Cost-Sharing Scheduling Games on Restricted Unrelated Machines

We study a very general cost-sharing scheduling game. An instance consists of k jobs and m machines and an arbitrary weighed bipartite graph denoting the job strategies. An edge connecting a job and a machine specifies that the job may choose the machine; edge weights correspond to processing times. Each machine has an activation cost that needs to be covered by the job assigned to it. Jobs assigned to a particular machine share its cost proportionally to the load they generate. Our game generalizes singleton cost-sharing games with weighted players. We provide a complete analysis of the game with respect to equilibrium existence, computation, convergence and quality – with respect to the total cost. We study both unilateral and coordinated deviations. We show that the main factor in determining the stability of an instance and the quality of a stable assignment is the machines’ activation-cost. Games with unitcost machines are potential games, and every instance has an optimal so...

• Type: Journal
• Year: 2015
• Where: SAGT
• Authors: Guy Avni, Tami Tamir
• Keywords: Game Theory, SAGT 2015