HD28
.MA 14
V-l
ALFRED
P.
WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
Agency Problems, Financial Contracting,
and Predation
Patrick Bolton
David Scharfstein
WP#
1986-88
February 1988
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
Agency Problems, Financial Contracting,
and Predation
Patrick Bolton
David Scharfstein
WP#
1986-88
February 1988
Agency Problems, Financial Contracting,
and Predation
by
Patrick Bolton
David Scharfstein'
First Draft: October 1987
This Draft: February 1988
Department
Harvard
University
and
School
of
of
Economics,
Sloan
Management, Massachusetts Institute of Technology, respectively. We are
grateful for helpful comments from Jean Tirole and workshop participants
at Harvard.
Abstract
present
We
in
investors
will
rivals'
theory
financial
problems
performance
a
contracting.
threaten not
poor.
is
predation
of
This
to
and
To
provide
encourages
competition based
mitigate
further
incentive
financing
competitors
on
if
ensure
to
agency
problems,
the
that
firm's
their
performance is indeed poor. Thus, an optimal contract balances the
conflicting
goals
predation may
or
of
may
deterring
not
occur
predation
in
and
equilibrium.
providing
Our
theory
incentives;
of
rational
predation differs from existing theories which view predation as an attempt
to convince
model,
rivals that remaining in the industry is unprofitable;
it is common knowledge that
in our
production in each period is profitable.
The analysis suggests that studying the interaction between the capital and
product
markets
can
provide
useful
organization and corporate finance.
insights
into
both
industrial
1.
Introduction
In
problems
in
"long-purse"
firms
paper,
this
drive
present
we
theory
a
"deep-pockets")
their
theory
constrained?
And,
model
attempt
(which
to
is
agency
Although the existing theory is
important
Why
questions.
firms
are
financially
even if firms are financially constrained,
these constraints lifted under the threat of predation?
We
on
financially constrained competitors out of business by
begs
it
based
in which cash-rich
of predation,
reducing their rivals' current cash flow.
suggestive,
predation
Our work is closest in spirit to the
financial contracting.
(or
of
answer
independent
of
emerge endogenously as
questions.
these
In
2
Section
in which
interest)
why aren't
2,
we
present a
constraints
financial
way of mitigating incentive problems.
a
We argue
that the commitment to terminate funding if the firm's performance is poor
ensures that the firm will not divert resources to itself at the expense of
investors.
3
This termination threat, however,
Rivals
competition.
performance
is
poor.
now
have
This
incentive
an
increases
the
is costly in the presence of
to
ensure
likelihood
that
the
firm's
that
the
firm's
contract is terminated and induces premature exit.
Section
account.
3
In
sensitivity of
There are
that
the
analyzes the optimal contract when this cost is taken into
general,
the
the
optimal response to predation is
to
lower
performance
of
the
refinancing decision to
two ways of doing this.
the
the
firm.
One way is to increase the likelihood
firm is refinanced if its performance is poor;
the
other is
to
lower the likelihood that the firm remains even if its performance is good.
Both strategies reduce the benefit of predation by lowering the effect of
predation on the likelihood of exit.
each of these strategies is optimal.
We
identify conditions under which
2
There
is
between
tradeoff
a
incentive problems;
reducing the
deterring
predation
sensitivity of the refinancing decision
discourages predation, but exacerbates the incentive problem.
the
mitigating
and
Depending on
importance of the incentive problem relative to the predation threat,
the equilibrium optimal contract may or may not deter predation.
conclude
We
these
introductory
three related literatures.
predation.
4
to
The first is the recent game -theoretic work on
This literature shares with ours the feature that predation is
rational. It differs, however,
convince
remarks by contrasting our paper
in that predation is viewed as an attempt to
rivals that it would be unprofitable to remain in the industry;
predation changes rivals' beliefs about industry demand or the predator's
costs.
In
there
paper,
our
is
common knowledge
that production
beliefs.
Rather,
each
Thus, predation does
period is a positive net present value investment.
not work by changing rivals'
in
predation adversely affects
the agency relationship between the firm and its creditors.
A second related literature (although not explicitly about predation)
is
the work on the
interaction between product-market competition and the
Brander and Lewis
capital market.
the earliest papers.
[1986]
and Maksimovic
[1985]
are
among
They point out that the objective function of equity
holders depends on the degree of leverage because equity holders receive
only the residual above the fixed debt obligation. If managers maximize the
value of equity,
their marginal production incentives will then depend on
the debt-to-equity ratio. Capital structure can therefore be used to induce
managers
equilibrium.
a
subset
compete
to
of
more
agressively
and
so
affects
product-market
The drawback of their work is that they restrict attention to
feasible
contracts were
financial
instruments.
