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A copy of this paper, and related work, is at
www.nuff.ox.ac.uk/economics/people/klemperer.htm
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\ \quad
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{\bf \ Auctions with Almost Common Values: }%
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{\bf The ``Wallet Game'' and its Applications}%
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{\bf \ \ }%
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(Invited Lecture to {\it European Economic Association} 1997 Congress)
Published in {\it European Economic Review }1998, 42(3-5), 757-69, May.
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Paul Klemperer%
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Nuffield College, Oxford University
Oxford OX1 1NF
England%
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Int Tel: +44 1865 278588
Int Fax: +44 1865 278557%
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email: paul.klemperer@economics.ox.ac.uk
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September 1997
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{\bf Abstract}
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We use a classroom game, the ``Wallet Game'', to show that slight
asymmetries between bidders can have very large effects on prices in
standard ascending (i.e. English) auctions of common-values objects.
Examples of small asymmetries are a small value advantage for one bidder or
a small ownership of the object by one bidder. The effects of these
asymmetries are greatly exarcabated by entry costs or bidding costs. We
discuss applications to Airwaves Auctions and Takeover Battles including the
Glaxo-Wellcome Merger. [82 words]%
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{\it Acknowledgment:} Some of the work reported here (especially section 4)
is based on joint work with Jeremy Bulow and Ming Huang. Part of it is based
on my March 1995 discussant's comments on Paul Milgrom's Marshall Lectures.
All of it has benefitted from extensive discussions with Jeremy Bulow.
Thanks are also due to Chris Avery, Tim Harford, Meg Meyer, Hyun Shin, and
other colleagues for helpful suggestions.%
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{\bf Keywords:} Auction theory, common values, winner's curse, takeovers,
mergers, corporate acquisitions, PCS auction, spectrum auction, airwaves
auction.%
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{\bf JEL Nos:} D44 (Auctions), G34 (Mergers, Acquisitions etc.), L96
(Telecommunications).\smallskip
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\section{Introduction}
In most auctions in practice, there are at least slight asymmetries between
bidders. For example, in a takeover battle the target company may have
slightly more synergy with one potential acquirer than with another.
Alternatively, one potential acquirer may already own a small stake in the
company. Or one potential acquirer may have a reputation for aggressive
bidding.
We will show that small asymmetries such as these can crucially affect who
wins, and at what price, in standard ascending auctions for common-value
objects. An apparently small advantage can greatly increase a bidder's
probability of winning, and greatly reduce the price he pays when he wins,
so these small asymmetries are also very bad news for sellers. Furthermore,
the effects of these asymmetries are magnified by bidding costs or entry
costs.
A common-value object is one that has the same actual value to each bidder,
even though different bidders may have access to different information about
what that actual value is. The most obvious examples are financial assets,
but oilfields are another frequently cited example. A takeover target has a
common value if the bidders are financial acquirers (e.g. LBO firms) who
will follow similar management strategies if successful. The Personal
Communications Spectrum (PCS) licenses sold by the U.S. Government in the
1995 ``Airwaves Auction'' probably also had very similar values to each of
the telecommunications companies that were bidding for them, even though
there was enormous uncertainty about what those values were.
However, although simple theory might treat all these examples as pure
common values, in practice there are typically small asymmetries between
bidders. We will refer to these auctions with small asymmetries as ``{\it %
almost }common value'' auctions, and will show that the distinction between
pure common values and almost common values is critical.
The intuition is that giving a bidder a slight advantage, e.g. a slightly
higher value when he wins, makes him bid a little more aggressively. While
this direct effect may be small, there is a large indirect effect in an
(almost) common-values auction. The bidder's competitors face an increased
``winner's curse'' (that is, it is more dangerous for them to win an auction
against an opponent who is bidding more aggressively). So the competitors
must bid more conservatively. So the advantaged bidder has a reduced
winner's curse and can bid more aggressively still, and so on. In
consequence, an apparently small edge for one bidder translates into a very
large competitive advantage in an ascending common-values auction.
