Dynamic Slot Allocations with Different Patience Levels

Abstract

This study considers a mechanism design problem in which service slots are allocated over time to buyers arriving at different periods. Some buyers can accept delayed service, whereas others cannot. Buyers have a multidimensional type representing their valuation and patience level. The seller fully commits to a mechanism with or without complete contingent contracts. We show that a deterministic mechanism is periodic ex-post incentive compatible if and only if the allocation rule is monotone in valuation and the "price equivalence" holds. In cases both with and without contingent contracts, the dynamic pivot mechanism with a reserve price maximizes the seller's expected revenue under a regularity condition, which is characterized by the linearity of the virtual valuation function. When the regularity holds, the fully optimal mechanism with contingent contracts is multi-contracting-proof, whereas the constrained optimal mechanism without contingent contracts is not.