Staudacher, J.; Wagner, F.; Filipp, J. Dynamic Programming for Computing Power Indices for Weighted Voting Games with Precoalitions. Games2022, 13, 6.
Staudacher, J.; Wagner, F.; Filipp, J. Dynamic Programming for Computing Power Indices for Weighted Voting Games with Precoalitions. Games 2022, 13, 6.
Staudacher, J.; Wagner, F.; Filipp, J. Dynamic Programming for Computing Power Indices for Weighted Voting Games with Precoalitions. Games2022, 13, 6.
Staudacher, J.; Wagner, F.; Filipp, J. Dynamic Programming for Computing Power Indices for Weighted Voting Games with Precoalitions. Games 2022, 13, 6.
Abstract
We study the efficient computation of power indices for weighted voting games with precoalitions amongst subsets of players (reflecting, e.g., ideological proximity) using the paradigm of dynamic programming. Starting from the state-of-the-art algorithms for computing the Banzhaf and Shapley-Shubik indices for weighted voting games we present a framework for fast algorithms for the three most common power indices with precoalitions, i.e. the Owen index, the Banzhaf-Owen index and the Symmetric Coalitional Banzhaf index, and point out why our new algorithms are applicable for large numbers of players. We discuss implementations of our algorithms for the three power indices with precoalitions in C++ and review computing times as well as storage requirements.
Keywords
cooperative game theory; power indices; weighted voting games; dynamic programming; precoalitions; Shapley value; Owen value; Banzhaf index.
Subject
Business, Economics and Management, Econometrics and Statistics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
