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 their communication links. The player who invests the most in a communication link obtains a compensation from the second one. We characterize this new allocation rule on the class of communication situations with cycle-free graphs by means of six axioms. The first two axioms, component efficiency and superfluous link property, are used to characterize the position value (Borm, Owen, and Tijs (1992)). Quasi-additivity is a weak version of the standard additivity axiom. Link decomposability captures the fact that the insurance system only allows compensations between players who share a link. Weak positivity states that if the communicative strength of a link is non null, its adjacent players cannot obtain a null payoff. Finally, weak power inversion reflects the compensation mechanism.
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