Approximate Nash Equilibria for Scheduling Game on Serial-Batching-Machines with Activation Cost

We consider the scheduling game with activation cost, where jobs as selfish agents compete for processing on serial-batching identical machines. Each job selects a machine (more precisely, a batch on a machine) for processing to minimize his disutility composed of the load of his machine and the fraction of activation cost. We claim that such a game may not admit any Nash equilibrium under the uniform sharing rule. We present an algorithm and prove that the schedule produced by the algorithm is a tight approximate Nash equilibria.