An axiomatization of the Banzhaf value
International Journal of Game Theory
On the complexity of cooperative solution concepts
Mathematics of Operations Research
An algorithm for finding the nucleolus of assignment games
International Journal of Game Theory
On the complexity of testing membership in the core of min-cost spanning tree games
International Journal of Game Theory
Computing the nucleolus of min-cost spanning tree games is NP-hard
International Journal of Game Theory
NP-completeness for calculating power indices of weighted majority games
Theoretical Computer Science
Reputation and social network analysis in multi-agent systems
Proceedings of the first international joint conference on Autonomous agents and multiagent systems: part 1
Shapley-Shubik and Banzhaf Indices Revisited
Mathematics of Operations Research
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Sharing the cost of multicast transmissions
Journal of Computer and System Sciences - Special issue on Internet algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Complexity of Counting in Sparse, Regular, and Planar Graphs
SIAM Journal on Computing
Two remarks on the power of counting
Proceedings of the 6th GI-Conference on Theoretical Computer Science
Anthill: A Framework for the Development of Agent-Based Peer-to-Peer Systems
ICDCS '02 Proceedings of the 22 nd International Conference on Distributed Computing Systems (ICDCS'02)
Distributed Sensor Networks: A Multiagent Perspective
Distributed Sensor Networks: A Multiagent Perspective
The Advantages of Compromising in Coalition Formation with Incomplete Information
AAMAS '04 Proceedings of the Third International Joint Conference on Autonomous Agents and Multiagent Systems - Volume 2
Multi-attribute coalitional games
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
Note: The complexity of power-index comparison
Theoretical Computer Science
Power in threshold network flow games
Autonomous Agents and Multi-Agent Systems
The cost of stability in weighted voting games
Proceedings of The 8th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
Power Indices in Spanning Connectivity Games
AAIM '09 Proceedings of the 5th International Conference on Algorithmic Aspects in Information and Management
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Overlapping coalition formation for efficient data fusion in multi-sensor networks
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
The Cost of Stability in Network Flow Games
MFCS '09 Proceedings of the 34th International Symposium on Mathematical Foundations of Computer Science 2009
Coalitional games in open anonymous environments
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
Computational complexity of weighted threshold games
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Decentralized control of cooperative systems: categorization and complexity analysis
Journal of Artificial Intelligence Research
Near-optimal anytime coalition structure generation
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
The Cost of Stability in Coalitional Games
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
Approximating power indices: theoretical and empirical analysis
Autonomous Agents and Multi-Agent Systems
A Survey of Game Theory as Applied to Network Security
HICSS '10 Proceedings of the 2010 43rd Hawaii International Conference on System Sciences
Coalition structure generation utilizing compact characteristic function representations
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Agent-based micro-storage management for the Smart Grid
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
Honor among thieves: collusion in multi-unit auctions
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
Proof systems and transformation games
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Minimal subsidies in expense sharing games
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
False-name manipulations in weighted voting games
Journal of Artificial Intelligence Research
A double oracle algorithm for zero-sum security games on graphs
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
Manipulating the quota in weighted voting games
Artificial Intelligence
On the complexity of the core over coalition structures
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Crowd IQ: aggregating opinions to boost performance
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
Cooperative Game Theory: Basic Concepts and Computational Challenges
IEEE Intelligent Systems
Agent failures in totally balanced games and convex games
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
Hi-index | 0.00 |
We consider how selfish agents are likely to share revenues derived from maintaining connectivity between important network servers. We model a network where a failure of one node may disrupt communication between other nodes as a cooperative 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. Power indices measure an agent's ability to affect the outcome of the game. We show that in our domain, such indices can be used to both determine the fair share of the revenues an agent is entitled to, and identify significant possible points of failure affecting the reliability of communication in the network. We show that in general graphs, calculating the Shapley and Banzhaf power indices is #P-complete, but suggest a polynomial algorithm for calculating them in trees. We also investigate finding stable payoff divisions of the revenues in CGs, captured by the game theoretic solution of the core, and its relaxations, the ε-core and least core. We show a polynomial algorithm for computing the core of a CG, but show that testing whether an imputation is in theε-core is coNP-complete. Finally, we show that for trees, it is possible to test for ε-core imputations in polynomial time.