serve price but cannot commit to not re-auction the good in the future when no
current bids exceed the reserve price. Assuming a fixed auction mechanism, they
demonstrate that as the lag before potential re-auction becomes short, the se-
quentially optimal (given re-auctioning) reserve-price produces the same expected
revenue as an auction with a reserve price equal to the seller’s valuation of the
good.
McAdams and Schwarz (2006) study the first-price auction with a seller tempted
to take further rounds of bids. The rational buyers will then prefer to wait before
making their best and final offers which induces the seller to bargain at length
with buyers. When the seller’s cost of soliciting another round of offers is very
small, the resulting equilibrium resembles that of the English auction.
Bester and Strausz (2001) and Skreta (2006) take a different route by allowing
only two rounds. However, now the second stage mechanism need not be fixed.
Bester and Strausz show that in the one buyer case the best mechanism is still
direct (however, Bester and Strausz, 2000, show that with more than one agent,
this no longer holds). But as opposed to the revelation principle, fully revealing
contracts need no longer be optimal. In Skreta’s framework, there is the additional
problem of informed principal at the second stage. Skreta (2006) shows that the
McAfee and Vincent auction is the optimal two-period mechanism for selling one
unit of a good.
Skreta (2007) is the only paper we are aware of that develops techniques of ana-
lyzing multi-stage, multi-agent mechanism design problems without commitment.
In her framework, the seller can re-auction the good if it has not been previously
sold. The innovation is that, unlike in McAfee and Vincent (1997), the seller may
employ any mechanism in way of doing this. A key assumption of Skreta’s analysis
is that there is an upper bound on the number of redesign rounds. For the sake of
a tradeoff, there is also discounting and this transforms the seller’s problem into
one of intertemporal optimization. However, the central feature of our framework
is that there is no bound on how many times the mechanism can be redesigned,
and there is no cost of waiting.8
The problem of redesign is also akin to the literature on resale in auctions
(Haile, 2000, and Zheng, 2002, are seminal contributions). Much of the focus in
this literature has been in identifying the optimal auction with resale.9 However,
this literature is fundamentally different in one respect: once the good is sold
to the buyers, the seller becomes privately informed which in general prevents
efficiency (due to Myerson and Satterthwaite, 1983). Thus the problem no longer
has the recursive structure that drives the analysis of this paper; that the design
problem and redesign problem are conceptually similar, and they should be solved
by using common principles.
Further connections to the literature are discussed in the final section.
The paper is organized as follows: Section 2 specifies the set-up and the game.
Section 3 defines the solution. The results are stated in Section 4. Section 5
8 Unlike this paper, Skreta (2007) also allows the seller to become privately informed along
the play, which is a considerable complication.
9 See especially Zheng (2002) but also Calzolari and Pavan (2006), Garratt and Troger (2006),
Pagnozzi (2007), Hafalir and Krishna (2008).