Solving quadratic multi-leader-follower games by smoothing the follower's best response. (4th March 2022)

• Record Type: Journal Article
• Authors: Herty, Michael; Steffensen, Sonja; Thünen, Anna
• Is Part Of: Optimization methods and software. Volume 37:Number 2(2022)
• Page Start: 772
• Page End: 799
• Publication Date: 2022-03-04
• Subjects: Multi-leader-follower games -- Nash equilibria -- game theory -- equilibrium problems with equilibrium constraints; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2020.1828412
• Languages: English
• ISSNs: 1055-6788

Abstract

ABSTRACT: We analyse the existence of Nash equilibria for a class of quadratic multi-leader-follower games using the nonsmooth best response function. To overcome the challenge of nonsmoothness, we pursue a smoothing approach resulting in a reformulation as a smooth Nash equilibrium problem. The existence and uniqueness of solutions are proven for all smoothing parameters. Accumulation points of Nash equilibria exist for a decreasing sequence of these smoothing parameters and we show that these candidates fulfil the conditions of S-stationarity and are Nash equilibria to the multi-leader-follower game. Finally, we propose an update on the leader variables for efficient computation and numerically compare nonsmooth Newton and subgradient methods.