Rules of encounter: designing conventions for automated negotiation among computers
Rules of encounter: designing conventions for automated negotiation among computers
The algorithm design manual
Computationally Manageable Combinational Auctions
Management Science
Coalition structure generation with worst case guarantees
Artificial Intelligence
Searching for Optimal Coalition Structures
ICMAS '00 Proceedings of the Fourth International Conference on MultiAgent Systems (ICMAS-2000)
Generating Coalition Structures with Finite Bound from the Optimal Guarantees
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
An improved dynamic programming algorithm for coalition structure generation
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 3
On representing coalitional games with externalities
Proceedings of the 10th ACM conference on Electronic commerce
Anytime optimal coalition structure generation
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 2
Coalition structure generation: dynamic programming meets anytime optimization
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
An anytime algorithm for optimal coalition structure generation
Journal of Artificial Intelligence Research
Near-optimal anytime coalition structure generation
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Methods for task allocation via agent coalition formation
Artificial Intelligence
Coalition structure generation in multi-agent systems with positive and negative externalities
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Coalition structure generation utilizing compact characteristic function representations
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Coalition structure generation in multi-agent systems with mixed externalities
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
Multiagent social learning in large repeated games
Multiagent social learning in large repeated games
Constant factor approximation algorithms for coalition structure generation
Autonomous Agents and Multi-Agent Systems
Multiagent resource allocation in the presence of externalities
CEEMAS'05 Proceedings of the 4th international Central and Eastern European conference on Multi-Agent Systems and Applications
Concise characteristic function representations in coalitional games based on agent types
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Games with ambiguous payoffs and played by ambiguity and regret minimising players
AI'12 Proceedings of the 25th Australasian joint conference on Advances in Artificial Intelligence
Coalitional games via network flows
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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Much of the literature on multi-agent coalition formation has focused on Characteristic Function Games, where the effectiveness of a coalition is not affected by how the other agents are arranged in the system. In contrast, very little attention has been given to the more general class of Partition Function Games, where the emphasis is on how the formation of one coalition could influence the performance of other co-existing coalitions in the system. However, these inter-coalitional dependencies, called externalities from coalition formation, play a crucial role in many real-world multi-agent applications where agents have either conflicting or overlapping goals. Against this background, this paper is the first computational study of coalitional games with externalities in the multi-agent system context. We focus on the Coalition Structure Generation (CSG) problem which involves finding an exhaustive and disjoint division of the agents into coalitions such that the performance of the entire system is optimized. While this problem is already very challenging in the absence of externalities, due to the exponential size of the search space, taking externalities into consideration makes it even more challenging as the size of the input, given n agents, grows from O(2^n) to O(n^n). Our main contribution is the development of the first CSG algorithm for coalitional games with either positive or negative externalities. Specifically, we prove that it is possible to compute upper and lower bounds on the values of any set of disjoint coalitions. Building upon this, we prove that in order to establish a worst-case guarantee on solution quality it is necessary to search a certain set of coalition structures (which we define). We also show how to progressively improve this guarantee with further search. Since there are no previous CSG algorithms for games with externalities, we benchmark our algorithm against other state-of-the-art approaches in games where no externalities are present. Surprisingly, we find that, as far as worst-case guarantees are concerned, our algorithm outperforms the others by orders of magnitude. For instance, to reach a bound of 3 given 24 agents, the number of coalition structures that need to be searched by our algorithm is only 0.0007% of that needed by Sandholm et al. (1999) [1], and 0.5% of that needed by Dang and Jennings (2004) [2]. This is despite the fact that the other algorithms take advantage of the special properties of games with no externalities, while ours does not.