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The Owen value is a modification of the Shapley value for games with a coalition
structure. In this paper, we propose another modification of the Shapley value
for monotone games with a coalition structure. This new value is a double-
extension of the Shapley value in the next sense: the amount obtained by an
union coincides with the Shapley value of the union in the quotient game, and the
players of each union share this amount proportionally to their Shapley values
in the game without unions. We give two characterizations of this new value.
The axiomatic systems used here can be compared with parallel axiomatizations
of the Owen value.
CitacióAlonso, J.; Carreras, F. "A proportional extension of the Shapley value for monotone games with a coalition structure". 2009.