A Note on the Uniqueness Proof in Goldstein and Pauzner (2005)

Goldstein and Pauzner (2005) establish a unique threshold equilibrium in a Diamond-Dybvig model with noisy private signals. Because the demand-deposit payoff is not monotone in the share of withdrawing agents, the standard global-games argument is unavailable, and the proof of their Theorem 1 rests on an auxiliary result, Lemma A1. This note reports two problems with it. The shift operator used to state parts (ii) and (iii) displaces the belief in the direction opposite to the one Part B requires; as printed, the asserted monotonicity fails. We derive the operator the argument needs from a difference property of the withdrawal share that the original proof uses without stating. Second, the justification of the strict monotonicity in part (iii) requires two conditions to hold jointly, and we exhibit a nonempty range of admissible contracts on which their intersection is empty. We close this gap through the upward jump of the utility difference at the upper dominance cutoff and complete the proof of Part B. The statement of Theorem 1 is unaffected.