Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
Improving local search heuristics for some scheduling problems. Part II
Discrete Applied Mathematics - Special issue on models and algorithms for planning and scheduling problems
Exact and Approximate Algorithms for Scheduling Nonidentical Processors
Journal of the ACM (JACM)
Expected Length of the Longest Probe Sequence in Hash Code Searching
Journal of the ACM (JACM)
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
Tight bounds for worst-case equilibria
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
The Structure and Complexity of Nash Equilibria for a Selfish Routing Game
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
On the complexity of price equilibria
Journal of Computer and System Sciences - STOC 2002
Nashification and the coordination ratio for a selfish routing game
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
The price of anarchy for polynomial social cost
Theoretical Computer Science
On the structure and complexity of worst-case equilibria
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
Facets of the Fully Mixed Nash Equilibrium Conjecture
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
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
The structure and complexity of Nash equilibria for a selfish routing game
Theoretical Computer Science
On the complexity of constrained Nash equilibria in graphical games
Theoretical Computer Science
How hard is it to find extreme Nash equilibria in network congestion games?
Theoretical Computer Science
Extending the notion of rationality of selfish agents: Second Order Nash equilibria
Theoretical Computer Science
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
Selfish load balancing under partial knowledge
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Hi-index | 0.01 |
We study extreme Nash equilibria in the context of a selfish routing game. Specifically, we assume a collection of n users, each employing a mixed strategy, which is a probability distribution over m parallel identical 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. 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 provide substantial evidence for the Fully Mixed Nash Equilibrium Conjecture, which states that the worst Nash equilibrium is the fully mixed Nash equilibrium, where each user chooses each link with positive probability. Specifically, we prove that the Fully Mixed Nash Equilibrium Conjecture is valid for pure Nash equilibria. Furthermore, we show, that under a certain condition, the social cost of any Nash equilibrium is within a factor of 2h(1 + ε) of that of the fully mixed Nash equilibrium, where h is the factor by which the largest user traffic deviates from the average user traffic.Considering pure Nash equilibria, we provide a PTAS to approximate the best social cost, we give an upper bound on the worst social cost and we show that it is N P-hard to approximate the worst social cost within a multiplicative factor better than 2 - 2/(m + 1).