Abstract: Bilevel programming problem provide a framework to deal with decision processes involving two decision makers with a hierarchical structure. The leader  at the upper level of the hierarchy and the follower at the lower level seek to optimize their   individual objective functions and control their own set of decision variables. Bilevel programming   problem involves two optimization problems where the constraint region of the upper level problem is   implicitly determined by another optimization problem. Bilevel programming problem is frequently encountered with in the fields of economy, industry, transportation, military, and so on. In this paper, we investigate the partial cooperation model for the bilevel programming problem in which the optimal reactions of the lower level problem is discrete and finite. We develop a general method for ascertaining the cooperation ratio in the partial cooperation model when the cooperation degree of the follower depends on the decision variables of the leader. Furthermore, we develop a new partial cooperation model of which the optimal is better than of the pessimistic model under suitable conditions. Then we derive some meaningful results based the proposed partial cooperation model. Finally, we show that the proposed partial cooperation model is feasible by two numerical examples.

Key words: bilevel programming, finite reactions, partial cooperation model, cooperation ratio, optimistic model, pessimistic model