Wang, Qian; Yang, Fengmei; Wang, Shouyang; Liu, Yi-Hsin Bilevel programs with multiple followers. (English) Zbl 1039.90072 Syst. Sci. Math. Sci. 13, No. 3, 265-276 (2000). Summary: 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. Cited in 4 Documents MSC: 90C29 Multi-objective and goal programming 90B30 Production models Keywords:multilevel programming; bilevel programming; multiple followers; Nash equilibrium; reaction set; single follower; Kuhn-Tucker conditions; branch and bound technique PDFBibTeX XMLCite \textit{Q. Wang} et al., Syst. Sci. Math. Sci. 13, No. 3, 265--276 (2000; Zbl 1039.90072)