Before revision:  The posted-price payment rules are then pinned down  in terms of the allocation rule and the threshold function up to a constant. The incentive compatibility constraints restrict the design of the posted-price payment rule by a regular condition .
After revision:  The posted-price payment rules are then pinned down in terms of the allocation rule by deriving a first-order condition. We show cases of relaxations of the principal's mechanism design problem and provide an approach to evaluate the loss of robustness of the dynamic incentive compatibility when the problem solving is relaxed due to analytical intractability. A case study is used to illustrate the theoretical results .