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

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  • Michael Herty
  • Sonja Steffensen
  • Anna Thunen

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.

Suggested Citation

  • Michael Herty & Sonja Steffensen & Anna Thunen, 2018. "Solving Quadratic Multi-Leader-Follower Games by Smoothing the Follower's Best Response," Papers 1808.07941, arXiv.org, revised Apr 2020.
    • Handle: RePEc:arx:papers:1808.07941
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    References listed on IDEAS

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