| Abstract: | In this paper, we are concerned with bilevel programs with multiple followers. Three new solution concepts are introduced for a bilevel programming problem with multiple followers. First, one sufficient condition for the existence of a Nash equilibrium reaction is presented and the continuity of the reaction set is discussed. Next, we show that a class of bilevel programs with multiple followers can be solved via solving a corresponding bilevel program with a single follower. Finally on the basis of a theorem proved via applying the Kuhn-Tucker conditions to the inner game problem, a branch and bound technique is developed for bilevel program with multiple followers. Two numerical examples are also given to illustrate the algorithm. |
