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arXiv · 1808.07941

Solving Quadratic Multi-Leader-Follower Games by Smoothing the Follower's Best Response

Michael Herty·Sonja Steffensen·Anna Thünen
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Abstract

We derive 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 fulfill 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.

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Michael Herty, Sonja Steffensen, Anna Thünen. 2018-08-23. Solving Quadratic Multi-Leader-Follower Games by Smoothing the Follower's Best Response. https://arxiv.org/abs/1808.07941

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