Before revision:  The payment rules are then pinned down up to a constant in terms of the allocation rule by deriving a first-order condition.
After revision:  A necessary condition is derived from envelope theorem, which explicitly formulates the state-dependent payment rules in terms of allocation rules. A class of monotone environment is considered to characterize the optimal stopping by a threshold rule. The posted-price payment rules are then pinned down up to a constant in terms of the allocation rule by deriving a first-order condition.