Communication in Weighted Networks: A Game Theoretic Approach

In this paper we generalize the allocation rule (point solution or value) known as the mixed value by introducing the weighted mixed value.The proposed solution assigns value in graph games where players, and/or links, have weights representing asymmetries of the players, and different flows, lengths, emotional intensities, trust in the transmission of the information, etc. in the links. We present several characterizations of this value using properties, such as mixed component efficiency, weighted mixed fairness, weighted balanced contributions and weighted balanced link contributions. These properties were inspired by the classical properties used to characterize the Myerson value and the position value.