Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/257583 
Year of Publication: 
2022
Citation: 
[Journal:] Games [ISSN:] 2073-4336 [Volume:] 13 [Issue:] 1 [Article No.:] 6 [Publisher:] MDPI [Place:] Basel [Year:] 2022 [Pages:] 1-17
Publisher: 
MDPI, Basel
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.
Subjects: 
Banzhaf index
cooperative game theory
dynamic programming
Owen value
power indices
precoalitions
Shapley value
weighted voting games
JEL: 
C71
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
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