In this paper we consider a multiobjective two-level integer programming problem in which there is not cordination between the decision maker at the upper level and the decision maker at the lower level. The decision maker at the upper level has an objective function and the decision maker at the lower level has multiple objective functions. The decision maker at the upper level must take account of multiple rational responses of the decision maker at the lower level in the problem. We examine two kinds of situations based on anticipation of the decision maker at the upper level; an optimistic anticipation and a pessimistic anticipation. Mathematical programming problems for obtaining the Stackelberg solutions based on two kinds of anticipation are formulated and three kinds of computational methods for obtaining the Stackelberg solutions are proposed. We carry out numerical experiments in order to demonstrate feasibility and effectiveness of the proposed methods.
