New partial cooperation model for bilevel programming problems

Partial cooperation models are studied for many years to solve the bilevel programming problems where the follower's optimal reaction is not unique. However, in these existed models, the follower's cooperation level does not depend on the leader's decision. A new model is proposed to solve this deficiency. It is proved the feasibility of the new model when the reaction set of the lower level is lower semi-continuous. And the numerical results show that the new model has optimal solutions when the reaction set of the lower level is discrete, lower semi-continuous and nonlower semi-continuous.