Coordination Mechanisms for Selfish Scheduling

  • Nicole Immorlica
  • Li Li
  • Vahab S. Mirrokni
  • Andreas Schulz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3828)


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 p ij 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.


Nash Equilibrium Completion Time Greedy Algorithm Coordination Mechanism Local Search Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Nicole Immorlica
    • 1
  • Li Li
    • 2
  • Vahab S. Mirrokni
    • 1
  • Andreas Schulz
    • 3
  1. 1.Massachusetts Institute of TechnologyCambridgeUSA
  2. 2.Bell LabsCenter for Networking ResearchMurray HillUSA
  3. 3.Operations Research CenterMITCambridgeUSA

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