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 .
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 .
R
Nash-s-stationary
Nash
R
smooth Nash equilbrium problem. We prove
a smooth Nash equilibrium problem. The
A
of solutions are proven
R
For
Accumulation points of Nash equilibria exist for
D
accumulation points of Nash equilibria exist
R
they fullfill
these candidates fulfill
A
and are Nash equilibria to the multi-leader-follower game
R
method
methods