Proof of Proposition 7, p. 29 — Δ_L > Λ_L

Let $(\theta_H,\theta_L,\alpha,\gamma,k,s)$ satisfy the standing assumptions $\theta_H>\theta_L>0$, $\alpha,\gamma\in(0,1)$, $k>0$, $s>0$. Then the low type's A-Learning threshold strictly exceeds its O-Learning threshold:

This is the paper's statement that the low-type buyers' motivation for truthful revelation is lower under A-Learning than under O-Learning.