Inefficiency of Nash equilibria
Mathematics of Operations Research
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Selfish traffic allocation for server farms
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
The price of anarchy is independent of the network topology
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Tight bounds for worst-case equilibria
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
How much can taxes help selfish routing?
Proceedings of the 4th ACM conference on Electronic commerce
Pricing network edges for heterogeneous selfish users
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Load balancing in the L/sub p/ norm
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Designing Networks for Selfish Users is Hard
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Selfish load balancing and atomic congestion games
Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
The price of anarchy of finite congestion games
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Selfish routing with atomic players
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
The price of anarchy of finite congestion games
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Sink Equilibria and Convergence
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
ACM SIGACT News
The effect of collusion in congestion games
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Network design with weighted players
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
The price of anarchy for polynomial social cost
Theoretical Computer Science
Convergence time to Nash equilibrium in load balancing
ACM Transactions on Algorithms (TALG)
Taxes for linear atomic congestion games
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Greedy distributed optimization of multi-commodity flows
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Convergence to approximate Nash equilibria in congestion games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
The effectiveness of Stackelberg strategies and tolls for network congestion games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Routing games with an unknown set of active players
Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems
Better bounds for online load balancing on unrelated machines
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Regret minimization and the price of total anarchy
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Atomic congestion games among coalitions
ACM Transactions on Algorithms (TALG)
Fast convergence to nearly optimal solutions in potential games
Proceedings of the 9th ACM conference on Electronic commerce
Scheduling to maximize participation
Theoretical Computer Science
A new model for selfish routing
Theoretical Computer Science
Nash equilibria in discrete routing games with convex latency functions
Journal of Computer and System Sciences
The Influence of Link Restrictions on (Random) Selfish Routing
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Congestion Games with Linearly Independent Paths: Convergence Time and Price of Anarchy
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Atomic Congestion Games: Fast, Myopic and Concurrent
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
The Local and Global Price of Anarchy of Graphical Games
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Efficient coordination mechanisms for unrelated machine scheduling
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Improving the Efficiency of Load Balancing Games through Taxes
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Malicious Bayesian Congestion Games
Approximation and Online Algorithms
Stackelberg Strategies and Collusion in Network Games with Splittable Flow
Approximation and Online Algorithms
Intrinsic robustness of the price of anarchy
Proceedings of the forty-first annual ACM symposium on Theory of computing
Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools
Management of Variable Data Streams in Networks
Algorithmics of Large and Complex Networks
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Atomic routing games on maximum congestion
Theoretical Computer Science
Strong and Pareto Price of Anarchy in Congestion Games
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Concurrent imitation dynamics in congestion games
Proceedings of the 28th ACM symposium on Principles of distributed computing
How hard is it to find extreme Nash equilibria in network congestion games?
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The Impact of Oligopolistic Competition in Networks
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How to find Nash equilibria with extreme total latency in network congestion games?
GameNets'09 Proceedings of the First ICST international conference on Game Theory for Networks
Performances of One-Round Walks in Linear Congestion Games
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
On Best Response Dynamics in Weighted Congestion Games with Polynomial Delays
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
On the Inefficiency Ratio of Stable Equilibria in Congestion Games
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Mediated Equilibria in Load-Balancing Games
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Non-cooperative facility location and covering games
Theoretical Computer Science
The hardness of selective network design for bottleneck routing games
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Scheduling to maximize participation
TGC'06 Proceedings of the 2nd international conference on Trustworthy global computing
Nonadaptive selfish routing with online demands
CAAN'07 Proceedings of the 4th conference on Combinatorial and algorithmic aspects of networking
Tradeoffs and average-case equilibria in selfish routing
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Stackelberg strategies for atomic congestion games
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Cost-balancing tolls for atomic network congestion games
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Total latency in singleton congestion games
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Tradeoffs and Average-Case Equilibria in Selfish Routing
ACM Transactions on Computation Theory (TOCT)
Taxes for linear atomic congestion games
ACM Transactions on Algorithms (TALG)
On the existence of pure nash equilibria inweighted congestion games
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Weighted congestion games: price of anarchy, universal worst-case examples, and tightness
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
The impact of altruism on the efficiency of atomic congestion games
TGC'10 Proceedings of the 5th international conference on Trustworthly global computing
Partition equilibrium always exists in resource selection games
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