If
the
space
expanded product -market equilibrium would,
of
feasible
in general,
be
3
very
Our
different.
paper,
derives
contrast,
in
feasible
of
set
the
contracts from first principles and analyzes optimal contracts within that
financial structure plays no role other
in these papers,
Furthermore,
set.
than through its effect on product -market strategy, whereas here, financial
policy also affects moral hazard problems within the firm.
Finally,
basic
our
framework bears
some
resemblance
Katz
to
[1987]
which considers a contract-design problem between a principal and an agent
in
which the agent's performance both influences and is
influenced by a
third party. Although Katz's main application is to bargaining between an
and a
agent
his
third party,
framework seems well-suited to analyze
the
interaction between product-market competition and the capital market.
2.
Contracting without Predation
There are two firms labelled A and B, who compete in periods
At
both
beginning of each period,
the
firms
incur
a
fixed
cost,
1
and
F.
2.
The
firms differ with respect to how they finance this cost. Firm A has a "deep
pocket";
cost.
it has
internally generated funds which it can use to finance this
"shallow pocket";
Firm B has a
it has
no working capital and must
raise all funds from the capital market.
The
first
step
in
analysis
our
is
to
characterize
relationship between firm B and its sources of capital.
contractual
the
We assume
that
there is one investor who makes a contract offer to firm B at the initial
date
0,
and
that
expected value.
firm
The
accepts
if
capital
for
a
market
contract provides
the
assumption that the
power may be unrealistic
well -functioning
B
investor has
firm
issuing public
with
many
competing
all
debt
non-negative
the
or
bargaining
equity in
investors.
a
However,
young companies requiring venture-capital financing or older ones placing
private
debt
or
equity are
likely
to
engage in explicit bargaining with
4
investors.
In
neither
reality
side
has
all
the
bargaining
power;
our
assumption simply sharpens our results without affecting their essential
character.
Firm B's profit in each period is either
the beginning
of each period,
with probability
6.
n-,
or
jr2
where
,
< ^2
wi
all players have common priors that
For simplicity,
the
discount rate
-
tt
At
tti
We assume
zero.
is
.
that the investment has positive net present value:
Later,
when
+ (1-6)7^2
Sn-^
IE
it
>
F.
we discuss the different implications of the model when
TTi
>
We
results
< F and
tt-,
F.
consider
particular
one
generalize
to
other
form
of
types
of
agency
problem,
agency problems.
although
our
We have chosen to
analyze this problem for its simplicity and the crispness of the results.
Our
discussion below details
applicability of our results
the
to
wide
a
variety of multi -period contracting problems.
The agency problem we analyze stems from the impossibility of making
the
financing
contract
explicitly
contingent
on
profit.
There
are
two
alternative interpretations underlying this assumption. One is that at the
end of each period, profit is privately observed by the firm. The other is
that while both the firm and creditor observe profit, it cannot be verified
by the courts.
In
whenever
a
one
ir-,
investor at
period model,
< F.
date
the
To see this,
1
if
the
investor would not
TT..
in
firm,
the
let R^ be the transfer from the firm to the
manager reports
that profit
Assuming the firm is protected by limited liability,
than
invest
R^^
is
rr^^,
i
-
1,2.
can be no greater
Clearly, the firm will report the profit level which minimizes the
Since R- <
payments to the investor.
receive at date
If instead
control
is
1
,
the most the investor can hope to
< F.
jt-,
relationship lasts for two periods,
the
whether
jtj
the
financing
receives
firm
second
the
in
investor can
the
period.
The
threat of not refinancing the firm in the second period if it defaults in
the first,
can be used to induce the firm to pay more than
n-,
in the first
period.
Formally,
revelation game.
of
profit.
its
analyze
we
The
problem
as
direct
a
terms of the contract are based on the firm's report
the
By
contract-design
the
Revelation Principle,
such a contract is perfectly
general
Suppose
the
investor gives
first-period production.
transfer at date
1
if the
be
the
date
to
finance
Finally,
F.
2
firm F dollars at date
above one-period model,
the
firm reports profits of
investor gives
second-period production.
second- round financing the
second period.
in
probability that the
Let P1
As
the
firm has
We
»r-
to
let R-
be
the
in the first period.
the
assume
firm F dollars at
that without
insufficient funds to operate
Below we show that this amounts to assuming that
let R-
finance
in
this
the
- ti <
7r2
be the transfer from the firm to the investor at date
if the first-period report is n-
and the second-period report is w
It is clear from the argument for the one-period model that
R^-i
•
-=
R^o*
the investor cannot make the second-period transfer depend on second-period
profit because the firm would always report the profit level corresponding
to
the
lower transfer.
