Model and extended Kuhn-Tucker approach for bilevel multi-follower decision making in a referential-uncooperative situation

When multiple followers are involved in a bilevel decision problem, the leader’s decision will be affected, not only by the reactions of these followers, but also by the relationships among these followers. One of the popular situations within this framework is where these followers are uncooperatively making decisions while having cross reference of decision information. This situation is called a referential-uncooperative situation in this paper. The well-known Kuhn-Tucker approach has been successfully applied to a oneleader-and-one-follower linear bilevel decision problem. This paper extends this approach to deal with the above-mentioned linear referential-uncooperative bilevel multifollower decision problem. The paper first presents a decision model for this problem. It then proposes an extended Kuhn-Tucker approach to solve this problem. Finally, a numeric example illustrates the application of the proposed Kuhn-Tucker approach.