I am looking for a Karush-Kuhn-Tucker transformation to the following three-level optimization problem:
$\displaystyle \max_{x_2} \frac{\left(x_{1} - x_{3} - 2\right)^{2}}{18 x_{1} - 18 x_{3}} \left(- x_{1} + x_{2}\right) \left(x_{2} - x_{3}\right) \\$
$\displaystyle \textrm{s.t.}\\ \displaystyle \max_{x_1} \frac{1}{72 \left(x_{1} - x_{3}\right)^{2}} \left(- x_{1} + x_{2}\right) \left(3 x_{1}^{2} + 2 x_{1} x_{2} - 2 x_{1} x_{3} - 2 x_{2} x_{3} + 2 x_{2} - x_{3}^{2} - 2 x_{3}\right)^{2} \\$
$\displaystyle \textrm{s.t.}\\$ $\max_{x_3} \frac{1}{72(x_{1} - x_{3})^{2}}(- x_{2} + x_{3})(x_{1}^{2} + 2 x_{1} x_{2} + 2 x_{1} x_{3} - 8 x_{1} - 2 x_{2} x_{3} + 2 x_{2} - 3 x_{3}^{2} + 6 x_{3})^{2} $
I am not quite sure how to proceed with it, do you have any tips to offer?
Thanks in advance.