A guided tour of Chernoff bounds
Information Processing Letters
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
Tight bounds for worst-case equilibria
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
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
Computing Nash equilibria for scheduling on restricted parallel links
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Structure and complexity of extreme Nash equilibria
Theoretical Computer Science - Game theory meets theoretical computer science
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Nash equilibria in discrete routing games with convex latency functions
Journal of Computer and System Sciences
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
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
Journal of Combinatorial Optimization
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In the resource allocation game introduced by Koutsoupias and Papadimitriou, n jobs of different weights are assigned to m identical machines by selfish agents. For this game, it has been conjectured by several authors that the fully mixed Nash equilibrium (FMNE) is the worst possible w.r.t. the expected maximum load over all machines. Assuming the validity of this conjecture, computing a worst-case Nash equilibrium for a given instance was trivial, and approximating the Price of Anarchy for this instance would be possible by approximating the expected social cost of the FMNE by applying a known FPRAS. We present a counter-example to this conjecture showing that fully mixed Nash equilibria cannot be used to approximate the Price of Anarchy. We show that the factor between the social cost of the worst Nash equilibrium and the social cost of the FMNE can be as large as the Price of Anarchy itself, up to a constant factor. In addition, we present an algorithm that constructs so-called concentrated equilibria that approximate the worst-case Nash equilibria within constant factors.