A Method for Solving Some Class of Multilevel Multi-leader Multi-follower Programming Problems
Multiple leaders with multiple followers games serve as an important model in game theory with many applications in economics, engineering, operations research and other fields. In this paper, we have reformulated a multilevel multi-leader multiple follower (MLMLMF) programming problem into an equivalent multilevel single-leader multiple follower (MLSLMF) programming problem by introducing a suppositional (or dummy) leader. If the resulting MLSLMF programming problem consist of separable terms and parameterized common terms across all the followers, then the problem is transformed into an 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 in both levels have common, but having different positive weights of, nonseparable terms.
KeywordsMultilevel multi-leader multi-follower programming Multilevel programming Multi-parametric programming Branch-and-bound
- 2.Ehrenmann, A.: Equilibrium problems with equilibrium constraints and their applications in electricity markets. Dissertation, Judge Institute of Management, Cambridge University, Cambridge, UK (2004)Google Scholar
- 8.Kulkarni, A.A.: Generalized Nash games with shared constraints: existence, efficiency, refinement and equilibrium constraints. Ph.d. Dissertation, Graduate College of the University of Illinois, Urbana, Illinois (2010)Google Scholar
- 11.Okuguchi, K.: Expectations and stability in oligopoly models. In: Lecture Notes in Economics and Mathematical Systems, vol. 138. Springer, Berlin (1976)Google Scholar
- 15.Su, C.L.: A sequential ncp algorithm for solving equlibrium problems with equilibrium constraints. Technical report, Department of Management Science and Engineering, Stanford University (2004)Google Scholar