# On the Position Value for Special Classes of Networks

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## Abstract

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.

## Keywords

TU-games Networks Communication situations Coalition formation Allocation protocols Position value## Notes

### Acknowledgements

We are grateful to Stefano Moretti and Roberto Lucchetti for helpful comments on a previous version of the paper.

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