistency is widely adopted in designing allocation rules for cooperative games. It imposes that the allocation rules give players the same payoff in the reduced game as in the initial cooperative game. The reduced game is obtained from the initial cooperative game by removing one or more players. In this paper, by extending the concept of consistency to cooperative games with coalition and graph structures, we establish a new axiomatization of the Owen graph value. Moreover, we give a comparison between the axiomatizations of the Owen, Banzhaf–Owen and symmetric coalitional Banzhaf graph values.