Forming coalitions in the face of uncertain rewards
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
On the complexity of cooperative solution concepts
Mathematics of Operations Research
Coalition, cryptography, and stability: mechanisms for coalition formation in task oriented domains
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
Coalitions among computationally bounded agents
Artificial Intelligence - Special issue on economic principles of multi-agent systems
On the complexity of testing membership in the core of min-cost spanning tree games
International Journal of Game Theory
Methods for task allocation via agent coalition formation
Artificial Intelligence
Anytime coalition structure generation: an average case study
Proceedings of the third annual conference on Autonomous Agents
Combinatorial optimization games
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Coalition structure generation with worst case guarantees
Artificial Intelligence
Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
On the core of the multicommodity flow game
Proceedings of the 4th ACM conference on Electronic commerce
Group Strategyproof Mechanisms via Primal-Dual Algorithms
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Cooperative facility location games
Journal of Algorithms - Special issue: SODA 2000
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
A kernel-oriented model for coalition-formation in general environments: implementation and results
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Coalition formation under uncertainty: bargaining equilibria and the Bayesian core stability concept
Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems
A linear approximation method for the Shapley value
Artificial Intelligence
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
Reasoning about coalitional games
Artificial Intelligence
Boolean combinations of weighted voting games
Proceedings of The 8th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
Easy and hard coalition resource game formation problems: a parameterized complexity analysis
Proceedings of The 8th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
Computational complexity of weighted threshold games
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Infeasibility certificates and the complexity of the core in coalitional games
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
On the complexity of compact coalitional games
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
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Coalition formation is a key problem in automated negotiation among self-interested agents, and other multiagent applications. A coalition of agents can sometimes accomplish things that the individual agents cannot, or can accomplish them more efficiently. Motivating the agents to abide by a solution requires careful analysis: only some of the solutions are stable in the sense that no group of agents is motivated to break off and form a new coalition. This constraint has been studied extensively in cooperative game theory: the set of solutions that satisfy it is known as the core. The computational questions around the core have received less attention. When it comes to coalition formation among software agents (that represent real-world parties), these questions become increasingly explicit.In this paper we define a concise, natural, general representation for games in characteristic form that relies on superadditivity. In our representation, individual agents' values are given as well as values for those coalitions that introduce synergies. We show that this representation allows for efficient checking of whether a given outcome is in the core. We then show that determining whether the core is nonempty is NP-complete both with and without transferable utility. We demonstrate that what makes the problem hard in both cases is determining the collaborative possibilities (the set of outcomes possible for the grand coalition); we do so by showing that if these are given, the problem becomes solvable in time polynomial in the size of the representation in both cases. However, we then demonstrate that for a hybrid version of the problem, where utility transfer is possible only within the grand coalition, the problem remains NP-complete even when the collaborative possibilities are given. Finally, we show that for convex characteristic functions, a solution in the core can be computed efficiently (in O(nl2) time, where n is the number of agents and l is the number of synergies), even when the collaborative possibilities are not given in advance.