We begin in section 2 by discussing a classroom example, the ``Wallet
Game'', which readers may wish to try in their own teaching, and then use it
to explain some recent auction outcomes. Section 3 discusses the Airwaves
Auction, Section 4 discusses takeover battles with ``toeholds'', and Section
5 discusses the 1995 Glaxo-Wellcome merger. These case studies suggest that
``almost common values'', that is, small asymmetries between bidders in an
otherwise common value setting, can be disastrous for revenues in an
ascending auction. So in section 6 we briefly discuss how a seller should
run an ``almost common values'' sale. Section 7 concludes.
\section{A Classroom Example: The Wallet Game}
Select two students, and have each privately check how much money is in his
or her wallet. Now announce that you will auction a prize equal to the
combined contents of the wallets to these two students using a standard
ascending (English) auction. That is, you will continuously raise the price
until one of the students quits the bidding, and you will then pay the other
student an amount equal to the combined contents of the wallets, in return
for the student paying you that final price.\footnote{%
If these stakes are too large for comfort, restrict the exercise to only the
low-denomination bills and coins in the wallets.}
Thus each student $i=1,2$ knows the amount $t_{i}$ of money in his or her
own wallet, and they are bidding for a prize of common value $v=t_{1}+t_{2}.$
How should the students bid?
It is easy to demonstrate that it is an equilibrium for each student $i$ to
remain in the bidding up to a price of $2t_{i}$: Given that the opponent
follows the same strategy, a student who wins at price $p$ knows that the
actual value is $v=t_{i}+\frac{p}{2}$ which is greater than $p$ iff $%
p<2t_{i}.$ So $i$ is pleased to be a winner at any price up to $2t_{i},$ but
would lose money if he ``won'' the auction at any higher price. In fact this
is the unique symmetric equilibrium.\footnote{%
Note that this equilibrium is independent of the distribution of the
signals, $t_{i}$ and $t_{j}$, and does not require that the distributions be
symmetric. (When we refer to this as the symmetric equilibrium, we mean only
that the strategies are symmetric functions of the signals.) Nor is the
equilibrium affected by risk-aversion.}
Note that players take account of the {\it winner's curse} in this
equilibrium. Conditional on the price having reached $2t_{i},$ $i$ knows
that the expected value of the prize exceeds the price, since $j$'s signal
is at least $\frac{p}{2}$ and so on average exceeds $\frac{p}{2}$. Yet
bidder $i$ must nevertheless quit, because $i$'s concern is not with the
expected value of $j$'s signal, but rather with its expected value
conditional on $i$ winning, that is just $\frac{p}{2}.$
However the symmetric equilibrium is not the only equilibrium. For example,
it is also an equilibrium for $i$ to stay in the bidding up to a price of $%
10t_{i}$ while $j$ quits at just $\frac{10}{9}t_{j}$. (If $i$ wins at $p$,
then $v=t_{i}+\frac{9p}{10}>p\Leftrightarrow p<10t_{i}$ while if $j$ wins at
$p$ then $v=t_{j}+\frac{p}{10}>p\Leftrightarrow p<\frac{10}{9}t_{j}.$%
\footnote{%
It is easy to construct a continuum of other asymmetric equilibria. To see
why, assume that at price $p$ bidder $i$ will quit if $t_{i}\leq \underline{t%
}_{i}(p)$. The first-order condition for $i$ is $\underline{t}_{i}(p)=p-%
\underline{t}_{j}(p)$ (because if $\underline{t}_{i}(p)p-\underline{t}_{j}(p)$ then type $\underline{t}_{i}$ would make
money if $j$ quits now so type $\underline{t}_{i}$ should stay in a little
longer). Similarly the first-order condition for $j$ is $\underline{t}%
_{j}(p)=p-\underline{t}_{i}(p).$ Since these first-order conditions are the
same, they cannot uniquely determine $\underline{t}_{i}(p).$ Hence for any
strictly increasing continuous functions $\phi _{1}(t_{1})$ and $\phi
_{2}(t_{2}),$ there is an equilibrium in which the marginal types who quit
at any price satisfy $\phi _{1}(t_{1})=\phi _{2}(t_{2}).$ See Milgrom (1981)
(who first noted this multiplicity) for more details.}) In this equilibrium
player $i$ wins a very high fraction of the time, and at any given price at
which he wins he finds more money in $j$'s wallet, so he makes more money,
than in the symmetric equilibrium. However player $j$ wins much less often,
and finds less money in $i$'s wallet when he does win, so he is worse off,
and the seller is also generally made much worse off.\footnote{%
Intuitively, the seller is worse off because player $j$ usually loses
quickly at a low price because each of $j$'s types is bidding so much less.
