Efficient algorithms for finding maximum matching in graphs
ACM Computing Surveys (CSUR)
The complexity of optimization problems
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
NP-completeness of some problems concerning voting games
International Journal of Game Theory
Easy problems for tree-decomposable graphs
Journal of Algorithms
A catalog of complexity classes
Handbook of theoretical computer science (vol. A)
Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
The complexity of stochastic games
Information and Computation
On the complexity of cooperative solution concepts
Mathematics of Operations Research
A taxonomy of complexity classes of functions
Journal of Computer and System Sciences
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
On the complexity of testing membership in the core of min-cost spanning tree games
International Journal of Game Theory
Algorithmic Aspects of the Core of Combinatorial Optimization Games
Mathematics of Operations Research
Graph ramsey theory and the polynomial hierarchy
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Constraint Processing
Matching games: the least core and the nucleolus
Mathematics of Operations Research
Cooperative facility location games
Journal of Algorithms - Special issue: SODA 2000
Traveling salesman games with the Monge property
Discrete Applied Mathematics
Marginal contribution nets: a compact representation scheme for coalitional games
Proceedings of the 6th ACM conference on Electronic commerce
Computing pure nash equilibria in graphical games via markov random fields
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Multi-attribute coalitional games
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Algorithms
Power and stability in connectivity games
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
Reasoning about coalitional games
Artificial Intelligence
Computing the nucleolus of weighted voting games
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Infeasibility certificates and the complexity of the core in coalitional games
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Complexity of constructing solutions in the core based on synergies among coalitions
Artificial Intelligence
On the complexity of compact coalitional games
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
The Cost of Stability in Coalitional Games
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
On the computational complexity of weighted voting games
Annals of Mathematics and Artificial Intelligence
On the power of structural decompositions of graph-based representations of constraint problems
Artificial Intelligence
Coalition structure generation utilizing compact characteristic function representations
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Exploiting multi-interface networks: Connectivity and Cheapest Paths
Wireless Networks
Monotone cooperative games and their threshold versions
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
Non-transferable utility coalitional games via mixed-integer linear constraints
Journal of Artificial Intelligence Research
The Computer Journal
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
Survey: Equilibria, fixed points, and complexity classes
Computer Science Review
Coalitional stability in structured environments
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
Overlapping coalition formation games: charting the tractability frontier
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
Handling negative value rules in MC-net-based coalition structure generation
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
Complementary cooperation, minimal winning coalitions, and power indices
Theoretical Computer Science
Hi-index | 0.00 |
Coalitional games model scenarios where players can collaborate by forming coalitions in order to obtain higher worths than by acting in isolation. A fundamental issue of coalitional games is to single out the most desirable outcomes in terms of worth distributions, usually called solution concepts. Since decisions taken by realistic players cannot involve unbounded resources, recent computer science literature advocated the importance of assessing the complexity of computing with solution concepts. In this context, the paper provides a complete picture of the complexity issues arising with three prominent solution concepts for coalitional games with transferable utility, namely, the core, the kernel, and the bargaining set, whenever the game worth-function is represented in some reasonably compact form. The starting points of the investigation are the settings of graph games and of marginal contribution nets, where the worth of any coalition can be computed in polynomial time in the size of the game encoding and for which various open questions were stated in the literature. The paper answers these questions and, in addition, provides new insights on succinctly specified games, by characterizing the computational complexity of the core, the kernel, and the bargaining set in relevant generalizations and specializations of the two settings. Concerning the generalizations, the paper shows that dealing with arbitrary polynomial-time computable worth functions-no matter of the specific game encoding being considered-does not provide any additional source of complexity compared to graph games and marginal contribution nets. Instead, only for the core, a slight increase in complexity is exhibited for classes of games whose worth functions encode NP-hard optimization problems, as in the case of certain combinatorial games. As for specializations, the paper illustrates various tractability results on classes of bounded treewidth graph games and marginal contribution networks.