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
Journal of the ACM (JACM)
Approximate local search in combinatorial optimization
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
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
Adaptive routing with stale information
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Sink Equilibria and Convergence
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Fast convergence to Wardrop equilibria by adaptive sampling methods
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
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
Fast convergence to nearly optimal solutions in potential games
Proceedings of the 9th ACM conference on Electronic commerce
Computing Approximate Nash Equilibria in Network Congestion Games
SIROCCO '08 Proceedings of the 15th international colloquium on Structural Information and Communication Complexity
Efficient coordination mechanisms for unrelated machine scheduling
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
On the Road to $\mathcal{PLS}$-Completeness: 8 Agents in a Singleton Congestion Game
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
On the complexity of nash dynamics and sink equilibria
Proceedings of the 10th ACM conference on Electronic commerce
Concurrent imitation dynamics in congestion games
Proceedings of the 28th ACM symposium on Principles of distributed computing
Congestion games: equilibria, convergence and complexity
GameNets'09 Proceedings of the First ICST international conference on Game Theory for Networks
Nash Dynamics in Constant Player and Bounded Jump Congestion Games
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
Performances of One-Round Walks in Linear Congestion Games
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
On Best Response Dynamics in Weighted Congestion Games with Polynomial Delays
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Approximate Pure Nash Equilibria via Lovász Local Lemma
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
The Impact of Social Ignorance on Weighted Congestion Games
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Nash Dynamics in Congestion Games with Similar Resources
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Approximating pure nash equilibrium in cut, party affiliation, and satisfiability games
Proceedings of the 11th ACM conference on Electronic commerce
On the equilibria of alternating move games
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Local search: simple, successful, but sometimes sluggish
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Computing pure Nash and strong equilibria in bottleneck congestion games
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
The complexity of equilibria in cost sharing games
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Distributed selfish load balancing on networks
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The complexity of approximate nash equilibrium in congestion games with negative delays
WINE'11 Proceedings of the 7th international conference on Internet and Network Economics
Convergence and approximation in potential games
Theoretical Computer Science
Proceedings of the 13th ACM Conference on Electronic Commerce
The price of anarchy in games of incomplete information
Proceedings of the 13th ACM Conference on Electronic Commerce
The speed of convergence in congestion games under best-response dynamics
ACM Transactions on Algorithms (TALG)
Dynamics of profit-sharing games
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Survey: Equilibria, fixed points, and complexity classes
Computer Science Review
Computing approximate pure Nash equilibria in congestion games
ACM SIGecom Exchanges
On the impact of fair best response dynamics
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
A theoretical examination of practical game playing: lookahead search
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
NP-hardness of pure Nash equilibrium in Scheduling and Network Design Games
Theoretical Computer Science
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The complexity of computing pure Nash equilibria in congestion games was recently shown to be PLS-complete. In this paper, we therefore study the complexity of computing approximate equilibria in congestion games. An alpha-approximate equilibrium, for α 1, is a state of the game in which none of the players can make an α-greedy step, i.e., an unilateral strategy change that decreases the player's cost by a factor of at least α. Our main result shows that finding an α-approximate equilibrium of a given congestion game is sc PLS-complete, for any polynomial-time computable α 1. Our analysis is based on a gap introducing PLS-reduction from FLIP, i.e., the problem of finding a local optimum of a function encoded by an arbitrary circuit. As this reduction is tight it additionally implies that computing an α-approximate equilibrium reachable from a given initial state by a sequence of α-greedy steps is PSPACE-complete. Our results are in sharp contrast to a recent result showing that every local search problem in PLS admits a fully polynomial time approximation scheme. In addition, we show that there exist congestion games with states such that any sequence of α-greedy steps leading from one of these states to an α-approximate Nash equilibrium has exponential length, even if the delay functions satisfy a bounded-jump condition. This result shows that a recent result about polynomial time convergence for α-greedy steps in congestion games satisfying the bounded-jump condition is restricted to symmetric games only.