A simple on-line bin-packing algorithm
Journal of the ACM (JACM)
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
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
The Price of Stability for Network Design with Fair Cost Allocation
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Selfish Routing and the Price of Anarchy
Selfish Routing and the Price of Anarchy
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Tight bounds for worst-case equilibria
ACM Transactions on Algorithms (TALG)
Performance Guarantees of Local Search for Multiprocessor Scheduling
INFORMS Journal on Computing
Convergence time to Nash equilibrium in load balancing
ACM Transactions on Algorithms (TALG)
Truthful Approximation Schemes for Single-Parameter Agents
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
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
Maximizing the minimum load for selfish agents
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
A note on semi-online machine covering
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Inefficiency of Nash equilibria with parallel processing policy
Information Processing Letters
The cost of selfishness for maximizing the minimum load on uniformly related machines
Journal of Combinatorial Optimization
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We consider a scheduling problem where each job is controlled by a selfish agent, who is only interested in minimizing its own cost, which is defined as the total load on the machine that its job is assigned to. We consider the objective of maximizing the minimum load (cover) over the machines. Unlike the regular makespan minimization problem, which was extensively studied in a game theoretic context, this problem has not been considered in this setting before.We study the price of anarchy (poa) and the price of stability (pos). We show that on related machines, both these values are unbounded. We then focus on identical machines. We show that the $\textsc{pos}$ is 1, and we derive tight bounds on the $\textsc{poa}$ for m ≤ 6 and nearly tight bounds for general m. In particular, we show that the $\textsc{poa}$ is at least 1.691 for larger m and at most 1.7. Hence, surprisingly, the $\textsc{poa}$ is less than the $\textsc{poa}$ for the makespan problem, which is 2. To achieve the upper bound of 1.7, we make an unusual use of weighting functions. Finally, in contrast we show that the mixed $\textsc{poa}$ grows exponentially with m for this problem, although it is only 驴(logm/loglogm) for the makespan.