Optimal dynamic mechanism design with deadlines

A seller maximizes revenue from selling an object in a dynamic environment, with buyers that differ in their patience: Each buyer has a privately known deadline for buying and a privately known valuation. First, we derive the optimal mechanism, neglecting the incentive constraint for the deadline. The deadline of the winner determines the time of the allocation and therefore also the amount of information available to the seller when he decides whether to allocate to a buyer. Depending on the shape of the markup that the seller uses, this can lead to a violation of the neglected incentive constraint. We give sufficient conditions on the type distribution under which the neglected constraint is fulfilled or violated. Second, for the case that the constraint cannot be neglected, we consider a model with two periods and two buyers. Here, the optimal mechanism is implemented by a fixed price in period one and an asymmetric auction in period two. The asymmetry, which is introduced to prevent the patient type of the first buyer from buying in period one leads to pooling of deadlines at the top of the type space.