Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
Simple local search problems that are hard to solve
SIAM Journal on Computing
On the complexity of cooperative solution concepts
Mathematics of Operations Research
Introduction to the Theory of Computation
Introduction to the Theory of Computation
Local Search in Combinatorial Optimization
Local Search in Combinatorial Optimization
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Approximate Local Search in Combinatorial Optimization
SIAM Journal on Computing
Marginal contribution nets: a compact representation scheme for coalitional games
Proceedings of the 6th ACM conference on Electronic commerce
Computing the nucleolus of weighted voting games
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Improved equilibria via public service advertising
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Proceedings of The 8th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
Coalitional affinity games and the stability gap
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
On the computational complexity of weighted voting games
Annals of Mathematics and Artificial Intelligence
Approximating pure nash equilibrium in cut, party affiliation, and satisfiability games
Proceedings of the 11th ACM conference on Electronic commerce
Local search: simple, successful, but sometimes sluggish
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Computing stable outcomes in hedonic games
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
Stable partitions in additively separable hedonic games
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
Convergence and approximation in potential games
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
On the power of nodes of degree four in the local max-cut problem
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Dynamics of profit-sharing games
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Existence of stability in hedonic coalition formation games
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
Computing desirable partitions in additively separable hedonic games
Artificial Intelligence
Stable marriage and roommate problems with individual-based stability
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
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We study the computational complexity of finding stable outcomes in hedonic games, which are a class of coalition formation games. We restrict our attention to a nontrivial subclass of such games, which are guaranteed to possess stable outcomes, i.e., the set of symmetric additively-separable hedonic games. These games are specified by an undirected edge-weighted graph: nodes are players, an outcome of the game is a partition of the nodes into coalitions, and the utility of a node is the sum of incident edge weights in the same coalition. We consider several stability requirements defined in the literature. These are based on restricting feasible player deviations, for example, by giving existing coalition members veto power. We extend these restrictions by considering more general forms of preference aggregation for coalition members. In particular, we consider voting schemes to decide if coalition members will allow a player to enter or leave their coalition. For all of the stability requirements we consider, the existence of a stable outcome is guaranteed by a potential function argument, and local improvements will converge to a stable outcome. We provide an almost complete characterization of these games in terms of the tractability of computing such stable outcomes. Our findings comprise positive results in the form of polynomial-time algorithms, and negative (PLS-completeness) results. The negative results extend to more general hedonic games.