Footnote 36, p. 15 — α̂₂(A) < α̂₁(A) for 0 < A < 1/4

Let $0 < A < 1/4$, $\hat\alpha_1(A) = 1 - A$ and $\hat\alpha_2(A) = \bigl(1 + \sqrt{1 - 4A}\bigr)/2$. Then

With costless advertising the equilibrium in which both firms target group $b$ survives on a smaller range of targeting precisions than at high advertising costs, where the threshold is $\hat\alpha_1(A)$.

Formalization Note The footnote states only $A < 1/4$; the hypothesis $A > 0$ is the model's standing assumption $0 < A < 1$ (§3). At $A = 0$ both thresholds equal $1$.