Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
The competitiveness of on-line assignments
Journal of Algorithms
Achieving network optima using Stackelberg routing strategies
IEEE/ACM Transactions on Networking (TON)
On-line routing of virtual circuits with applications to load balancing and machine scheduling
Journal of the ACM (JACM)
Algorithmic mechanism design (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Heuristic Algorithms for Scheduling Independent Tasks on Nonidentical Processors
Journal of the ACM (JACM)
Algorithms for Scheduling Tasks on Unrelated Processors
Journal of the ACM (JACM)
Stackelberg scheduling strategies
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
Performance Guarantees of Local Search for Multiprocessor Scheduling
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
How much can taxes help selfish routing?
Proceedings of the 4th ACM conference on Electronic commerce
Computing Nash equilibria for scheduling on restricted parallel links
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Selfish load balancing and atomic congestion games
Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
Optimizing cost and performance for multihoming
Proceedings of the 2004 conference on Applications, technologies, architectures, and protocols for computer communications
Fairness and load balancing in wireless LANs using association control
Proceedings of the 10th annual international conference on Mobile computing and networking
Tolls for Heterogeneous Selfish Users in Multicommodity Networks and Generalized Congestion Games
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
User-level performance of channel-aware scheduling algorithms in wireless data networks
IEEE/ACM Transactions on Networking (TON)
Convergence time to Nash equilibria
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
Truthful algorithms for scheduling selfish tasks on parallel machines
Theoretical Computer Science
(Almost) optimal coordination mechanisms for unrelated machine scheduling
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Designing networks with good equilibria
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
The impact of local policies on the quality of packet routing in paths, trees, and rings
Journal of Scheduling
Coordinating Competitive Agents in Dynamic Airport Resource Scheduling
MATES '07 Proceedings of the 5th German conference on Multiagent System Technologies
Non-preemptive Coordination Mechanisms for Identical Machine Scheduling Games
SIROCCO '08 Proceedings of the 15th international colloquium on Structural Information and Communication Complexity
Non-cooperative Cost Sharing Games Via Subsidies
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Efficient coordination mechanisms for unrelated machine scheduling
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Worst-Case Nash Equilibria in Restricted Routing
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Coordination mechanisms for selfish scheduling
Theoretical Computer Science
Theoretical Computer Science
The price of stability in selfish scheduling games
Web Intelligence and Agent Systems
Non-clairvoyant Scheduling Games
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Covering Games: Approximation through Non-cooperation
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Selfish Scheduling with Setup Times
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Price of anarchy in parallel processing
Information Processing Letters
Mechanism Design for Decentralized Online Machine Scheduling
Operations Research
Tradeoffs and average-case equilibria in selfish routing
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Partition equilibrium always exists in resource selection games
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
Improving the price of anarchy for selfish routing via coordination mechanisms
ESA'11 Proceedings of the 19th European conference on Algorithms
Scheduling selfish tasks: about the performance of truthful algorithms
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
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In machine scheduling, a set of n jobs must be scheduled on a set of m machines. Each job i incurs a processing time of pij on machine j and the goal is to schedule jobs so as to minimize some global objective function, such as the maximum makespan of the schedule considered in this paper. Often in practice, each job is controlled by an independent selfish agent who chooses to schedule his job on machine which minimizes the (expected) completion time of his job. This scenario can be formalized as a game in which the players are job owners; the strategies are machines; and the disutility to each player in a strategy profile is the completion time of his job in the corresponding schedule (a player’s objective is to minimize his disutility). The equilibria of these games may result in larger-than-optimal overall makespan. The ratio of the worst-case equilibrium makespan to the optimal makespan is called the price of anarchy of the game. In this paper, we design and analyze scheduling policies, or coordination mechanisms, for machines which aim to minimize the price of anarchy (restricted to pure Nash equilibria) of the corresponding game. We study coordination mechanisms for four classes of multiprocessor machine scheduling problems and derive upper and lower bounds for the price of anarchy of these mechanisms. For several of the proposed mechanisms, we also are able to prove that the system converges to a pure Nash equilibrium in a linear number of rounds. Finally, we note that our results are applicable to several practical problems arising in networking.