A losing bidder can still purchase the prize from the winner after
the auction. We show why a strong bidder may prefer to drop out of the
auction before the price has reached her valuation and acquire the prize
in the aftermarket: a strong bidder may be in a better bargaining
position in the aftermarket if her rival won at a relatively low price.
So it can be common knowledge that, in equilibrium, a weak bidder will
win the auction and, even without uncertainty about relative valuations,
resale will take place. The possibility of reselling to a strong bidder
attracts weak bidders to participate in the auction and raises the
seller's revenue.
1. Introduction
* Before the UK "third-generation" (3G) mobile-phone
licenses auction in 2000, it was known that one of the bidders, Orange,
was going to be sold after the auction. (1) All other potential buyers
knew that, provided Orange was among the winning firms, even if they
lost the auction, they could still obtain a license by acquiring Orange.
This is indeed what happened: NTL, a consortium controlled by France
Telecom, first raised the auction price and then dropped out, allowing
Orange to win one of the licenses on sale. (2) After the auction, France
Telecom took over Orange. Similarly, after the European 3G auctions,
Telia, the biggest telecom company in northern Europe, took over Sonera,
a smaller and debt-burdened telecom company, and obtained the licenses
that Sonera had won in Germany, Italy, Spain, and Norway.
Winning an auction is not the only chance for a potential buyer to
acquire the object on sale. A losing bidder can also obtain the prize
after the auction, by purchasing it from a winning bidder. A weak (i.e.,
low-value) bidder then has an incentive to bid more than his valuation
of the auction prize, in order to win and later resell to a strong
(i.e., high-value) bidder. And a strong bidder has a choice between
outbidding her competitor during the auction, and letting him win the
auction and then purchasing the prize in the aftermarket. (3)
It may be expected that a stronger bidder always prefers to raise
the auction price in order to weaken her competitor, and so be able to
purchase the prize cheaply after the auction. Furthermore, as a weak
bidder knows that the price will rise until his surplus is reduced to
zero, it may be expected that he never wants to participate in the
auction at all. Neither of these statements is necessarily true,
however. We will show that, when wealth constraints matter, a strong
bidder is in a better bargaining position in the resale market if the
weak bidder has won at a low rather than high price. Therefore, even the
weak bidder has an incentive to participate in the auction and bid
aggressively, as he knows that the strong bidder will let him win at a
low price, rather than outbid him. (4)
The reason is that, when a project with uncertain value is on sale,
a wealth-constrained bidder enjoys limited liability (as he cannot lose
more than his wealth) and treats the auction prize as an option: if the
project turns out to be unprofitable, instead of continuing to invest in
it, the bidder can declare bankruptcy and liquidate his wealth. (5) Then
a very high auction price, by increasing the potential loss from bad
projects, reduces the expected profit of a strong bidder more than the
expected profit of a weak and wealth-constrained bidder, and hence
reduces the strong bidder's surplus in the resale market.
Therefore, in order to purchase in the aftermarket, during the auction
the strong bidder does not bid above a certain price, thus allowing the
weak bidder to win.
So it can be common knowledge that resale will take place after the
auction, even if the order of bidders' valuations--and the fact
that the order will not change--is commonly known.
However, there are also reasons why a strong bidder may prefer to
raise the auction price at least some distance before dropping out. If a
wealth-constrained bidder has to pay a borrowing cost to finance his
bid, a higher auction price reduces his profit by a greater amount, and
improves the strong bidder's bargaining position in the resale
market. So the presence of a borrowing cost pins down a particular price
at which the strong bidder chooses to drop out of the auction.
Our broader point is that, when bargaining in the resale market is
affected by the price paid by the auction winner, the share of the
resale surplus that a strong bidder can appropriate depends on the
auction price, and hence a strong bidder is not indifferent about the
price her rival pays in the auction. (6) The reasons we explore for this
are wealth effects due to limited liability and borrowing cost, but the
point is more general. For example, when bidding against a risk-averse
rival, a strong bidder may want to raise the auction price if, by
reducing the winner's residual wealth, this reduces her
rival's bargaining power in the resale market. Or, if the managers
of a weak firm are willing to resell the prize at a fixed markup over
the auction price (to justify their strategy with shareholders), then a
strong bidder may want to drop out of the auction at a lower price, in
order to purchase the prize more cheaply from the winner.
Of course, if valuations change after the auction, resale can occur
when another potential buyer turns out to have a higher valuation than
the winner. This may happen because additional buyers appear after the
auction (as in Milgrom, 1987; Bikhchandani and Huang, 1989; Haile, 1999;
Bose and Deltas, 1999), or because bidders' valuations change after
the auction (as in Haile, 2000, 2001, 2003). (7) By contrast, in our
model, the uncertain component of the prize's value is common to
all bidders, and all potential buyers can participate in the auction.
Therefore, the ex post efficient allocation is known before the auction
starts. So resale in our model does not arise because of unexpected
gains from trade: even with complete information about bidders'
valuations, resale may take place in equilibrium. (8) Moreover, our
results do not depend on any bidder entering the auction or dropping out
of the auction when indifferent about doing so--in our model, resale
arises even with bidding and resale costs.
Garratt and Troger (2006) show that, even without valuations
changing after the auction, in a second-price auction there are
equilibria in which a weak bidder who has no value for the prize bids a
high price (expecting not to pay it) and induces a strong bidder to bid
zero, so that the weak bidder wins the auction at price zero and then
resells at a profit to the strong bidder. (9) However, in contrast to
our model, these equilibria are not unique and rely upon the weak bidder
bidding a price higher than the maximum price he would be happy to pay
(even after taking into account the surplus he can obtain in the resale
market).
Resale increases the seller's revenue by giving even bidders
who know they are weak a chance to win the auction, and hence an
incentive to participate and bid aggressively. By contrast, resale was
not allowed in some of the European 3G mobile-phone license auctions,
possibly costing the governments billions of dollars. (10)
Whether resale takes place depends on the borrowing cost and on the
weak bidder's initial wealth. A high borrowing cost makes a weak
bidder unwilling to bid aggressively, because it reduces his profit when
he does not declare bankruptcy. This makes resale harder. And a high
initial wealth reduces the effect of limited liability, because it
increases the loss of the weak bidder in case of bankruptcy. This also
makes resale harder. Therefore, to induce a resale equilibrium, the
seller may want to reduce the weak bidder's wealth or improve the
terms on which he can finance his bid. (11)
The rest of the article is organized as follows. A numerical
example is analyzed in the next section. Section 3 presents the model
and discusses the effects of a wealth constraint on a bidder's
profit. Section 4 proves that a strong bidder may prefer to drop out of
an auction against a weaker competit