Most of the time, the government of the affected country cannot handle the entire relief operations. Under such conditions, international organizations act independently but are obliged to obey the law of the country. In this paper, we propose a dynamic multi-level programming where the affected country and international organizations dynamically change their roles, being leader or follower, according to a game. The application of the proposed model is investigated for a case problem where real data are utilized to design a network for humanitarian logistics during potential earthquakes. The advantages of using multi-level modeling against considering just one player's point of view are provided to guide decision-makers under a variety of conditions. The results show for the first three periods, the gov-ernment of the affected area cannot handle the demand for the rescue operation. Thus, the international suppliers act as the leader for the first three periods. However, by decreasing the demand for the rescue operation in the last three periods, the government can manage the evacuation operation properly.