The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Network flow problems and congestion games: complexity and approximation results
Network flow problems and congestion games: complexity and approximation results
Computing Equilibria in Anonymous Games
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
On the impact of combinatorial structure on congestion games
Journal of the ACM (JACM)
Discretized Multinomial Distributions and Nash Equilibria in Anonymous Games
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Symmetries and the complexity of pure Nash equilibrium
Journal of Computer and System Sciences
Strong and Pareto Price of Anarchy in Congestion Games
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Pure Nash equilibria: hard and easy games
Journal of Artificial Intelligence Research
Strong Nash Equilibria in Games with the Lexicographical Improvement Property
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Computing pure Nash and strong equilibria in bottleneck congestion games
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
Strong and correlated strong equilibria in monotone congestion games
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
On the quality and complexity of pareto equilibria in the job scheduling game
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
NP-hardness of pure Nash equilibrium in Scheduling and Network Design Games
Theoretical Computer Science
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We consider the computational complexity of coalitional solution concepts in scenarios related to load balancing such as anonymous and congestion games. In congestion games, Pareto-optimal Nash and strong equilibria, which are resilient to coalitional deviations, have recently been shown to yield significantly smaller inefficiency. Unfortunately, we show that several problems regarding existence, recognition, and computation of these concepts are hard, even in seemingly special classes of games. In anonymous games with constant number of strategies, we can efficiently recognize a state as Pareto-optimal Nash or strong equilibrium, but deciding existence for a game remains hard. In the case of player-specific singleton congestion games, we show that recognition and computation of both concepts can be done efficiently. In addition, in these games there are always short sequences of coalitional improvement moves to Pareto-optimal Nash and strong equilibria that can be computed efficiently.