deletions | additions       diff --git a/section_Bi_level_formulation_subsection__.tex b/section_Bi_level_formulation_subsection__.tex  index 8e95415..5ae2df6 100644  --- a/section_Bi_level_formulation_subsection__.tex  +++ b/section_Bi_level_formulation_subsection__.tex 
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The system described above is linear, so KKT conditions are sufficient for global optimum.  Hence, we can refer to this problem as to the equations system with inner variables and outer parameters.  If we denote it as $E(\hat{g}, \hat{c}; g, p, \theta, \lambda, \chi, \sigma, \nu, \omega)$ \omega) = 0$  than required subproblems used to filter the Nash Equilibrium are formulated as $E(\hat{g}^{(s,p)}, \hat{c}^{(s,p)}; g^{sp}, p^{sp}, \theta^{sp}, \lambda^{sp}, \chi^{sp}, \sigma^{sp}, \nu^{sp}, \omega^{sp})$, \omega^{sp}) = 0$,  where \begin{description}  \item[$\hat{g}^{(s,p)}$] is equal to current $\hat{g}_u$ value for $u\notin p$ and fixed on strategy level for others;  \item[$\hat{c}^{(s,p)}$] ditto for bidded cost;