On generalized Nash equilibrium problems with linear coupling constraints and mixed-integer variables

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 t...

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Bibliographic Details
Published in:Optimization Vol. 68; no. 1; pp. 197 - 226
Main Author: Sagratella, Simone
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 02.01.2019
Taylor & Francis LLC
Subjects:
Branch and bound methods
Coupling
Economic models
enumerative method
Equilibrium
equilibrium selection
Game theory
Generalized Nash equilibrium problem
Methods
mixed-integer nonlinear problem
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Summary: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.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2018.1545125