On the Position Value for Special Classes of Networks

This paper deals with a particular class of TU-games, whose cooperation is restricted by a network structure. We consider a communication situation (or graph game) 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 interpretation of the position value, introduced by Borm et al. (SIAM J Discret Math 5(3):305–320, 1992), since it turns out that a specific symmetric rule leads to this solution concept. Moreover, we investigate the problem of computing the position value on particular classes of networks.