Complexity of Control by Adding or Deleting Edges in Graph-Restricted Weighted Voting Games
ECAI 2023(2023)
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 connected coalitions are taken into consideration for calculating the players’ power indices. We focus on the probabilistic Penrose–Banzhaf index [5] and the Shapley–Shubik index [18] and study the computational complexity of manipulating these games by an external agent who can add edges to or delete edges from the graph. For the problems modeling such scenarios, we raise some of the lower bounds obtained by Kaczmarek and Rothe [9] from NP- or DP-hardness to PP-hardness, where PP is probabilistic polynomial time. We also solve one of their open problems by showing that it is a coNP-hard problem to maintain the Shapley–Shubik index of a given player in a graph-restricted weighted voting game when edges are deleted.
MoreTranslated text
Key words
complexity,voting,games,edges,graph-restricted
AI Read Science
Must-Reading Tree
Example
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined