A best-response approach for equilibrium selection in two-player generalized Nash equilibrium problems. (2nd December 2019)

• Record Type: Journal Article
• Authors: Dreves, Axel
• Is Part Of: Optimization. Volume 68:Number 12(2019)
• Page Start: 2269
• Page End: 2295
• Publication Date: 2019-12-02
• Subjects: Generalized Nash equilibrium problem -- Jacobi-type method -- equilibrium selection -- discrete approach; 49M25 -- 91A05 -- 91A10 -- 91A40; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1646743
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we propose a best-response approach to select an equilibrium in a two-player generalized Nash equilibrium problem. In our model we solve, at each of a finite number of time steps, two independent optimization problems. We prove that convergence of our Jacobi-type method, for the number of time steps going to infinity, implies the selection of the same equilibrium as in a recently introduced continuous equilibrium selection theory. Thus the presented approach is a different motivation for the existing equilibrium selection theory, and it can also be seen as a numerical method. We show convergence of our numerical scheme for some special cases of generalized Nash equilibrium problems with linear constraints and linear or quadratic cost functions.