On the complexity of cooperative solution concepts
Mathematics of Operations Research
Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Marginal contribution nets: a compact representation scheme for coalitional games
Proceedings of the 6th ACM conference on Electronic commerce
Complexity of constructing solutions in the core based on synergies among coalitions
Artificial Intelligence
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
Proceedings of The 8th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
Constrained coalitional games: formal framework, properties, and complexity results
Proceedings of The 8th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
Local Search Algorithms for Core Checking in Hedonic Coalition Games
ICCCI '09 Proceedings of the 1st International Conference on Computational Collective Intelligence. Semantic Web, Social Networks and Multiagent Systems
The Cost of Stability in Coalitional Games
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
Stochastic local search for core membership checking in hedonic games
Transactions on computational collective intelligence I
Core non-emptiness checking in hedonic games via difference logic
KES-AMSTA'10 Proceedings of the 4th KES international conference on Agent and multi-agent systems: technologies and applications, Part I
Non-transferable utility coalitional games via mixed-integer linear constraints
Journal of Artificial Intelligence Research
On the complexity of core, kernel, and bargaining set
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
Subsidies, stability, and restricted cooperation in coalitional games
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Computing cooperative solution concepts in coalitional skill games
Artificial Intelligence
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This paper characterizes the complexity of the core in coalitional games. There are different proposals for representing coalitional games in a compact way, where the worths of coalitions may be computed in polynomial time. In all those frameworks, it was shown that core non-emptiness is a co-NP-hard problem. However, for the most general of them, it was left as an open problem whether it belongs to co-NP or it actually is an harder problem. We solve this open problem in a positive way; indeed, we are able to show that, for the case of transferable payoffs, the problem belongs to co-NP for any compact representation of the game where the worths of coalitions may be computed in polynomial time (also, non-deterministic polynomial time), encompassing all previous proposals of this kind. This is proved by showing that games with empty cores have small infeasibility certificates. The picture is completed by looking at coalitional games with non-transferable payoffs. We propose a compact representation based on marginal contribution nets. Also in this case, we are able to settle the precise complexity of core non-emptiness, which turns out to be Σ2p-complete.