Optimal Dynamic Auctions for Revenue Management

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.