Control by Adding or Deleting Edges in Graph-Restricted Weighted Voting Games

Abstract

Graph-restricted weighted voting games generalize weighted voting games, a well-studied class of succinct simple games, by embedding them into a communication structure: a graph whose vertices are the players some of which are connected by edges. In such games, only sufficiently connected coalitions are taken into consideration for calculating the players' power indices. Focusing on the probabilistic Penrose-Banzhaf index (which Dubey and Shapley proposed in 1979 as an alternative to the normalized Penrose-Banzhaf index) and the Shapley-Shubik index, we study control of these games by an agent who can add edges to or delete edges from the given graph. We determine upper and lower bounds on how much such control actions can change a distinguished player's power and we study the computational complexity of the related problems.