In this example, if the players' signals are both drawn from the same
uniform distribution starting at zero, $j$ loses 94\% of the time and the
seller's expected revenue is 20\% lower than in the symmetric equilibrium.
For general results about when the seller is made worse off, see Bulow and
Klemperer (1996) and also Bulow and Klemperer (1997) who emphasise that
there are, however, some cases in which the seller is not worse off.} Thus
the pure common-value game has many equilibria which have very different
properties. It should not therefore be a surprise that there are ``almost
common-value'' games that are close to this game and have equilibria that
are close to very asymmetric equilibria of this game. (And the equilibria of
these ``almost common-value'' games are often unique.)
In the following sections we will discuss applications to auctions that are
almost common values; each can be illustrated by a tiny modification of the
Wallet Game, but the outcome of each is very different from the symmetric
equilibrium of the Wallet Game.
\section{Small private value advantages: the Airwaves Auction}
Consider the sale of the Los Angeles PCS license in the Airwaves Auction.
While the license's value was very hard to estimate, it was probably worth
very similar amounts to several bidders, except that one bidder, Pacific
Telephone, had a small but distinct advantage. Pacific Telephone already had
a database on potential local customers for the new services, its brand-name
was already well known, and its executives were familiar with California.%
\footnote{%
Pacific Telephone also had no wireless properties prior to the auction, so
had a strategic reason to enter the market as a hedge against its declining
wireline business. There might also be other small economies of scope
between the wireless and wireline businesses.} The situation was thus well
illustrated by the Wallet Game, with the small difference that if player 1
(representing Pacific Telephone) wins the auction he earns a small bonus
prize.\footnote{%
Although many licenses were for sale simultaneously in the Airwaves Auction,
the situation for a single license such as Los Angeles was very similar to
that of the Wallet Game, i.e. a standard ascending auction for a single
object.} (Player 2 receives no bonus for winning.)
How would a small bonus, say \pounds 1 in the Wallet Game, affect the
bidding? The answer is that player 1 {\it always} wins in equilibrium. The
intuition is clear. At any price at which player 2 wins the auction, player
1 would make more money than player 2 makes by winning, so if player 2 is
willing to stay, then player 1 strictly prefers not to quit. Another way to
see this is that since player 1 earns a \pounds 1 bonus by winning, player 1
will bid \pounds 1 more aggressively than before for any given behaviour of
player 2, i.e. 1 bids as if his signal is $t_{1}+$\pounds 1. But this
magnifies player 2's {\it winner's curse}. When 2 wins against 1 at any
given price, 2 will find \pounds 1 less money in 1's wallet. So 2 must bid
more cautiously, as if his signal is $t_{2}-$\pounds 1. But this reduces 1's
winner's curse. He will now find \pounds 1 more in 2's wallet at any given
price at which 2 quits. So 1 actually bids \pounds 2 more aggressively,
magnifying 2's winner's curse further, so 2 bids \pounds 2 more
conservatively, etc. So in equilibrium 2 cannot bid beyond the amount in his
own wallet, $t_{2}$. Player 1 always stays in until player 2 quits, and so
always wins.\footnote{%
This equilibrium (which was noted in Bikhchandani (1988)) corresponds to an
extreme asymmetric equilibrium among those described in the previous
section. Each of the equilibria described there (see note 3) can be obtained
by allowing 1 to receive a private value ``bonus'' of $K\phi _{1}(t_{1})$
contingent on winning, while 2 would receive $K\phi _{2}(t_{2})$ contingent
on winning, and then letting $K$ be arbitrarily small. Furthermore in the
modified game the equilibria are the unique perfect Bayesian equilibria if
the $t_{i}$ have finite support. Thus we have selected here the equilibrium
obtained by taking $\phi _{1}(\cdot )$ arbitrarily large relative to $\phi
_{2}(\cdot )$.},\footnote{%
