Complexity of comparison of influence of players in simple games

Understand

Coalitional voting games appear in different forms in multi-agent systems, social choice and threshold logic.

• In this paper, the complexity of comparison of influence between players in coalitional voting games is characterized.
• The possible representations of simple games considered are simple games represented by winning coalitions, minimal winning coalitions, weighted voting game or a multiple weighted voting game.
• The influence of players is gauged from the viewpoint of basic player types, desirability relations and classical power indices such as Shapley-Shubik index, Banzhaf index, Holler index, Deegan-Packel index and Chow parameters.