The schematic representation of the outer problem is as follow \[\begin{aligned} &\sum_u c_u g_u \rightarrow extr && \\ &s.t.&& \\ &\quad E(\hat{g},\hat{c}; \phi, \psi) =0 && \text{candidate system} \\ &\quad E(\hat{g}^{(s,p)}, \hat{c}^{(s,p)}=0; \phi^{sp},\psi^{sp})\quad \forall (s,p) \in S(p) && \text{fixed decisions} \\ &\quad \pi_p = && \text{profit equation} \\ &\quad \pi >= \pi && \text{NE filter}\end{aligned}\]