A weighted position value

We provide a generalization of the position value (Meessen 1988) that allows players to benefit from transfers of worth by investing in communication links. The player who invests the most in a communication link obtains transfers of worth from the second one. We characterize this new allocation rule on the class of cycle free graphs by means of four axioms. The first two axioms, component efficiency and superfluous link property, are used to characterize the position value (Meessen (1988), Borm, Owen, and Tijs (1992)). Quasi-additivity is a weak version of the standard additivity axiom. The weighting axiom captures the fact that the allocation of players should be increasing with their level of investment