Convergence time to Nash equilibrium in load balancing

Eyal Even-Dar, Alex Kesselman, Yishay Mansour

Research output: Contribution to journalArticlepeer-review

Abstract

We study the number of steps required to reach a pure Nash equilibrium in a load balancing scenario where each job behaves selfishly and attempts to migrate to a machine which will minimize its cost. We consider a variety of load balancing models, including identical, restricted, related, and unrelated machines. Our results have a crucial dependence on the weights assigned to jobs. We consider arbitrary weights, integer weights, k distinct weights, and identical (unit) weights. We look both at an arbitrary schedule (where the only restriction is that a job migrates to a machine which lowers its cost) and specific efficient schedulers (e.g., allowing the largest weight job to move first). A by-product of our results is establishing a connection between various scheduling models and the game-theoretic notion of potential games. We show that load balancing in unrelated machines is a generalized ordinal potential game, load balancing in related machines is a weighted potential game, and load balancing in related machines and unit weight jobs is an exact potential game.

Original languageEnglish
Article number1273348
JournalACM Transactions on Algorithms
Volume3
Issue number3
DOIs
StatePublished - 1 Aug 2007

Keywords

  • Convergence time
  • Game theory
  • Nash equilibrium

Fingerprint

Dive into the research topics of 'Convergence time to Nash equilibrium in load balancing'. Together they form a unique fingerprint.

Cite this