A probabilistic position value

Amandine Ghintran (1, 2) , Enrique Gonzalez-Aranguena (3) , Conrado Manuel (4)

1 GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne
2 EQUIPPE - Economie Quantitative, Intégration, Politiques Publiques et Econométrie
3 departemento de Estadìstica e Investigaciòn Operativa III
4 Trier University

In this article, we generalize the position value, defined by Meessen (1988) for the class of deterministic communication situations, to the class of generalized probabilistic com- munication situations (G ́ Gomez et al. (2008)). We provide two characterizations of this new allocation rule. Following in Slikker's (2005a) footsteps, we characterize the probabilistic position value using probabilistic versions of component efficiency and balanced link con- tributions. Then we generalize the notion of link potential, defined by Slikker (2005b) for the class of deterministic communication situations, to the class of generalized probabilistic communication situations, and use it to characterize our allocation rule. Finally, we show that these two characterizations are logically equivalent.

Mots clés: Game Theory; TU Games; Graph-restricted Games; Position Value

Domaines: Gestion des risques [q-fin.RM]

Amandine Ghintran, Enrique Gonzalez-Aranguena, Conrado Manuel. A probabilistic position value. 2011. ⟨hal-00988137⟩