\begin{equation}
	\begin{aligned}
		&\pi_i - \pi_{ij} < \pi_i - \pi_i\pi_j\\
		&\pi_i - \pi_{ij} < \pi_i(1 - \pi_j)\\
		&\frac{\pi_i - \pi_{ij}}{\pi_i(1 - \pi_j)} < 1\\
		&1 - \frac{\pi_i - \pi_{ij}}{\pi_i(1 - \pi_j)} > 0\\
		&\frac{\pi_{ij} - \pi_i\pi_j}{\pi_i(1 - \pi_j)} > 0 
	\end{aligned}
	\label{H}
\end{equation}
