Orders of Criticality in Graph Connection Games

Marco Dall'Aglio (1) , Vito Fragnelli (2) , Stefano Moretti (3)

1 Department of Economics and Finance
2 University of eastern piedmont of Novara
3 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

The order of criticality of a player in a simple game and two indices inspired by the reasoning à la Shapley and à la Banzhaf were introduced in two previous papers [3] and [4], respectively, mainly having in mind voting situations. Here, we devote our attention to graph connection games, and to the computation of the order of criticality of a player. The indices introduced in [4] may be used as centrality measures of the edges in preserving the connection of a graph.

Mots clés: Order of criticality; Shapley value; Banzhaf value; Graph connection games

Domaines: Informatique [cs]

Marco Dall'Aglio, Vito Fragnelli, Stefano Moretti. Orders of Criticality in Graph Connection Games. Lecture Notes in Computer Science, 2019, Transactions on Computational Collective Intelligence XXXIV, 11890, pp.35-46. ⟨10.1007/978-3-662-60555-4⟩. ⟨hal-02361339⟩