Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
Optimization, approximation, and complexity classes
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
On total functions, existence theorems and computational complexity
Theoretical Computer Science
Playing large games using simple strategies
Proceedings of the 4th ACM conference on Electronic commerce
Market sharing games applied to content distribution in ad-hoc networks
Proceedings of the 5th ACM international symposium on Mobile ad hoc networking and computing
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
The complexity of computing a Nash equilibrium
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Computing Nash Equilibria: Approximation and Smoothed Complexity
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Approximating nash equilibria using small-support strategies
Proceedings of the 8th ACM conference on Electronic commerce
Progress in approximate nash equilibria
Proceedings of the 8th ACM conference on Electronic commerce
Convergence to approximate Nash equilibria in congestion games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Inapproximability of pure nash equilibria
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Fast convergence to nearly optimal solutions in potential games
Proceedings of the 9th ACM conference on Electronic commerce
On the impact of combinatorial structure on congestion games
Journal of the ACM (JACM)
An optimization approach for approximate Nash equilibria
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
On approximate nash equilibria in network design
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Efficient nash computation in large population games with bounded influence
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
A note on approximate nash equilibria
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
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We extend the study of the complexity of computing an ε -approximate Nash equilibrium in symmetric congestion games from the case of positive delay functions to delays of arbitrary sign. Our results show that with this extension the complexity has a richer structure, and it depends on the exact nature of the signs allowed. We first prove that in symmetric games with increasing delay functions and with α -bounded jump the ε -Nash dynamic converges in polynomial time when all delays are negative, similarly to the case of positive delays. We are able to extend this result to monotone delay functions. We then establish a hardness result for symmetric games with increasing delay functions and with α -bounded jump when the delays can be both positive and negative: in that case computing an ε -approximate Nash equilibrium becomes PLS-complete, even if each delay function is of constant sign or of constant absolute value.