Optimal
dynamic auctions for revenue management
Gustavo Vulcano, Garrett van Ryzin and Costis
Maglaras,
Appeared in Management Science, 48(11):
1388-1407.
Abstract:
We consider a variation of the traditional single-leg,
multi-period revenue management problem in which consumers act strategically
and bid for units of a fixed capacity over time. Buyers compete directly
against each other within a period as in a traditional auction and indirectly
with bidders in other periods through the opportunity cost of capacity assessed
by the seller. The number of bidders in each period, as well as the individual
bidders' valuations, are random. For this setting, we prove that dynamic
variants of the first-price and second-price auction mechanisms maximize the
seller's expected revenue. We also show explicitly how to compute and implement
these optimal mechanisms.
The optimal mechanisms are compared to a stylized
version of a traditional revenue management mechanism, in which list prices are
used in each period together with capacity controls. The traditional revenue
management mechanism is proven to be optimal in the limiting cases when there
is at most one bidder per period or asymptotically when the number of bidders
and units to be sold grows large. For other cases, numerical comparisons show
that the revenue benefits from an optimal mechanism increase as 1) the number
of bidders per period increases, 2) the total number of bidders relative to
capacity is moderate or large, 3) the dispersion in buyers' valuations
increases, and 4) the variability in the number of bidders per period
increases. These results suggest that heterogeneity in buyers' valuations, an
ability to aggregate buyers into a small number of bidding periods and/or some
level of scarcity in the goods are required to achieve significant gains from
the use of an optimal auction mechanism.
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