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Bilevel programs with multiple followers. (English) Zbl 1039.90072

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.

MSC:

90C29 Multi-objective and goal programming
90B30 Production models
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