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
A catalog of complexity classes
Handbook of theoretical computer science (vol. A)
Journal of the ACM (JACM)
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Computing equilibria in multi-player games
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
The computational complexity of nash equilibria in concisely represented games
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
The influence of neighbourhood and choice on the complexity of finding pure Nash equilibria
Information Processing Letters
Computing correlated equilibria in multi-player games
Journal of the ACM (JACM)
On the Hardness and Existence of Quasi-Strict Equilibria
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
On the complexity of nash dynamics and sink equilibria
Proceedings of the 10th ACM conference on Electronic commerce
Computing pure Nash equilibria in symmetric action graph games
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Pure Nash equilibria: complete characterization of hard and easy graphical games
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
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Strategic games may exhibit symmetries in a variety of ways. A common aspect, enabling the compact representation of games even when the number of players is unbounded, is that players cannot (or need not) distinguish between the other players. We define four classes of symmetric games by considering two additional properties: identical payoff functions for all players and the ability to distinguish oneself from the other players. Based on these varying notions of symmetry, we investigate the computational complexity of pure Nash equilibria. It turns out that in all four classes of games Nash equilibria can be computed in TC0 when only a constant number of actions is available to each player, a problem that has been shown intractable for other succinct representations of multi-player games. We further show that identical payoff functions make the difference between TC0-completeness and membership in AC0, while a growing number of actions renders the equilibrium problem NP-complete for three of the classes and PLS-complete for the most restricted class for which the existence of a pure Nash equilibrium is guaranteed. Finally, our results extend to wider classes of threshold symmetric games where players are unable to determine the exact number of players playing a certain action.