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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 |
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