Sequential auction

A sequential auction is an auction in which several items are sold, one after the other, to the same group of potential buyers. In a sequential first-price auction (SAFP), each individual item is sold using a first price auction, while in a sequential second-price auction (SASP), each individual item is sold using a second price auction.

A sequential auction differs from a combinatorial auction, in which many items are auctioned simultaneously and the agents can bid on bundles of items. A sequential auction is much simpler to implement and more common in practice. However, the bidders in each auction know that there are going to be future auctions, and this may affect their strategic considerations. Here are some examples.

Example 1.^[1] There are two items for sale and two potential buyers: Alice and Bob, with the following valuations:

• Alice values each item as 5, and both items as 10 (i.e., her valuation is additive).
• Bob values each item as 4, and both items as 4 (i.e., his valuation is unit demand).

In a SASP, each item is put to a second-price-auction. Usually, such auction is a truthful mechanism, so if each item is sold in isolation, Alice wins both items and pays 4 for each item, her total payment is 4+4=8 and her net utility is 5 + 5 − 8 = 2. But, if Alice knows Bob's valuations, she has a better strategy: she can let Bob win the first item (e.g. by bidding 0). Then, Bob will not participate in the second auction at all, so Alice will win the second item and pay 0, and her net utility will be 5 − 0 = 5.

A similar outcome happens in a SAFP. If each item is sold in isolation, there is a Nash equilibrium in which Alice bids slightly above 4 and wins, and her net utility is slightly below 2. But, if Alice knows Bob's valuations, she can deviate to a strategy that lets Bob win in the first round so that in the second round she can win for a price slightly above 0.

Example 2.^[2] Multiple identical objects are auctioned, and the agents have budget constraints. It may be advantageous for a bidder to bid aggressively on one object with a view to raising the price paid by his rival and depleting his budget so that the second object may then be obtained at a lower price. In effect, a bidder may wish to “raise a rival’s costs” in one market in order to gain advantage in another. Such considerations seem to have played a significant role in the auctions for radio spectrum licenses conducted by the Federal Communications Commission. Assessment of rival bidders’ budget constraints was a primary component of the pre-bidding preparation of GTE’s bidding team.