482 RWTH Publication No: 731223        2018        IGPM482.pdf
TITLE Solving Quadratic Multi-Leader-Follower Games by Smoothing the Follower’s Best Response
AUTHORS Michael Herty, Sonja Steffensen, Anna Thünen
ABSTRACT We derive Nash-s-stationary 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 smooth Nash equilbrium problem. We prove existence and uniqueness for all smoothing parameters. For a decreasing sequence of these smoothing parameters accumulation points of Nash equilibria exist and we show that they fullfill the conditions of s-stationarity. Finally, we propose an update on the leader variables for efficient computation and numerically compare nonsmooth Newton and subgradient method.
KEYWORDS Multi-Leader-Follower Games, Nash Equilibria, Nonsmooth Newton, Subgradient Method, Game Theory, Equilibrium Problems with Equilibrium Constraints
DOI 10.1080/10556788.2020.1828412
PUBLICATION Optimization, Methods and Software, 2020
NOTE updated 04/2020