Inefficiency of Nash equilibria
Mathematics of Operations Research
Achieving network optima using Stackelberg routing strategies
IEEE/ACM Transactions on Networking (TON)
Journal of the ACM (JACM)
Improved Results for Stackelberg Scheduling Strategies
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Pricing network edges for heterogeneous selfish users
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
The price of anarchy is independent of the network topology
Journal of Computer and System Sciences - STOC 2002
Stackelberg Scheduling Strategies
SIAM Journal on Computing
The maximum latency of selfish routing
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Edge Pricing of Multicommodity Networks for Heterogeneous Selfish Users
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Tolls for Heterogeneous Selfish Users in Multicommodity Networks and Generalized Congestion Games
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Selfish Routing in Capacitated Networks
Mathematics of Operations Research
Selfish Routing and the Price of Anarchy
Selfish Routing and the Price of Anarchy
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
On the severity of Braess's paradox: designing networks for selfish users is hard
Journal of Computer and System Sciences - Special issue on FOCS 2001
Stackelberg thresholds in network routing games or the value of altruism
Proceedings of the 8th ACM conference on Electronic commerce
Congestion games with malicious players
Proceedings of the 8th ACM conference on Electronic commerce
The effectiveness of Stackelberg strategies and tolls for network congestion games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Altruism, selfishness, and spite in traffic routing
Proceedings of the 9th ACM conference on Electronic commerce
The “Price of Anarchy” Under Nonlinear and Asymmetric Costs
Mathematics of Operations Research
Fast, Fair, and Efficient Flows in Networks
Operations Research
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Stackelberg strategies for atomic congestion games
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Braess's paradox, fibonacci numbers, and exponential inapproximability
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
On the inefficiency of equilibria in congestion games
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
The price of optimum in a matching game
SAGT'11 Proceedings of the 4th international conference on Algorithmic game theory
Efficiency of restricted tolls in non-atomic network routing games
SAGT'11 Proceedings of the 4th international conference on Algorithmic game theory
Conflicting Congestion Effects in Resource Allocation Games
Operations Research
The effectiveness of stackelberg strategies and tolls for network congestion games
ACM Transactions on Algorithms (TALG)
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We investigate the impact of Stackelberg routing to reduce the price of anarchy in network routing games. In this setting, an α fraction of the entire demand is first routed centrally according to a predefined Stackelberg strategy and the remaining demand is then routed selfishly by (nonatomic) players. Although several advances have been made recently in proving that Stackelberg routing can, in fact, significantly reduce the price of anarchy for certain network topologies, the central question of whether this holds true in general is still open. We answer this question negatively by constructing a family of single-commodity instances such that every Stackelberg strategy induces a price of anarchy that grows linearly with the size of the network. Moreover, we prove upper bounds on the price of anarchy of the largest-latency-first (LLF) strategy that only depend on the size of the network. Besides other implications, this rules out the possibility to construct constant-size networks to prove an unbounded price of anarchy. In light of this negative result, we consider bicriteria bounds. We develop an efficiently computable Stackelberg strategy that induces a flow whose cost is at most the cost of an optimal flow with respect to demands scaled by a factor of 1 + √1-α. Finally, we analyze the effectiveness of an easy-to-implement Stackelberg strategy, called SCALE. We prove bounds for a general class of latency functions that includes polynomial latency functions as a special case. Our analysis is based on an approach that is simple yet powerful enough to obtain (almost) tight bounds for SCALE in general networks.