Inefficient Corporate Takeovers
under
Multidimensional Signals
Jeongsun Yun
Kookmin University
Motivation
•
•
Control contests are an important feature in the market for
corporate controls

Management in control may refuse to negotiate

Multiple managements may compete for the control of one
target firm
Factors such as incomplete information may affect outcomes of
control contests

Hubris – overconfident management overestimates the value
of the merged company

Toeholds – toeholders prone to overbidding

Competition among multiple bidders
2
Motivation
•
One of the most provocative issues regarding control contests
under incomplete information is whether the target company is
acquired by the most efficient management

Most of previous works point to ex ante asymmetry among
bidders as the driving force of the inefficient takeovers
such as toeholds and hubris

While it has largely remained unexplored how inefficient
takeovers arise in the literature of M&As, auction theory
suggests that incomplete but symmetric information may
drive inefficient allocation of objects on an auction
3
Motivation
•
•
Auction theory suggests that an inefficient allocation of an
object on an auction arises if bidders are subject to
multidimensional signals

The value of the object is the sum of the common and
private values

Bidders have only symmetric but incomplete information
about the common value while they have private
information regarding their own private values
Inefficient allocations arise because a bidder with the lower
private value may win the contest if it has a higher common
value signal

It remains uncertain after the contest whether the winner
has the highest private value or the highest common value
signal
4
Motivation
•
•
Models of auction theory focus on analyzing how inefficient
allocations can be prevented

Inefficient allocations can be prevented if there are many
competitors

In the takeover markets, however, competitors are rare
On the other hand, those models fail to predict how the
frequency of inefficient takeovers is determined
5
Purpose of the paper
•
•
Provide a framework in which incomplete information
regarding the synergy of acquisitions drives inefficient
takeovers on the basis of auction theory

Bidders have private information on their private values

An important feature of our model is that bidders observe a
noisy signal of the common value

Show that inefficient takeovers may arise if a bidder with a
low private value observes a high common value signal
Investigate how often inefficient takeovers arise

Show that the probability of inefficient takeovers is a
function of the precision of information on common value

In particular, there is a non-monotonic relationship
between the two
6
Conclusions
•
The target firm may be acquired inefficiently if the noisy signal of
the common value is sufficiently precise

Takeovers are efficient only if a bidder with a highest private
value wins the contest

However, this may not hold if information on the common
value is sufficiently precise that the conditional expectation of
value of the firm given a high common value signal is higher
than that of the value given a low common value signal
regardless of the private value

We show that inefficient takeovers arise with a positive
probability if information is sufficiently precise
7
Conclusions
•
The probability of inefficient takeovers does not monotonically
decrease or increase in information precision

Inefficient takeovers arise only if information regarding the
common value is sufficiently precise

Furthermore, the probability decreases the more precise
information is since it is less likely that bidders observe
different signals

Therefore, the probability of inefficient takeovers is strictly
positive only if information is sufficiently precise and
decreases the more precise it is

On the other hand, however, inefficient takeovers are not
observed if information is not sufficiently precise

This suggests that the probability of inefficient takeovers is a
non-monotonic function of information
precision
8
Model
•
•
Market for control

A target firm – normalized to be of no value

Competing managements – i  {1,2}
Synergy of acquisition

Depends on both managements (private value : c i ) in
control and states of nature (common value: v )

The private and common values are independent of each
other

The value of the target firm under the control of management
i is the sum of private and common values
V ( , i )  c i  v
9
Model
•
The Common Value
1. Common value depends on the state of nature 
where   {g , b}
2. Given, the common value is denoted by
where v g  vb
v
3.  is equally likely
•
The Private value
1. Private value is a binary random variable with probabilty ½
c i {0, c}
2. Private values are independent of each other and of common
value
10
Model
•
Private value

Private value
c i is private information of management i
c i {0, c}
•

c s are equally likely and independent of 

c i andc j are independent of each other
i
Private value determines which management is more efficient

The common value does not depend on the management in
control

Therefore, the management with the highest private value is
the most efficient
11
Information structure
•
Common value



 is not observable by any parties
Management i observes a noisy signal s i of 
1
i
where Pr( s   |  )   ,    1
2
i
For given s , the common value is
v( s i  g )  vg  (1   )vb
•
Estimation of the common value depends on 

For given v( s i  g ) increases as  increases

This implies that the more precise information regarding the
common value , the estimation of the common value given
high signal increases while that of the common value given
low signal decreases
12
Properties of a noisy signal
•
Probability that bidders observe the same signal
Pr( s i  g | s j  g )  


•
2
 (1   ) 2
Conditional probability that one bidder observes g is greater
if its opponent observes g as  increases because 1    1
2
This implies that as  increases, bidding managements are
more likely to observe the same signal
An important difference of our model from previous models of
auctions lies in that bidders information is correlated while in
previous models bidders observe mutually independent signals

Furthermore, the correlation increases the more precise
information is
13
Noisy Signal and the Common Value
•
Aggregated information ( s1 , s 2 ) and the common value

Were aggregated information observable, the common value
would be estimated as follows
2
v( g , g ) 
v(b, b) 
vg 
 2  (1 ) 2
(1 ) 2
 2  (1 ) 2
v ( g , b) 
1
2
vg 
vg 
1
2
vb
14
(1 ) 2
 2  (1 ) 2
2
 2  (1 ) 2
vb
vb
Noisy Signal and the Common Value
•
The common value depends on how well ( s1 , s 2 )represents
the true state of nature (i.e. how close  is to 1)


•
As  increases, v( g , g ) increases and v(b, b)
decreases
v ( g , b ) is not affected by 
This property of the common value is not taken into
consideration in previous models

Previous models do not analyze how information precision
may affect the estimation of the common value

