On the complexity of cooperative solution concepts
Mathematics of Operations Research
Introduction to Multiagent Systems
Introduction to Multiagent Systems
On the computational complexity of qualitative coalitional games
Artificial Intelligence
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
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
On the computational complexity of coalitional resource games
Artificial Intelligence
Complexity of constructing solutions in the core based on synergies among coalitions
Artificial Intelligence
Solving coalitional resource games
Artificial Intelligence
Arbitrators in overlapping coalition formation games
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
Complexity of coalition structure generation
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
Concise characteristic function representations in coalitional games based on agent types
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 3
Graph-based coalitional games: an analysis via characteristics
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
PRIMA'11 Proceedings of the 14th international conference on Agents in Principle, Agents in Practice
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
Proof systems and transformation games
Annals of Mathematics and Artificial Intelligence
Fostering Cooperation through Dynamic Coalition Formation and Partner Switching
ACM Transactions on Autonomous and Adaptive Systems (TAAS)
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Coalitions and cooperation are key topics in multi-agent systems (mas). They enable agents to achieve goals that they may not have been able to achieve independently. A range of previous studies have found that many problems in coalitional games tend to be computationally intractable - that is, the computational complexity grows rapidly as a function of the number of participating agents. However, these hardness results generally require that each agent is of a different type. Here, we observe that in many mas settings, while the number of agents may grow, the number of different types of agents remains small. We formally define the notion of agent types in cooperative games. We then re-examine the computational complexity of the different coalition formation problems when assuming that the number of agent types is fixed. We show that most of the previously hard problems become polynomial when the number of agent types is fixed. We consider multiple different game formulations and representations (characteristic function with subadditive utilities, crg, and graphical representations) and several different computational problems (including stability, core-emptiness, and Shapley value).