A more formal way to see the result is to use iterated deletion of dominated
strategies: if 1's maximum signal is $\overline{t}$, then 2 should never bid
more than $t_{2}+$ $\overline{t}$ so, after eliminating strategies of 2 that
bid more than this, 1's type $t_{1}=$ $\overline{t}-1$ should stay in
forever, so 2 should never bid more than $t_{2}+$ $\overline{t}-1$, so 1's
type $t_{1}=$ $\overline{t}-2$ should stay in forever, etc.},\footnote{%
Avery and Kagel (1997) have experimentally investigated sealed-bid
second-price auctions in this context. Since these auctions are
strategically equivalent to ascending auctions (with two bidders) the
equilibria are identical, although experimental subjects often respond
differently to the two auction forms.}
What happened in the Airwaves Auction? Pacific Telephone indeed won the Los
Angeles license, and at a price that most commentators thought was very low.%
\footnote{%
The price for the single Los Angeles license was \$26 per head of
population. Compare this with Chicago where two licenses were sold for \$31
per head of population. Yet most commentators thought LA's demographics were
superior to Chicago's (Southern Californians are characterised as rich,
loving new toys like portable phones, and spending much of their time stuck
on highways with little else to do than phone), so that LA should have
yielded the higher price.
\par
Perhaps the surprise is that the Los Angeles price wasn't even worse than it
was. One reason is that even bidders who know they are going to lose may
have incentives to bid. Bidding may force the ultimate winner to pay more
and so make him a weaker competitor in other auctions, and the Airwaves
Auction rules meant that bidding on one license allowed you to delay
``showing your hand'' about which other licenses you might be interested in.}%
,\footnote{%
A similar situation developed in New York, and its license was also sold
rather cheaply (\$17 per head of population).}
\section{Small ownership advantages: Takeovers with Toeholds}
Takeover battles are essentially ascending auctions and are often close to
common values, especially when the contestants are ``financial bidders''
such as LBO firms who would manage the target company in similar ways.
However it is common for one or more bidders to have a small ownership
stake, or ``toehold'', in the target prior to the auction. Assume initially
just one bidder has such a toehold of (small) size $\theta .$ Then the
situation is well modelled by the Wallet Game with the difference that
player 1 (representing the toeholder) receives fraction $\theta $ of the
wallets' sale price.
How would player 1 receiving a small fraction of the revenues affect the
bidding in the Wallet Game? The answer, again, is that player 1 {\it always}
wins in equilibrium. The reason is that player 1 has incentive to stay in
the bidding a little longer than if he had no ownership stake, because doing
so pushes up the price at which the wallets are sold.\footnote{%
Absent an ownership stake, player 1 would quit where he would expect to make
no profit as a winner at the current price. Bidding the price up $%
\varepsilon $ further earns him fraction $\theta $ of the additional $%
\varepsilon $ with probability close to 1, for small $\varepsilon $, but
with small probability $o(\varepsilon )$ he ``wins'' the auction and so
loses $(1-\theta )\varepsilon $. Since $\theta \varepsilon >(1-\theta
)\varepsilon o(\varepsilon )$ for sufficiently small $\varepsilon ,$ for any
$\theta ,$ player 1 always bids a little more aggresively than without the
ownership stake.} This magnifies 2's winner's curse (2 will find less money
in 1's wallet at any given winning price), so 2 must quit earlier,
alleviating 1's winner's curse so 1 can bid yet more aggressively, etc. As
in the case where 1 has a small private value advantage, if only 1 has a
``toehold'' then 2 cannot in equilibrium bid beyond his own signal, $t_{2}$,
while player 1 stays in until 2 quits and player 1 always wins. Bulow, Huang
and Klemperer (1997) show that even when both players have toeholds, the
player with the larger toehold has a very substantial advantage even when
both toeholds are arbitrarily small (though the player with the larger
toehold does not always win).
