Abstract:

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.