Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Dynamic Programming for Computing Power Indices for Weighted Voting Games with Precoalitions

Version 1 : Received: 23 November 2021 / Approved: 25 November 2021 / Online: 25 November 2021 (08:15:34 CET)

How to cite: Staudacher, J.; Wagner, F.; Filipp, J. Dynamic Programming for Computing Power Indices for Weighted Voting Games with Precoalitions. Preprints 2021, 2021110462 (doi: 10.20944/preprints202111.0462.v1). Staudacher, J.; Wagner, F.; Filipp, J. Dynamic Programming for Computing Power Indices for Weighted Voting Games with Precoalitions. Preprints 2021, 2021110462 (doi: 10.20944/preprints202111.0462.v1).

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

SOCIAL SCIENCES, Econometrics & Statistics

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