Title of the lecture
“Orders of Criticality in Graph Connection Games”
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 by Dall'Aglio, Fragnelli, Moretti in 2016 and 2019, 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 the second paper may be used as centrality measures of the edges in preserving the connection of a graph.