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 the parity argument and other inefficient proofs of existence
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
Journal of the ACM (JACM)
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
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
On the Impact of Combinatorial Structure on Congestion Games
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
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 complexity of pure Nash equilibria in player-specific network congestion games
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Convergence and approximation in potential games
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Market sharing games applied to content distribution in ad hoc networks
IEEE Journal on Selected Areas in Communications
Near-Potential Games: Geometry and Dynamics
ACM Transactions on Economics and Computation - Special Issue on Algorithmic Game Theory
Hi-index | 0.00 |
We study the convergence time of Nash dynamics in two classes of congestion games --- constant player congestion games and bounded jump congestion games. It was shown by Ackermann and Skopalik [2] that even 3-player congestion games are PLS-complete. We design an FPTAS for congestion games with constant number of players. In particular, for any *** 0, we establish a stronger result, namely, any sequence of (1 + *** )-greedy improvement steps converges to a (1 + *** )-approximate equilibrium in a number of steps that is polynomial in *** *** 1 and the size of the input. As the number of strategies of a player can be exponential in the size of the input, our FPTAS result assumes that a (1 + *** )-greedy improvement step, if it exists, can be computed in polynomial time. This assumption holds in previously studied models of congestion games, including network congestion games [9] and restricted network congestion games [2]. For bounded jump games, where jumps in the delay functions of resources are bounded by β , we show that there exists a game with an exponentially long sequence of *** -greedy best response steps that does not converge to an *** -approximate equilibrium, for all *** ≤ β o (n /logn ), where n is the number of players and the size of the game is O (n ). So in the worst case, Nash dynamics may fail to converge in polynomial time to such an approximate equilibrium. We also prove the same result for bounded jump network congestion games. In contrast, we observe that it is easy to show that a β 2n -approximate equilibrium is reached in at most n best response steps.