In fact, there is substantial empirical evidence that ownership of a toehold
increases a bidder's chance of winning a contested takeover battle, and also
some evidence that having a toehold may reduce the price the winning bidder
pays.\footnote{%
See Walkling (1985), Betton and Eckbo (1995) and Bulow, Huang, and Klemperer
(1997) for details.}
The same point---that one bidder's small ownership advantage may both
greatly increase that bidder's probability of winning, and also reduce the
price he pays---also applies in other settings. One currently topical
application is to the sale of ``stranded assets'' by public utilities. In
these sales of assets that are worth far less than book value, state public
utilities commissions promise to reimburse utilities' shareholders a
fraction $(1-\theta )$ of the difference between the asset's sale price and
the book value, so the utility effectively has an ownership stake of $\theta
$ of the auctioned asset.\footnote{%
That is the utility is \pounds $\theta $ better off if the asset is sold to
someone else for \pounds 1 more, and is only $\pounds (1-\theta )$ worse off
if it must bid an extra \pounds 1 to win the auction, so the utility's
position is strategically identical to owning fraction $\theta $ in our
model.} Other applications include the sharing of profits in bidding rings,
creditors' bidding in bankruptcy auctions, and the negotiation of a
partnership's dissolution.\footnote{%
See Englebrecht-Wiggans (1994), Burkart (1995), and Cramton, Gibbons, and
Klemperer (1987), respectively, for these three applications.}
\section{\ Small bidding costs: the Glaxo-Wellcome Merger}
In the preceding examples, if player 1 is known to have a higher actual
value or to have the only ownership stake, player 2 never wins. More
generally, e.g. if player 2 also has an ownership stake but a smaller one
than 1's, or player 2 also has a private value but probably a smaller one
than 1's,\footnote{%
Consider, for example, the model $v_{1}=(1+\alpha _{1})t_{1}+t_{2},\quad
v_{2}=t_{1}+(1+\alpha _{2})t_{2}$ where $\alpha _{1}>\alpha _{2}$ so 1's
private value component, $\alpha _{1}t_{1},$ exceeds 2's, $\alpha _{2}t_{2},$
unless 2 has a much higher signal than 1. See Bulow and Klemperer (1997) for
discussion and analysis of this kind of model.} player 2 wins rarely, and
makes very little profit even when he does win.\footnote{%
Consider the profit 2 makes conditional on winning with $t_{2}=\widehat{t}$,
versus the profit 1 makes conditional on winning with $t_{1}=\widehat{t}.$
The marginal type of 2 that would have just won when in fact $t_{2}=\widehat{%
t}$ wins, is typically higher than the marginal type of 1 that would have
just won when in fact $t_{1}=\widehat{t}$ wins (because 2 is bidding less
aggressively, so his types are quitting faster as the price rises). So 2
makes lower informational rents on average than 1 does, that is, lower
expected profits, conditional on winning.} Thus even small costs of bidding
or of entering the auction will prevent player 2 from competing at all. In
this case the final price may be even lower than in the preceding examples
in which player 2 at least stayed in the bidding up to the price $(t_{2})$
that he knew the object was worth based only on his own information. Thus
small entry or bidding costs can greatly exarcabate the effects of one
player having a small advantage in an almost common value auction.
As an application, consider Glaxo's 1995 \pounds 9 billion takeover bid for
the Wellcome drugs company (a takeover that created the world's largest
drugs group). It was probably generally believed that although the exact
value was uncertain, Wellcome was worth broadly similar amounts to each of
half a dozen major drugs companies, except that there were also particular
synergies that made Wellcome worth a little more to Glaxo than to any other
potential bidder. Thus the situation was probably that of the variant of the
Wallet Game in which one bidder has a small private value advantage. However
there were also bidding costs which were non-trivial (tens of \pounds\
millions) even though they were small compared with the stakes involved.%
\footnote{%
Glaxo's own fees were reported to be \pounds 30 million net of stamp duty.}
What happened? After Glaxo's first \pounds 9 billion bid, Wellcome solicited
higher counteroffers and received serious expressions of interest from two
potential counterbidders: it was reported that Zeneca was prepared to offer
about \pounds 10 billion if it could be sure of winning, while Roche was
considering an \pounds 11 billion offer.\footnote{%
See {\it Financial Times} 8/3/95 p. 26, 27, 32. (To be precise, the
potential bidders are described as ``understood to be Zeneca'', ``thought to
be Roche'', etc.)} The difficulty was that neither of the potential bidders
wished to enter an auction that they expected to lose.\footnote{%
This expectation had been reinforced by the fact that ``Glaxo had let it be
known that it would almost certainly top a rival bid''. ({\it Financial Times%
} 8/3/95 p.32.) See our discussion of reputation effects in Section 7.} And
the result was that neither of them actually entered the bidding. So
Wellcome was sold at the original \pounds 9 billion bid price, and its
shareholders received literally billions of pounds less than they might have.%
\footnote{%
Similarly, in the PCS Auction some potential bidders including MCI---one of
the U.S.'s largest phone companies---failed to enter the auction at all. And
there is evidence that ``greater toeholds increase the probability of a
successful single-bid contest by lowering both the chance of entry by a
rival bidder and target management resistance'' (Betton and Eckbo (1995)).}
\section{How should you sell an Almost {\bf Common Value} Object?\quad}
\subsection{\quad First-price auctions}
The previous sections suggest that standard ascending auctions may be very
unprofitable for sellers of almost common value objects, so what should
sellers do instead?
