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

Joanna Kaczmarek, Jörg Rothe, Nimrod Talmon

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.

Original languageAmerican English
Title of host publicationECAI 2023 - 26th European Conference on Artificial Intelligence, including 12th Conference on Prestigious Applications of Intelligent Systems, PAIS 2023 - Proceedings
EditorsKobi Gal, Ann Nowe, Grzegorz J. Nalepa, Roy Fairstein, Roxana Radulescu
PublisherIOS Press BV
Number of pages8
ISBN (Electronic)9781643684369
StatePublished - 28 Sep 2023
Event26th European Conference on Artificial Intelligence, ECAI 2023 - Krakow, Poland
Duration: 30 Sep 20234 Oct 2023

Publication series

NameFrontiers in Artificial Intelligence and Applications


Conference26th European Conference on Artificial Intelligence, ECAI 2023

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence


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