An axiomatic characterization of a value for games in partition function form

An extension of the Shapley value for games in partition function form is proposed in the paper. We introduce a version of the marginal contributions for environments with externalities. The dummy property related to it is defined. We adapt the system of axioms provided by Shapley (A value for n-Person games. In: Kuhn H, Tucker A (eds) Contributions to the theory of games II. Princeton University Press, Princeton, pp 307317, 1953) to characterize our value. In addition, we discuss a relationship between the a-Shapley values proposed by Fujinaka (On the marginality principle in partition function form games. Mimeo, Graduate School of Economics, Kobe University, Japan, 2004) and the values constructed through the average approach provided by Macho-Stadler et al. (J Econ Theory 135:339-356, 2007).