On the inefficiency of equilibria in linear bottleneck congestion games
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
Reducing the maximum latency of selfish ring routing via pairwise cooperations
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
Local and global price of anarchy of graphical games
Theoretical Computer Science
Selfish Traffic Allocation for Server Farms
SIAM Journal on Computing
Routing (un-) splittable flow in games with player-specific affine latency functions
ACM Transactions on Algorithms (TALG)
Optimal cost sharing protocols for scheduling games
Proceedings of the 12th ACM conference on Electronic commerce
Inner product spaces for MinSum coordination mechanisms
Proceedings of the forty-third annual ACM symposium on Theory of computing
Congestion games with failures
Discrete Applied Mathematics
Restoring pure equilibria to weighted congestion games
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Social context congestion games
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
Efficiency of restricted tolls in non-atomic network routing games
SAGT'11 Proceedings of the 4th international conference on Algorithmic game theory
Exact Price of Anarchy for Polynomial Congestion Games
SIAM Journal on Computing
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
Selfish service installation in networks
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
Price of anarchy for polynomial wardrop games
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
Exact price of anarchy for polynomial congestion games
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Convergence and approximation in potential games
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Nash equilibria, the price of anarchy and the fully mixed nash equilibrium conjecture
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
On the price of anarchy and stability of correlated equilibria of linear congestion games,,
ESA'05 Proceedings of the 13th annual European conference on Algorithms
The hardness of network design for unsplittable flow with selfish users
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Symmetry in network congestion games: pure equilibria and anarchy cost
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Atomic selfish routing in networks: a survey
WINE'05 Proceedings of the First international conference on Internet and Network Economics
SOFSEM'06 Proceedings of the 32nd conference on Current Trends in Theory and Practice of Computer Science
Tight bounds for selfish and greedy load balancing
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Routing (un-) splittable flow in games with player-specific linear latency functions
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Network games with atomic players
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Atomic congestion games among coalitions
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
On the price of stability for designing undirected networks with fair cost allocations
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
On the price of stability for undirected network design
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
The price of collusion in series-parallel networks
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
WINE'11 Proceedings of the 7th international conference on Internet and Network Economics
Efficiency analysis of load balancing games with and without activation costs
Journal of Scheduling
Intrinsic robustness of the price of anarchy
Communications of the ACM
Convergence and approximation in potential games
Theoretical Computer Science
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)
The equivalence of uniform and Shapley value-based cost allocations in a specific game
Operations Research Letters
Pairwise cooperations in selfish ring routing for minimax linear latency
Theoretical Computer Science
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)
On the Existence of Pure Nash Equilibria in Weighted Congestion Games
Mathematics of Operations Research
Contention issues in congestion games
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
On bidimensional congestion games
SIROCCO'12 Proceedings of the 19th international conference on Structural Information and Communication Complexity
On the impact of fair best response dynamics
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Probabilistic techniques in algorithmic game theory
SAGA'07 Proceedings of the 4th international conference on Stochastic Algorithms: foundations and applications
Strong price of anarchy for machine load balancing
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Selfishness level of strategic games
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
A theoretical examination of practical game playing: lookahead search
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
The price of anarchy for selfish ring routing is two
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
Optimal Cost Sharing for Resource Selection Games
Mathematics of Operations Research
On a generalized Cournot oligopolistic competition game
Journal of Global Optimization
Price of stability in polynomial congestion games
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
Social context congestion games
Theoretical Computer Science
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The essence of the routing problem in real networks is that the traffic demand from a source to destination must be satisfied by choosing a single path between source and destination. The splittable version of this problem is when demand can be satisfied by many paths, namely a flow from source to destination. The unsplittable, or discrete version of the problem is more realistic yet is more complex from the algorithmic point of view; in some settings optimizing such unsplittable traffic flow is computationally intractable.In this paper, we assume this more realistic unsplittable model, and investigate the "price of anarchy", or deterioration of network performance measured in total traffic latency under the selfish user behavior. We show that for linear edge latency functions the price of anarchy is exactly $2.618 for weighted demand and exactly $2.5 for unweighted demand. These results are easily extended to (weighted or unweighted) atomic "congestion games", where paths are replaced by general subsets. We also show that for polynomials of degree d edge latency functions the price of anarchy is dδ(d). Our results hold also for mixed strategies.Previous results of Roughgarden and Tardos showed that for linear edge latency functions the price of anarchy is exactly 4/3 under the assumption that each user controls only a negligible fraction of the overall traffic (this result also holds for the splittable case). Note that under the assumption of negligible traffic pure and mixed strategies are equivalent and also splittable and unsplittable models are equivalent.