TY - GEN

T1 - Power and stability in connectivity games

AU - Bachrach, Yoram

AU - Rosenschein, Jeffrey S.

AU - Porat, Ely

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

KW - Computational complexity

KW - Network Reliability

KW - Power indices

UR - http://www.scopus.com/inward/record.url?scp=84899939291&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84899939291

SN - 9781605604701

T3 - Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS

SP - 981

EP - 988

BT - 7th International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS 2008

PB - International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)

T2 - 7th International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS 2008

Y2 - 12 May 2008 through 16 May 2008

ER -