On the position value of special classes of networks

A cooperative game with transferable utility (TU-game) describes a situation in which all players can freely interact with each other, i.e. every coalition of players is able to form and cooperate. However, this is not the case in many real world scenarios. A typical situation is when there exists a restriction on the communication possibilities among players. Different approaches to model the restrictions of the interaction possibilities among players exist in literature. This paper deals with a particular class of TU-games, those whose cooperation is restricted by a network structure. We consider a communication situation in which a network is produced by subsequent formation of links among players and at each step of the network formation process, the surplus generated by a link is shared between the players involved, according to some rule. As a consequence, we obtain a family of solution concepts that we investigate on particular network structures. This approach provides a different interepretation of the position value since it turns out that a specific simmetric rule leads to this solution concept. Moreover, we provide formulas for the position value on trees and cycles for canonical games.