Values of games with weighted graphs

• TU games with cooperation restricted by means of a weighted network.
• Several interpretations of the link weight: capacity, flow, distance, cost.
• Different weighted restricted-graph games depending on the weights meaning.
• Weighted Myerson values: the Shapley value of the restricted games.
• Characterization and Link/weight monotonicity of weighted Myerson values.

In this paper we deal with TU games in which cooperation is restricted by means of a weighted network. We admit several interpretations for the weight of a link: capacity of the communication channel, flow across it, intimacy or intensity in the relation, distance between both incident nodes/players, cost of building or maintaining the communication link or even probability of the relation (as in Calvo, Lasaga, and van den Noweland, 1999). Then, according to the different interpretations, we introduce several point solutions for these restricted games in a way parallel to the familiar environment of Myerson. Finally, we characterize these values in terms of the (adapted) component efficiency, fairness and balanced contributions properties and we analyze the extent to which they satisfy a link/weight monotonicity property.