The most obvious answer is: use a first-price auction, that is, a
``sealed-bid'' auction in which each bidder independently makes a single
``best and final offer'' and the highest bidder wins the auction at the
price he bid. In this auction format bidders have no opportunity to update
their beliefs about their opponents or to condition their behaviour on their
opponents' behaviour, so cannot follow strategies such as staying in forever
until the opponent quits. So a small advantage for one player translates
only to small changes in players' bidding strategies, and the equilibrium
remains close to the first-price equilibrium of the original game.\footnote{%
The critical difference between first-price and ascending auctions is in the
indirect, or ``strategic'', effect. With ascending auctions, bidding
strategies are ``strategic substitutes'' (and very strongly so) in the
terminology introduced by Bulow, Geanakoplos and Klemperer (1985), that is,
when bidder 1 bids more, bidder 2 must bid less because conditional on
winning at any price his revenue is lower. With first-price auctions, the
indirect effect is ambiguous: when player 1 bids more, player 2 wants to bid
{\it less }on the grounds that his marginal profit when he wins is lower,
but {\it more} on the grounds that his probability of winning is lower so
increasing his bid is less costly---when bidders' signals are uniform these
effects cancel and the effect of player 1 bidding a little more is zero
where the bidding ranges coincide. Thus the logic that when 1 bids a small
amount more, 2 bids a similar amount less, so 1 bids an additional similar
amount more, so 2 bids an additional similar amount less, etc., does not
apply in first-price auctions.}Also, since even the weaker player therefore
earns reasonable profits, small entry or bidding costs have almost no
effect. Furthermore, it is a standard result that in the original game the
first-price auction (as well as the symmetric equilibrium of the ascending
auction) is seller-optimal under reasonable conditions.\footnote{%
The conditions required are that the players' signals, $t_{i},$ are
independently drawn from a common distribution, that the players are
risk-neutral, that ``marginal revenue is downward sloping '', and that the
object must be sold (see Bulow and Klemperer (1996)). See Bulow and
Klemperer (1997) for a detailed analysis of the reasonableness of these
conditions.} So the first-price auction remains close to optimal when one
player has a small advantage.\footnote{%
I do not know of any general theorem proving this. See Bulow, Huang and
Klemperer (1997) for the case of small ownership advantages, and Avery and
Kagel (1997) theorem 2.6 for an example with small private value advantages.
See Milgrom (1997) section 2 proposition 9, and Bikhchandani (1988) for
other related results.}
This result may explain why first-price auctions are typically used in many
almost-common-value settings such as the sale of oil leases.\footnote{%
In addition to the effects we have discussed, oil-lease sales involve
repeated interactions between bidders and so are also particularly
vulnerable to the reputation effects discussed in Bikhchandani (1988). See
section 7.} However there are other factors that may make simple first-price
auctions less attractive in the takeover and PCS settings we have emphasised.%
\footnote{%
Bulow and Klemperer (1997) show that rationing (as, for example in Initial
Public Offerings) may be desirable with almost common values, because
rationing reduces winners' curses by creating more winners (just as prices
seemed to be lower in some regions where one PCS license was sold relative
to many regions where two licenses were sold).}
\subsection{How to Auction the Airwaves}
In the Airwaves Auction many PCS licenses were sold using a simultaneous
ascending auction.\footnote{%
Multiple licenses are open for bidding at the same time, and remain open as
long as there is any bidding on any of them. There are also other rules
including ``activity'' rules that specify minimum bidding rates that a
bidder must satisfy to remain eligible to win licenses; these rules prevent
the auction from taking too long.
