In traditional distributed computing the users and owners of the computational resources usually belong to the same administrative domain. Therefore all users are equally entitled to use the resources. The situation is completely different in large-scale emergent distributed computing systems, such as Grid systems, where the roles of the users are asymmetric as regards their access rights and usage of resources. Further, unlike traditional distributed computing case, Grid systems introduce

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... rchical levels, which are to be taken into account for optimizing the overall system's performance. In this paper we present a Stackelberg game for modelling asymmetric users' behavior in Grid scheduling scenario. We define a two-level game with a Leader at the first level and the rest of users, called Followers, at the second one. The Leader is responsible for computing a planning of his tasks, which is usually a large fraction of the total pool of tasks in the batch. The Followers try to select the best strategy for the assignments of their tasks subject to Leader's strategy. The Stackelberg game is then translated into a hierarchical optimization problem, which is solved by Genetic Algorithm (GA) on the Leader's level and by ad hoc heuristic combined with GA on the Followers' level. We have experimentally evaluated the approach through a benchmark of static instances and report computational results for resource utilization, makespan and flowtime.