On generalized Nash equilibrium problems with linear coupling constraints and mixed-integer variables. (2nd January 2019)

• Record Type: Journal Article
• Authors: Sagratella, Simone
• Is Part Of: Optimization. Volume 68:Number 1(2019)
• Page Start: 197
• Page End: 226
• Publication Date: 2019-01-02
• Subjects: Generalized Nash equilibrium problem -- mixed-integer nonlinear problem -- enumerative method -- equilibrium selection; 90C33 -- 90C11 -- 90C57 -- 91A10 -- 91A65 -- 65K10; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1545125
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: We define and discuss different enumerative methods to compute solutions of generalized Nash equilibrium problems with linear coupling constraints and mixed-integer variables. We propose both branch-and-bound methods based on merit functions for the mixed-integer game, and branch-and-prune methods that exploit the concept of dominance to make effective cuts. We show that under mild assumptions the equilibrium set of the game is finite and we define an enumerative method to compute the whole of it. We show that our branch-and-prune method can be suitably modified in order to make a general equilibrium selection over the solution set of the mixed-integer game. We define an application in economics that can be modelled as a Nash game with linear coupling constraints and mixed-integer variables, and we adapt the branch-and-prune method to efficiently solve it.