\par
The method was developed by McAfee, Milgrom and Wilson and, though we will
criticise it below, it was probably the best among the many competing
methods proposed at the time of the auction. For further details see the
excellent expositions in McAfee and McMillan (1996) and, especially, Milgrom
(1997).} This kind of auction facilitates the formation of efficient
networks, because bidders can get some sense about whether they are likely
winners on one license before committing too much money to buying related
licenses. Furthermore, it is typically more likely in an ascending auction
than in another type of auction that the bidder with the highest actual
valuation wins, which is efficient.\footnote{%
Efficiency was the stated objective of the auction.}
However, raising government revenue is also valuable in that it reduces the
need for other taxes with their associated deadweight losses. So the
deleterious effects of ascending auctions on seller revenues are important,
and although pure first-price auctions would generate very little
information to facilitate network formation, the following auction design
might have captured many of the benefits of the design actually used without
having its costs:
\begin{enumerate}
\item Run the actual auction used except allow 2 winners, i.e.
``finalists'', on each property. These finalists pay no money, but must
compete in the next stage.
\item Allocate each property by a first-price auction in which only the 2
finalists compete.\footnote{%
If there are $N$ identical (or almost identical) properties, allow $N+1$
finalists from stage 1 to compete in a sealed-bid stage 2 in which each of
the $N$ ultimate winners pays his own stage-2 bid. (For example, in the 1995
auction $N=2$ in many regions. The highest sealed-bidder would choose first
among the 2 licenses.) The design is most useful when the number of bidders
with clear advantages is $N.$} They must bid at least their final stage-1
bids.\footnote{%
The order of the stage-2 allocation is probably not critical. It could, for
example, be highest-priced stage-1 property first.}
\end{enumerate}
Note that running the second stage as a first-price auction overcomes the
problems this paper has emphasised by giving weaker bidders a reason to
enter and stay in the auction.\footnote{%
In the actual auction some important potential bidders failed to enter the
auction at all. See note 21.} It is possible that using this mechanism even
some of the stage-1 prices, let alone the ultimate prices, could have been
higher than the prices actually achieved by the existing design.
Of course, the proposed design is constructed with the benefit of hindsight.
It must also be emphasised that the optimal design choice for any future
auction would also be affected by situation-specific details we have not
discussed here.\footnote{%
The proposed design also has the advantage of reducing the risk of bidders
colluding. Furthermore, if bidders are risk-averse this increases its
profitability relative to that of the design actually used. Finally, it also
captures most of the benefits that an ascending auction captures when there
is affiliation (see Milgrom and Weber (1982)). In general, it works badly
only if (i) network effects are very important (there is a greater risk of
complementary properties being won by different bidders under this design)
{\it and} resale markets are very inefficient, or (ii) government revenue is
much less important than allocating the licenses to the highest-value users
{\it and} resale markets are very inefficient. However, the existing design
now has the advantage of having been tested and refined in practice, and the
problems discussed in this paper may be mitigated by an appropriate choice
of the numbers and sizes of the licenses to be auctioned.
\par
Some additional issues about the design are discussed in Bulow and Klemperer
(1997).}
\subsection{How to Sell a Company\protect\footnote{%
Obviously, space permits only the briefest analysis, focusing on avoiding
the problems pointed out in this paper.}}
The potential problem with selling a company through a first-price auction
is one of credibility: can management credibly commit to accept the highest
bid and refuse to consider higher subsequent offers?\footnote{%
Although the expected value of the winning first-price bid exceeds the
expected price from an ascending auction in our context, the actual winning
first-price bid will typically be below the runner-up's willingness to pay
after the runner-up has observed that bid, in which case the runner-up may
be willing to make another bid. See Burrough and Helyar (1990) for an
amusing account of the takeover battle for RJR Nabisco which included
several successive supposedly-final first-price auctions for the company.}
It may be legally difficult to do so, and directors may also be very
reluctant to face a possible stockholder law suit asking why they are
refusing to consider higher offers.
