Chapter

Automata, Languages and Programming

Volume 2719 of the series Lecture Notes in Computer Science pp 502-513

Date:

Convergence Time to Nash Equilibria

  • Eyal Even-DarAffiliated withSchool of Computer Science, Tel-Aviv University
  • , Alex KesselmanAffiliated withSchool of Computer Science, Tel-Aviv University
  • , Yishay MansourAffiliated withSchool of Computer Science, Tel-Aviv University

* Final gross prices may vary according to local VAT.

Get Access

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 (such as allowing the largest weight job to move first).