COMPUTING POWER INDICES FOR WEIGHTED VOTING GAMES VIA DYNAMIC PROGRAMMING

被引：6

作者：

Staudacher, Jochen ^{[1
]}

Koczy, Laszlo A. ^{[2
,3
]}

Stach, Izabella ^{[4
]}

Filipp, Jan ^{[1
]}

Kramer, Marcus ^{[1
]}

Noffke, Till ^{[1
]}

Olsson, Linus ^{[1
]}

Pichler, Jonas ^{[1
]}

Singer, Tobias ^{[1
]}

机构：

[1] Hsch Kempten, Fak Informat, Bahnhofstr 61, D-87435 Kempten, Germany

[2] Ctr Econ & Reg Studies, Inst Econ, Toth Kalman U 4, H-1097 Budapest, Hungary

[3] Budapest Univ Technol & Econ, Dept Finance, Magyar Tudosok Korutja 2, H-1112 Budapest, Hungary

[4] AGH Univ Sci & Technol, Al Mickiewicza 30, PL-30059 Krakow, Poland

来源：

OPERATIONS RESEARCH AND DECISIONS | 2021年 / 31卷 / 02期

关键词：

cooperative game theory; power indices; weighted voting games; dynamic programming; minimal winning coalitions;

D O I：

10.37190/ord210206

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

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.

引用

页码：123 / 145

页数：23

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