Dynamic Mechanism Design for Online Commerce

Abstract

Motivated by electronic commerce, this paper is a mechanism design study for sellers of multiple identical items. In the market environment we consider, participants are risk neutral and time-sensitive, with the same discount factor; potential buyers have unit demand and arrive sequentially according to a renewal process; and valuations are drawn independently from the same regular distribution. From the Revelation Principle, we can restrict our attention to direct dynamic mechanisms taking a sequence of valuations and arrival epochs as a strategic input. We define two properties (discreteness and stability), and prove that under a regularity assumption on the inter-arrival time distribution, we may at no cost of generality consider only mechanisms satisfying them. This effectively reduces the mechanism input to a sequence of valuations, allowing us to formulate the problem as a dynamic program (DP). Because this DP is equivalent to a well-known infinite horizon asset-selling problem, we can finally characterize the optimal mechanism as a sequence of posted prices increasing with each sale. Our numerical study indicates that, with uniform valuations, the benefit of dynamic pricing over a fixed posted price may be small. Besides, posted prices are preferable to online auctions for a large number of items or high interest rate, but in other cases auctions are close to optimal and significantly more robust.