New axiomatizations of the Owen value

Differential marginality states that two players’ payoffs change by the same amount with respect to two games if their productivity (measured by the marginal contributions) changes by the same amount, that is, they are symmetric in the difference of these games. This principle can be applied to characterize the Owen value for games with coalition structure. In this paper we suggest two relaxations of differential marginality within unions by requiring that two players are either mutually dependent or necessary rather than symmetric in the difference of two games under consideration. Similarly, we also introduce two relaxations of differential marginality between unions. Based on these weak versions of differential marginality, we provide two new characterizations of the Owen value for games with coalition structure.