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
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
The Price of Stability for Network Design with Fair Cost Allocation
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Fairness and optimality in congestion games
Proceedings of the 6th ACM conference on Electronic commerce
On the Impact of Combinatorial Structure on Congestion Games
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Algorithmic Game Theory
Pure nash equilibria in player-specific and weighted congestion games
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
On the complexity of pure-strategy nash equilibria in congestion and local-effect games
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
The equilibrium existence problem in finite network congestion games
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
Pure Nash equilibria in player-specific and weighted congestion games
Theoretical Computer Science
On the complexity of nash dynamics and sink equilibria
Proceedings of the 10th ACM conference on Electronic commerce
Nash Dynamics in Constant Player and Bounded Jump Congestion Games
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
Local search: simple, successful, but sometimes sluggish
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
On the Existence of Pure Nash Equilibria in Weighted Congestion Games
Mathematics of Operations Research
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Network congestion games with player-specific delay functions do not necessarily possess pure Nash equilibria. We therefore address the computational complexity of the corresponding decision problem, and show that it is NP-complete to decide whether such games possess pure Nash equilibria. This negative result still holds in the case of games with two players only. In contrast, we show that one can decide in polynomial time whether an equilibrium exists if the number of resources is constant. In addition, we introduce a family of player-specific network congestion games which are guaranteed to possess equilibria. In these games players have identical delay functions, however, each player may only use a certain subset of the edges. For this class of games we prove that finding a pure Nash equilibrium is PLS-complete even in the case of three players. Again, in the case of a constant number of edges an equilibrium can be computed in polynomial time. We conclude that the number of resources has a bigger impact on the computation complexity of certain problems related to network congestion games than the number of players.