Convergence Time to Nash Equilibria

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).

• Type: Conference
• Year: 2003
• Where: ICALP
• Authors: Eyal Even-Dar, Alexander Kesselman, Yishay Mansour
• Keywords: ICALP 2003, Load Balancing Models, Load Balancing Scenario, Pure Nash Equilibrium, Theoretical Computer Science