On total functions, existence theorems and computational complexity
Theoretical Computer Science
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
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
On the complexity of equilibria
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
Algorithms, Games, and the Internet
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Pure Nash equilibria: hard and easy games
Proceedings of the 9th conference on Theoretical aspects of rationality and knowledge
Computing equilibria for congestion games with (im)perfect information
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Computing Nash equilibria for scheduling on restricted parallel links
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
How to route and tax selfish unsplittable traffic
Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
Bounds for the convergence rate of randomized local search in a multiplayer load-balancing game
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Coordination mechanisms for congestion games
ACM SIGACT News
Computing correlated equilibria in multi-player games
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Fast convergence of selfish rerouting
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Selfish routing with incomplete information
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
On nash equilibria for a network creation game
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Distributed selfish load balancing
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Structure and complexity of extreme Nash equilibria
Theoretical Computer Science - Game theory meets theoretical computer science
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
Tight bounds for worst-case equilibria
ACM Transactions on Algorithms (TALG)
Computing equilibria for a service provider game with (Im)perfect information
ACM Transactions on Algorithms (TALG)
Algorithms for pure Nash equilibria in weighted congestion games
Journal of Experimental Algorithmics (JEA)
Utilitarian resource assignment
Journal of Discrete Algorithms
The price of anarchy for polynomial social cost
Theoretical Computer Science
On the structure and complexity of worst-case equilibria
Theoretical Computer Science
On the convergence of multicast games in directed networks
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
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
Routing selfish unsplittable traffic
ACM Transactions on Algorithms (TALG)
Mixed Nash equilibria in selfish routing problems with dynamic constraints
Theoretical Computer Science
Computing correlated equilibria in multi-player games
Journal of the ACM (JACM)
Atomic congestion games among coalitions
ACM Transactions on Algorithms (TALG)
Scheduling to maximize participation
Theoretical Computer Science
Deterministic monotone algorithms for scheduling on related machines
Theoretical Computer Science
A new model for selfish routing
Theoretical Computer Science
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Nash equilibria in discrete routing games with convex latency functions
Journal of Computer and System Sciences
The Price of Anarchy on Uniformly Related Machines Revisited
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Approximate Strong Equilibrium in Job Scheduling Games
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Facets of the Fully Mixed Nash Equilibrium Conjecture
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Theoretical Computer Science
How Hard Is It to Find Extreme Nash Equilibria in Network Congestion Games?
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
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
Conflicting Congestion Effects in Resource Allocation Games
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Worst-Case Nash Equilibria in Restricted Routing
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Pure Nash equilibria in player-specific and weighted congestion games
Theoretical Computer Science
Fair cost-sharing methods for scheduling jobs on parallel machines
Journal of Discrete Algorithms
Quality of routing congestion games in wireless sensor networks
Proceedings of the 4th Annual International Conference on Wireless Internet
Atomic routing games on maximum congestion
Theoretical Computer Science
On the complexity of constrained Nash equilibria in graphical games
Theoretical Computer Science
Pure Nash equilibria: hard and easy games
Journal of Artificial Intelligence Research
How hard is it to find extreme Nash equilibria in network congestion games?
