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
The price of anarchy for polynomial social cost
Theoretical Computer Science
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We study an intensively studied resource allocation game introduced by Koutsoupias and Papadimitriou where n weighted jobs are allocated to m identical machines. It was conjectured by Gairing et al. that the fully mixed Nash equilibrium is the worst Nash equilibrium for this game w. r. t. the expected maximum load over all machines. The known algorithms for approximating the so-called “price of anarchy” rely on this conjecture. We present a counter-example to the conjecture showing that fully mixed equilibria cannot be used to approximate the price of anarchy within reasonable factors. In addition, we present an algorithm that constructs so-called concentrated equilibria that approximate the worst-case Nash equilibrium within constant factors.