Thus,
first-period reported profit
-t-
TT-i
;
let R
is
w-.
be the second-period transfer if the
Limited liability implies R
< w^ - R^
the second-period transfer can be no more than the surplus cash from
6
first period,
the
The
~
tt^
^i
pl^s the minimum profit in the second period,
>
contract maximizes the expected profits of the investor
optimal
subject to the following constraints:
profit at dates
1
and
(incentive compatibility);
2
not violate limited liability;
(iii)
(ii)
its
the contract does
the firm opts to sign the contract at
(individual rationality). Formally, the problem is the following:
date
(1)
the firm truthfully reveals
(i)
maximize
-F +
+ P^{R^-F)] + (1-5) [R2 + /92(R^-F)].
^[R]^
(iSi.Ri.R^)
subject to
- R2 + /92(^-R
(IC)
TTj
(LL)
Ti > Ri-
TT^
(IR)
- R^ +
~ ^1
^[Tr-j^
> R^,
TT-j^
"*"
> ^2 ~ ^1
)
"•"
i
Pi(^-^^)'.
= 1,2;
+ (1-«)[t2 - R2 + ^2^'^"^^] ^
/9i('i--R''")]
'^•
The incentive-compatibility constraint (IC) ensures that when profit is
high the firm does not report that profit is low. If profit is ^2, the firm
receives some surplus in the first period if it reports
n2<
to
however,
report
by setting
tth
,
since
/Si
the
since Ri < wi <
n-,
< ^2 ^^^ investor makes it costly for the firm
firm generally
receives
surplus
in
the
second
period.
Omitted
constraint
demonstrated
from
ensuring
later
this
that
that
because at an optimum,
formulation
firm
the
this
R2 >
reports
constraint
tti,
the
is
and hence
rather
tt-i
is
the
incentive-compatibility
not
than
binding.
^2
This
•
^^
i^
follows
firm could never meet its
7
first-period obligation. Note also that the firm truthfully reveals profit
— R^o-
in the second period because R-i
Finally, observe that the limited-
liability constraints (LL) imply that the individual-rationality constraint
(IR)
is
not binding.
remainder
The
of
section
this
devoted
is
establishing
to
that
investors will use the refinancing decision as part of an optimal incentive
scheme.
Analysis of the optimal contract is simplified by the following
two lemmas
Lemma
1
Constraint (IC) is binding.
Lemma
2
An optimal contract sets both second-period transfers, R
and R
Lemma
1,
contracting
2
equal to n^.
,
which we prove in the Appendix,
Lemma
problems.
which
2,
is
prove
also
we
standard feature of
a
in
Appendix,
the
establishes that since there is no refinancing threat in the second period,
the most the investor can receive from the firm at that time is the minimum
profit level,
Making
tt-,.
use
these
of
observations,
two
maximization
the
problem
simplifies to:
(2)
maximize
-F +
+ ^2(1~^)
R-|^
('^~F)
- ;9i[^F + (l-^)jr -
subject to the limited-liability constraint,
"^
Let
(Rt,
-k
Pi,
immediately that
tt-.
sign of e? + (l-^)7r -
tt,
(*)
e? + {1-9)^ -
TT^
^2'
.
•=
R-i
> R
•
,
i
- 1,2.
-^
-k
R2
tt-
tt-j^],
denote
and ^2
.
> 0,
If
""
^
•
the
optimal
The values of
contract.
P-,
It
follows
and R2 depend on the
;9i
=
and from (IC)
and
from
(IC)
contracts
R2
,
R2 = t;
,
It
T]^.
-=
satisfy the
also
is reversed,
if the inequality (*)
straightforward
is
establish
to
- 1,
fi-,
that
these
limited-liability constraints and the omitted
incentive constraint.
The basic idea underlying this result is as follows.
and ^2 "
(IC)
^>
Given
Ri
-=
jr-i
,
implies
r5 = ^T + (l-/90(^-7r,).
The expression,
is
tt-tt-,,
the
firm's expected surplus in the second period
given that the firm is refinanced.
first period,
firm reduces by (l-/3i)
the
A marginal
surplus.
this
By reporting
expected value of reporting
reduction in
n-,.
rather than
n-,
in the
the probability that it receives
therefore
fi-,
it increases by
Hence,
7r2
lowers
rr-n-,
by
n—rr-,
the
the amount the
investor can require the firm to pay when it reports profit of n2 in the
first period.
first-period profit is ^2 with probability 1-6,
Since
increase in expected profit to the investor from reducing
(1-^
)
(tt-tt-, )
.
The cost
expected profit
loss)
(or
to
investor
the
forced to exit if first-period profit is
It
follows
that
R*)
/3-]^
-
1
(resp.
0)
tti
of
^(tt-i-F)
/9i
is
is the foregone
when
the
firm
is
.
if
Alternatively, the pair
less) than ^(tt-j-F).