One way around the credibility problem may be to run a first-price auction
and award the winner a ``break-up fee'',\footnote{%
This is a fee that is payable to the winner of the first auction in the
event that it does not ultimately win the company.} options to buy stock, or
options to purchase some of the company's divisions on favourable terms;
this may make it unprofitable for any other bidder to enter a higher
subsequent bid. Thus our analysis can justify the use of ``lock-up''
provisions to support the credibility of a first-price auction.
If running a first-price auction is too difficult (e.g. lock-up provisions
may themselves be legally vulnerable), a second strategy is to try to
``level the playing field'' between unequal bidders by, e.g., selling a
small ownership stake, or equivalently options, to the weaker bidder so that
the bidders can compete on more equal terms in a standard ascending auction.%
\footnote{%
See Bulow, Huang and Klemperer (1997) for further analysis of this
possibility. Note that having options with an exercise price below the
current bidding level is strategically equivalent to having a small
ownership stake.} Finally, it may be possible to directly compensate a
second bidder for entering an auction, or for competing more aggressively in
it.\footnote{%
For example, Bell South was paid \$54 million for entering the takeover
battle for LIN Broadcasting in competition with Craig McCaw. (See {\it %
Economist} 15/6/96, p.83.)} Thus our analysis can justify offering
inducements to a ``white-knight'' to enter the bidding.\footnote{%
Of course the favoured white knight must be the weaker bidder.},\footnote{%
Why, then, did Wellcome offer no inducements to another potential bidder to
compete with Glaxo (including the possibility of accepting the ``lock-up''
bid of about \pounds 10 billion that Zeneca is thought to have offered)? In
this case it may not have been legally possible. In particular, Wellcome's
largest shareholder (the Wellcome Trust) had obtained Glaxo's original bid
in return for an undertaking not to encourage another bidder (though the
Wellcome Trust retained the ability to accept a higher offer). See {\it %
Financial Times }8/3/95, p.32. Thus with almost common values, committing to
an ascending auction may make it easier to obtain the original offer that
puts a company into play, at the expense of obtaining the best price for the
company after the first bid has been made.}
\section{\protect\smallskip \protect\smallskip Conclusion}
We have shown that the outcomes of standard auctions are highly sensitive to
small asymmetries between bidders in (almost) common value settings. We have
emphasised small value advantages, small ownership shares, and small entry
costs, but in any real problem there may be a number of other ``small''
features that may lead to very bad outcomes for a seller. For example, if
your opponent is cash-constrained and will be a weaker competitor in the
future if he pays a higher price now, then this may give you a small
incentive to push up the price a little further today, and be strategically
equivalent to a small value or ownership advantage. Reputation effects may
also be critical. We have already seen that even in the completely symmetric
case, asymmetric equilibria can be supported simply by the more aggressive
player believing that his opponent will be less aggressive, and vice versa.
Bikhchandani (1988) showed that in repeated common-value auctions it may be
very easy to develop reputations that support very asymmetric outcomes;
bidding a little more aggressively today is rational if it reinforces the
bidder's reputation for aggressive behaviour tomorrow.
The immediate moral is that a standard ascending auction may be a very
dangerous choice for a seller in an almost common value setting. A wider
moral is that auction theory ought to pay more attention to bidder
asymmetries. We have spent too long on the symmetric case just because it is
easier.\footnote{%
Honourable exceptions, in addition to those papers already mentioned,
include Maskin and Riley (1996) and Riley and Li (1997) who have done
important work on asymmetric private value auctions. Stevens (1994) analyses
asymmetric private value auctions among firms for workers. However small
bidder advantages generally have only small effects in private value
auctions, at least when there are no entry or bidding costs. When bidders
must pay entry costs, Gilbert and Klemperer (1997) show bidder asymmetries
can make rationing (i.e. an ex-post inefficient auction) more attractive to
a seller than market-clearing (which corresponds to the outcome of an
ascending auction).}%
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{\bf References}%
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