Approximating power indices

Yoram Bachrach, Evangelos Markakis, Ariel D. Procaccia, Jeffrey S. Rosenschein, Amin Saberi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

28 Scopus citations

Abstract

Many multiagent domains where cooperation among agents is crucial to achieving a common goal can be modeled as coalitional games. However, in many of these domains, agents are unequal in their power to affect the outcome of the game. Prior research on weighted voting games has explored power indices, which reflect how much "real power" a voter has. Although primarily used for voting games, these indices can be applied to any simple coalitional game. Computing these indices is known to be computationally hard in various domains, so one must sometimes resort to approximate methods for calculating them. We suggest and analyze randomized methods to approximate power indices such as the Banzhaf power index and the Shapley-Shubik power index. Our approximation algorithms do not depend on a specific representation of the game, so they can be used in any simple coalitional game. Our methods are based on testing the game's value for several sample coalitions. We also show that no approximation algorithm can do much better for general coalitional games, by providing lower bounds for both deterministic and randomized algorithms for calculating power indices.

Original languageAmerican English
Title of host publication7th International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS 2008
PublisherInternational Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)
Pages925-932
Number of pages8
ISBN (Print)9781605604701
StatePublished - 2008
Event7th International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS 2008 - Estoril, Portugal
Duration: 12 May 200816 May 2008

Publication series

NameProceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS
Volume2
ISSN (Print)1548-8403
ISSN (Electronic)1558-2914

Conference

Conference7th International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS 2008
Country/TerritoryPortugal
CityEstoril
Period12/05/0816/05/08

Keywords

  • Power indices
  • Randomized algorithms

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