In our model, information precision is one of the most
important determinants of the estimation
15
Information and Anomaly in Estimation
• For a sufficiently large  , the estimated value of the firm with
the highest private value may be exceeded by that of the bidder
without private value with a positive probability

•
Lemma 1. Suppose c  vb  12 (v g  vb ) . Then, there exists
a  that is sufficiently close to 1 such that
c  v(b, b)  v( g , b)
An important implication of lemma 1 is that as  increases, it
may happen that bidders with a lower value can estimate the
value of the firm to be higher than bidders with a higher value
depending on the common signal

Therefore, bidders with a higher value is not guaranteed to
bid a higher price if the bidding strategies increase in the
estimation of the value of the firm
16
Benchmark – Pure Common Value Auction
•
Suppose the control contest were a pure common value auction
i
c
 0 for sure for i=1, 2
 This is true if
•
The value of the firm is the common value
i
j
(
s
,
s
), the value of the firm
 Given aggregated information
v( s i , s j ) depends on how well  represents the true state
of nature
•
Inefficient takeovers cannot be defined

The value of the firm does not depend on whichever
management is in control

Therefore, whichever management wins the contest, it is
efficient as long as the synergy is positive, which we assume
to be true throughout the paper
17
Benchmark – Pure Common Value Auction
•
Proposition 1. The following bidding strategy is a symmetric
equilibrium.
 ( si )  v( si , si )

In the symmetric equilibrium considered above, bidding
strategy is not affected by how well each bidder is informed

In the symmetric equilibrium above, bidders bid as if for
given s i aggregated information were given by (s i , s i )

For aggregated information s i  s j , the firm is acquired by
bidder i for v(s j , s j )

This is consistent with previous models of a pure common
value auction with symmetric but incomplete information
18
Multidimensional Signals and the Value of the Firm
•
The value of the firm is the sum of the private and common
values; were signal observable,
V ( s i , s j : ci )  ci  v ( s i , s j )

For given private information, the value of the firm is
V (s i : ci )  ci  v(s i ) where v( s i )
expected common value given s i

denotes the
Objective function of the management in determining
bidding strategy is to maximize the following
19
Inefficient takeovers – bidding strategy
•
 2  (1   ) 2
c
(vg  vb )
2( 2  (1   ) 2 )
Proposition 2. Suppose
. Then, the
following is a symmetric equilibrium : for i=1, 2,
 ( s i , ci )  ci  v( s i , s i )
•
An important implication of proposition 2 is that corporate
takeovers are not always efficient if  is sufficiently large and/or
if private value is not large enough relative to common value
difference

Lemma 1 suggests that  ( g ,0)   (b, c) in proposition 2

Therefore, the firm is acquired by a bidder with a high
common value signal, if any, regardless of the private value

Since, however, the firm is most valuable under the
management with the highest private value, the equilibrium
involves inefficient takeovers with a positive probability
20
Inefficient takeovers - intuition
•
Inefficient takeovers result because it is impossible to aggregate
information on the common value in equilibrium

 2  (1   ) 2
Note that under the assumption that c  2( 2  (1   ) 2 ) (vg  vb ),
c  v(b, b)  v( g , b)

Therefore,  ( g ,0)  v( g , g )   (b, c)  c  v(b, b)

This suggests that a bidder with the highest (private) value
may not be able to win the contest if its common value signal
is low

This happens only if the noisy signal of the common value is
sufficiently precise
21
Inefficient takeovers - probability
2
2
c
  (1   )
(vg  vb ) . The
2
2
2(  (1   ) )
•
Proposition 3. Suppose
probability of inefficient takeovers decreases as  increases
•
The intuition behind proposition 3 is that the probability that
bidders observe different common value signals decreases as 
increases
•
However, this does not necessarily imply that the probability of
inefficient allocation monotonically decreases in 

For a sufficiently small  , the inequality in proposition
does not hold and, hence, no inefficient takeovers

This important implication has not been explored in previous
research
22
Efficient takeovers
•
 2  (1 ) 2
 2  (1 ) 2
Proposition 4. Suppose c 
(v g  vb ) .
Then, the following bidding strategy is a symmetric equilibrium
where inefficient takeovers do not arise:
 ( s i , ci )  ci  v( s i , s i )
•
Note that the bidding strategy in proposition 4 is the same as that
in proposition 2
•
Unlike in proposition 2, however, inefficient takeovers do not
arise in proposition 4
 2  (1 ) 2
 2  (1 ) 2

(v g  vb )
The assumption that c 
amounts to assuming c  v(b, b)  v( g , g )

Therefore, the firm is always acquired by the highest private
value bidder
23
Contributions
•
•
In our model, the reason for inefficient takeovers is consistent
with previous models of auctions

A high-common value signal bidder may estimate synergy
to be higher than a low-common value signal bidder even
if the latter is more efficient

Consequently, a bidder with the highest private value may
not be able to win the contest
Unlike previous models, however, our model assumes that
bidders observe a noisy signal of the common value

Previous models assume bidders’ information is mutually
independent

We emphasize that bidders’ information is correlated with
each other since they are a noisy signal of common value
24
Contributions
•
Propositions 3 and 4 jointly imply that the probability of
inefficient takeovers does not monotonically decrease or increase
in information precision

The reversion of ordering arises only if bidders observe
different common value signals

Furthermore, the probability that bidders observe different
common value signals decreases the more precise the signal is

On the other hand, however, this reversion does not arise if
information is not sufficiently precise

Hence, the conclusion
25
Further works to be done
•
It will have to be examined whether there exists any symmetric
equilibrium exists if :
  (1 )
  (1 )
(
v

v
)

c

(v g  vb )
g
b
  (1 )
  (1 )
2
2
2
2
2
2
2
2
26