Pareto-optimal Algorithms for Scheduling Games on Parallel-batching Machines with Activation Cost

We study one scheduling game with activation cost, where each game involves [Formula: see text] jobs being processed on [Formula: see text] parallel-batching identical machines. Each job, as an agent, selects a machine (more precisely, a batch on a machine) for processing to minimize his disutility, which consists of the load of his machine and his share in the machine’s activation cost. We prove that Nash equilibrium may not exist for the scheduling game. We design a polynomial-time algorithm to produce pareto-optimal schedules for two special cases of the scheduling game. Finally, we show that the general form of the scheduling game has pareto-optimal schedule by an improved polynomial-time algorithm, and prove that the schedule is a tight [Formula: see text]-approximate Nash equilibria.