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

共 50 条

[1] Dynamic Programming for Computing Power Indices for Weighted Voting Games with Precoalitions
Staudacher, Jochen
Wagner, Felix
Filipp, Jan
GAMES, 2022, 13 (01):
[2] Faster algorithms for computing power indices in weighted voting games
Klinz, B
Woeginger, GJ
MATHEMATICAL SOCIAL SCIENCES, 2005, 49 (01) : 111 - 116
[3] Dynamic programming algorithms for computing power indices in weighted multi-tier games
Wilms, Ingo
Wilms, Ingo
MATHEMATICAL SOCIAL SCIENCES, 2020, 108 : 175 - 192
[4] Computing power indices for large voting games
Leech, D
MANAGEMENT SCIENCE, 2003, 49 (06) : 831 - 838
[5] Computing power indices in weighted multiple majority games
Algaba, E
Bilbao, JM
Fernandez-García, JR
López, JJ
MATHEMATICAL SOCIAL SCIENCES, 2003, 46 (01) : 63 - 80
[6] A Pseudo-Polynomial Algorithm for Computing Power Indices in Graph-Restricted Weighted Voting Games
Skibski, Oskar
Michalak, Tomasz P.
Sakurai, Yuko
Yokoo, Makoto
PROCEEDINGS OF THE TWENTY-FOURTH INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE (IJCAI), 2015, : 631 - 637
[7] ANNEXATIONS AND MERGING IN WEIGHTED VOTING GAMES The Extent of Susceptibility of Power Indices
Lasisi, Ramoni O.
Allan, Vicki H.
ICAART 2011: PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON AGENTS AND ARTIFICIAL INTELLIGENCE, VOL 2, 2011, : 124 - 133
[8] Merging and Splitting for Power Indices in Weighted Voting Games and Network Flow Games on Hypergraphs
Rey, Anja
Rothe, Joerg
STAIRS 2010: PROCEEDINGS OF THE FIFTH STARTING AI RESEARCHERS' SYMPOSIUM, 2011, 222 : 277 - 289
[9] Computing the nucleolus of weighted voting games
Elkind, Edith
Pasechnik, Dmitrii
PROCEEDINGS OF THE TWENTIETH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS, 2009, : 327 - +
[10] An approach via generating functions to compute power indices of multiple weighted voting games with incompatible players
Francisco Neto, Antonio
Fonseca, Carolina Rodrigues
ANNALS OF OPERATIONS RESEARCH, 2019, 279 (1-2) : 221 - 249

← 1 2 3 4 5 →