A team-based competitive environment is a complex multiagent environment, in which agents are required to coordinate with each other not only to enhance their collective behavior, but also to compete with the other team. An interesting research problem in such an environment is the role assignment problem (RAP). The problem requires agents to decide the roles they should take based on real-time feedback from a dynamically changing environment. In this paper, we aim to provide a new strategy that is based on the Minority Game (MG) model, i.e., the MG strategy, for assisting a team to perform effective role assignments in such an environment. Through experiments in our previous work, we have demonstrated that the MG strategy is helpful for RAP in RoboCup Simulation League. In this paper, with a more generic competitive environment such as DynaGrid, we find that the MG strategy is not always effective. It can help agents do effective roles assignments in the case that the targets mov...