Revenue maximizing with return policy when buyers have uncertain valuations

This paper examines the optimal mechanism design problem when buyers have uncertain valuations. This uncertainty can only be resolved after the actual transactions take place and upon incurring significant post-purchase cost. We focus on two different settings regarding how the seller values a returned object (salvage value). We first study the case where the salvage value is exogenously determined. We find that the revenue maximizing mechanism is deterministic and “separable”. We illustrate that the optimal revenue can be implemented by a mechanism with a “no-questions-asked” return policy. In addition, we show that “linear return policies” are suboptimal when the hazard rates of initial estimates are monotone. We next examine the case where the salvage value is endogenously determined. We demonstrate that “separability” no longer holds and the “recall” of buyers is necessary in the optimal mechanism.