The Theory And Algorithm On Bilevel Programs With Multiple Followers

This thesis studies bilevel programs with multiple followers in which there exists information exchange among the followers. Its applications include mang different areas,mcluding agricultural applications,economic analysis and so on, so this area attracts more and more attention.1. Due to the problem of coordinating between the higher level and the lower level, in the absence of any further information one of the Pareto-optimal solutions cannot be said to be better than the others. This demands an user to find as many Pareto-optimal solutions as possible. It is well known that for a game problem the set of all the Nash equilibria may be empty. Existence of an equilibrium is the most fundamental issue in Game Theroy. Then based on the concept of a Nash equilibrium in Game Theory and the idea of Goal Programming, we introduce a Nash-ideal-point concept, so we can get a new solution concept for the problem. This is an efficient way to avoid the uncertainty cased by the multiple potential reactions. At the same time that may simplify the mathematical model. The existence of a solution is proven under some mild condition, A property of...