Multi-parametric approach for multilevel multi-leader-multi-follower games using equivalent reformulations

Abstract:

Multilevel multi-leader multi-follower games address compromises among multiple interacting decision agents within a hierarchical system in which multiple followers are involved at each lower-level unit and more than one decision maker (multiple leaders) are involved in the upper-level. The leaders' decisions are affected not only by reactions of the followers but also by various relationships among the leaders themselves. In general, multiple-leaders multiple-followers (MLMF) game serve as an important modeling tool in game theory with many applications in economics, engineering, operations research and other fields. In this paper, we have reformulated a multilevel-MLMF game into an equivalent multilevel single-leader multi-follower (SLMF) game by introducing a suppositional (or dummy) leader, and hence the multiple leaders in the original problem become followers in the second level. If the resulting multilevel-SLMF game consists of separable terms and parameterized common terms across all the followers, then the problem is further transformed into equivalent multilevel programs having a single leader and single follower at each level of the hierarchy. The proposed solution approach can solve multilevel multi-leader multi-follower problems whose objective values at all levels have common but having different positive weights of non-separable terms. This result improves the work of Kulkarni and Shanbhag (2015).

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APA

Belete, Z (2024). Multi-parametric approach for multilevel multi-leader-multi-follower games using equivalent reformulations. Afribary. Retrieved from https://afribary.com/works/multi-parametric-approach-for-multilevel-multi-leader-multi-follower-games-using-equivalent-reformulations

MLA 8th

Belete, Zewde "Multi-parametric approach for multilevel multi-leader-multi-follower games using equivalent reformulations" Afribary. Afribary, 30 Mar. 2024, https://afribary.com/works/multi-parametric-approach-for-multilevel-multi-leader-multi-follower-games-using-equivalent-reformulations. Accessed 22 Dec. 2024.

MLA7

Belete, Zewde . "Multi-parametric approach for multilevel multi-leader-multi-follower games using equivalent reformulations". Afribary, Afribary, 30 Mar. 2024. Web. 22 Dec. 2024. < https://afribary.com/works/multi-parametric-approach-for-multilevel-multi-leader-multi-follower-games-using-equivalent-reformulations >.

Chicago

Belete, Zewde . "Multi-parametric approach for multilevel multi-leader-multi-follower games using equivalent reformulations" Afribary (2024). Accessed December 22, 2024. https://afribary.com/works/multi-parametric-approach-for-multilevel-multi-leader-multi-follower-games-using-equivalent-reformulations

Multi-parametric approach for multilevel multi-leader-multi-follower games using equivalent reformulations

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