Theoretical Computer Science
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
On Best Response Dynamics in Weighted Congestion Games with Polynomial Delays
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Maximizing the Minimum Load: The Cost of Selfishness
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Strong Nash Equilibria in Games with the Lexicographical Improvement Property
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
A dynamic approach for load balancing
Proceedings of the Fourth International ICST Conference on Performance Evaluation Methodologies and Tools
Evolutionary equilibrium in Bayesian routing games: Specialization and niche formation
Theoretical Computer Science
Approximate strong equilibrium in job scheduling games
Journal of Artificial Intelligence Research
Convergence time to Nash equilibria
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Nashification and the coordination ratio for a selfish routing game
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Scheduling to maximize participation
TGC'06 Proceedings of the 2nd international conference on Trustworthy global computing
A unified approach to congestion games and two-sided markets
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
A network creation game with nonuniform interests
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
Managing end-user preferences in the smart grid
Proceedings of the 1st International Conference on Energy-Efficient Computing and Networking
Taxes for linear atomic congestion games
ACM Transactions on Algorithms (TALG)
Local search: simple, successful, but sometimes sluggish
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
On the packing of selfish items
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
Network uncertainty in selfish routing
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
Extending the notion of rationality of selfish agents: Second Order Nash equilibria
Theoretical Computer Science
Optimal cost sharing protocols for scheduling games
Proceedings of the 12th ACM conference on Electronic commerce
Equilibria problems on games: Complexity versus succinctness
Journal of Computer and System Sciences
Atomic routing games on maximum congestion
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
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
Symmetry in network congestion games: pure equilibria and anarchy cost
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
On the structure and complexity of worst-case equilibria
WINE'05 Proceedings of the First international conference on Internet and Network Economics
A simple graph-theoretic model for selfish restricted scheduling
WINE'05 Proceedings of the First international conference on Internet and Network Economics
A cost mechanism for fair pricing of resource usage
WINE'05 Proceedings of the First international conference on Internet and Network Economics
Game-Theoretic analysis of internet switching with selfish users
WINE'05 Proceedings of the First international conference on Internet and Network Economics
Atomic selfish routing in networks: a survey
WINE'05 Proceedings of the First international conference on Internet and Network Economics
Nash equilibria in all-optical networks
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
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Tight bounds for selfish and greedy load balancing
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
The price of approximate stability for scheduling selfish tasks on two links
Euro-Par'06 Proceedings of the 12th international conference on Parallel Processing
Multicast transmissions in non-cooperative networks with a limited number of selfish moves
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Pure nash equilibria in games with a large number of actions
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
On nash equilibria in non-cooperative all-optical networks
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
On nash equilibria for multicast transmissions in ad-hoc wireless networks
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Congestion games, load balancing, and price of anarchy
CAAN'04 Proceedings of the First international conference on Combinatorial and Algorithmic Aspects of Networking
Experimental results for stackelberg scheduling strategies
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
Efficient convergence to pure nash equilibria in weighted network congestion games
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
Demand allocation games: integrating discrete and continuous strategy spaces
WINE'11 Proceedings of the 7th international conference on Internet and Network Economics
Game-theoretic analysis of Internet switching with selfish users
Theoretical Computer Science
Conflicting Congestion Effects in Resource Allocation Games
Operations Research
On the Existence of Pure Nash Equilibria in Weighted Congestion Games
Mathematics of Operations Research
Selfish load balancing under partial knowledge
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Extending the notion of rationality of selfish agents: second order Nash equilibria
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Congestion games with player-specific constants
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Congestion games with capacitated resources
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
Convergence of best-response dynamics in games with conflicting congestion effects
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
Optimal Cost Sharing for Resource Selection Games
Mathematics of Operations Research
Non-cooperative games on multidimensional resource allocation
Future Generation Computer Systems
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In this work, we study the combinatorial structure and the computational complexity of Nash equilibria for a certain game that models selfish routing over a network consisting of m parallel links. We assume a collection of n users, each employing a mixed strategy, which is a probability distribution over links, to control the routing of its own assigned traffic. In a Nash equilibrium, each user selfishly routes its traffic on those links that minimize its expected latency cost, given the network congestion caused by the other users. The social cost of a Nash equilibrium is the expectation, over all random choices of the users, of the maximum, over all links, latency through a link.We embark on a systematic study of several algorithmic problems related to the computation of Nash equilibria for the selfish routing game we consider. In a nutshell, these problems relate to deciding the existence of a Nash equilibrium, constructing a Nash equilibrium with given support characteristics, constructing the worst Nash equilibrium (the one with maximum social cost), constructing the best Nash equilibrium (the one with minimum social cost), or computing the social cost of a (given) Nash equilibrium. Our work provides a comprehensive collection of efficient algorithms, hardness results (both as NP-hardness and #P-completeness results), and structural results for these algorithmic problems. Our results span and contrast a wide range of assumptions on the syntax of the Nash equilibria and on the parameters of the system.