Issue: 2021/Vol.31/No.2, Pages 123-145

COMPUTING POWER INDICES FOR WEIGHTED VOTING GAMES VIA DYNAMIC PROGRAMMING

Jochen Staudacher, László Á. Kóczy, Izabella Stach, Jan Filipp, Marcus Kramer, Till Noffke, Linuss Olsson, Jonas Pichler, Tobias Singer

Full paper (PDF)    RePEC

Cite as: J. Staudacher, L. Á. Kóczy, I. Stach, J. Filipp, M. Kramer, T. Noffke, L. Olsson, J. Pichler, T. Singer. Computing power indices for weighted voting games via dynamic programming. Operations Research and Decisions 2021: 31(2), 123-145. DOI 10.37190/ord210205

Abstract
We study the efficient computation of power indices for weighted voting games using the paradigm of dynamic programming. We survey the state-of-the-art algorithms for computing the Banzhaf and Shapley–Shubik indices and point out how these approaches carry over to related power indices. Within a unified framework, we present new efficient algorithms for the Public Good index and a recently proposed power index based on minimal winning coalitions of the smallest size, as well as a very first method for computing the Johnston indices for weighted voting games efficiently. We introduce a software package providing fast C++ implementations of all the power indices mentioned in this article, discuss computing times, as well as storage requirements.

Keywords: cooperative game theory, power indices, weighted voting games, dynamic programming, minimal

Received: 1 November 2020    Accepted: 19 April 2021