Optimal dynamic mechanism design with deadlines

Abstract

Abstract. A dynamic mechanism design problem with multi-dimensional private information is studied. There is one object and two buyers who arrive in two different periods. In addition to his privately known valuation, the first buyer also has a privately known deadline for purchasing the object. The seller wants to maximize revenue.Depending on the type distribution, the incentive compatibility constraint for the deadline may or may not be binding in the optimal mechanism. Sufficient conditions on the type distribution and examples are given for either case.An optimal mechanism for the binding case is derived. It can be implemented by a fixed price in period one and an asymmetric auction in period two. The asymmetry prevails even if the valuations of both buyers are identically distributed. In order to prevent buyer one from buying in the first period when his deadline is two, the seller sets a reserve price that is lower than in the classical (Myerson, 1981) optimal auction and gives him a (non-linear) bonus. The bonus leads to robust bunching at the top of the type-space. The optimal mechanism can be characterized in terms of generalized virtual valuations which depend endogenously on the allocation rule.

Revenue Management with Forward-Looking Buyers

“…This model is very rich, allowing buyers to arrive and leave the market over time and the distribution of entering buyers to vary. Mierendorff (2009) considers a two-period version of a similar model and provides a complete characterization of the optimal contract. Su (2007) considers a model with heterogeneous values and discount rates, examining how the interaction of these terms determines the optimal price paths.…”

Welfare-maximizing assignment of agents to hierarchical positions

“…An equivalent assumption is found in Mierendorff (2009). All power distribution functions satisfy this assumption, as well as those with nondecreasing density, and with exponential densities ke g(v) where g…”

Dynamic Mechanism Design: An Introduction

“…If the modeling assumptions are relaxed, each of these two main predictions may fail and complete solutions seem difficult to obtain. See, for example, the analysis in Mierendorff (2016) for the case where the agents are forward looking but may disappear or have different discount factors.…”