Power and stability in connectivity games

Yoram Bachrach, Jeffrey S. Rosenschein, Ely Porat

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

25 Scopus citations

Abstract

We consider computational aspects of a game theoretic approach to network reliability. Consider a network where failure of one node may disrupt communication between two other nodes. We model this network as a simple coalitional game, called the vertex Connectivity Game (CG). In this game, each agent owns a vertex, and controls all the edges going to and from that vertex. A coalition of agents wins if it fully connects a certain subset of vertices in the graph, called the primary vertices. We show that power indices, which express an agent's ability to affect the outcome of the vertex connectivity game, can be used to identify significant possible points of failure in the communication network, and can thus be used to increase network reliability. We show that in general graphs, calculating the Banzhaf power index is #P-complete, but suggest a polynomial algorithm for calculating this index in trees. We also show a. polynomial algorithm for computing the core of a CG, which allows a stable division of payments to coalition agents.

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)
Pages981-988
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

  • Computational complexity
  • Network Reliability
  • Power indices

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