[^1.
of reducing
(or perhaps benefit)
^-i
the
(1-^)
k
{^-i,
(tt-ttj^)
-k
R2
)
is
greater
(resp.
is given by
11,
n-^]
if F <
[ttj^
- (1-^)7^]/^
(0,
tt)
if F >
[tt-j^
- (1-^)^]/^
-
Both of these conditions are identical to the conditions implied by (*)
If
TT-i
< F, the investor actually benefits by not refinancing the firm:
in the second period,
the investor only receives
ttj^
and puts up F.
Thus,
9
reducing
unambiguously increases investor profit.
p-i
than F,
greater
however,
second-period profit
the
of
cost
^(tt-i-F),
expected first-period profit of
note that if
met
and
will
investor
the
outweigh
will
(1-9) (n—n-,)
second-period profit of
set
- F,
n-^
^i
is sufficiently
benefit of
the
In this case,
.
F,
although
0;
•=
n-,
investor of foregoing expected
the
substantially greater than
is not
ir-,
to
If
*
increased
—
P-,
But
1.
condition (*) will
investor
the
be
foregoes
this is offset by the greater first-period
profit.
we
Finally,
must
determine
earns non-negative profit.
profit;
transfer of
a
optimal)
Clearly, if
expected profit
greater than
can verify that
[tt-^
of F such that the
profit
;ri
(1-6 )n]/ (2-6)
+
[n-,
is
is
-
If
F
tt-i
-i-
<
the
investor
the investor earns positive
> F,
tt-,
in each period is feasible
and earns positive profit.
investor's
period
n-,
conditions under which
the
(although perhaps not
-
^t
F,
0,
Thus,
(l-^)(7r-F).
- t and the
R2
must be no
F
for the investor to invest at date 0. One
+ (l-e)T!]/(2-6) >
[tt-^
- (l-6)7r]/6
so there is a range
,
firm operates in the first period but exits if first(This
ttt.
establishes
that
and
(*)
the
non-negative
profit condition can be met simultaneously.)
The above results are summarized in the following proposition.
Proposition
+
(l-6)n)/(2-e)
(i)
(ii)
2.1
.
1
:
The investor invests at date
Under this condition,
R^^
-=
tt-j^,
pI
- 1. rJ =
ttj^
if F < (n^ - (l-e)n)/e;
/9^
- 0,
ff
if
R2 =
Interpretation
(-n-^
0,
if and only if F <
P2 " 1-
- (l-e)^)/e < F <
(ttj^
-1-
Furthermore,
(l-^)^)/(2-5)
.
(n-,
10
The focus of this paper is on the contract described in case (ii) of
Proposition
In
1.
that
investor
the
case,
uses
threat
the
refinancing the firm as a way of mitigating incentive problems.
only
not
model,
payments
are
contingent
but
on performance,
not
of
In this
the
firm's
access to future capital is also explicitly contingent on performance.
believe
We
that
contract
this
captures
important
an
feature
of
corporate -financing arrangements. In venture -capital financing, the venture
capitalist almost never provides the entrepreneur with enough capital up
front
see
to
a
new product from its early test-marketing stage to full-
production.
scale
financing
arrangements
Initially,
the
Sahlman
(See
venture
take
the
form
capitalist
of
provides
commitment".
capital
"staged
enough money
to
financing
fund
to
the
the venture capitalist may
on the firm's performance in this early stage,
further
finance
Conditional
firm's start-up needs like research and product development.
provide
venture-
typical
Instead,
[1986].)
and
test-marketing,
then
full-scale
production.
There are at least two reasons why such contracts are used.
they are a means
turn out
the
to be
venture
Therefore,
Second,
staged
staged
of limiting the financier's exposure should the venture
an unprofitable one.
will
First,
be
more
financing
financing
willing
Entrepreneurs who have confidence in
to
minimizes
arrangements
contracts
accept
problems
enable
of
the
of
adverse
venture
this
form.
selection.
capitalist
to
mitigate incentive problems that inevitably arise between entrepreneurs and
financiers.
The requirement that the firm return to the venture capitalist
for further funding limits the extent to which management will pursue its
own
interests
at
the
formalizes this idea.
expense
of
the
venture
capitalist.
Our
model
11
The model applies to more than just venture capital.
More generally,
debt contracts requiring fixed repayments at fixed dates bear many of the
same
features of the
contract described in case
of the proposition.
(ii)
creditors will generally renew or extend existing
If repayments
are met,
credit lines;
otherwise,
the debtor is denied access to further financing
and the creditor receives all or part of the firm's assets.
interpret
We can
debt obligation,
value
of
resemblance
tti
and
,
If not,
Gale
to
can
be
Hellwig
and
justified
as
[1985],
optimal
an
by
assets;
otherwise,
model,
their
An
investor.
the
reports low profit,
denied
is
Indeed,
show
who
access
further
to
our model bears some
that
contract.
the
contract
optimal
In
standard
a
debt
one-period
their
the
the
incentives.
cost
of
consider
fully
if
firm
the
reporting
low
profit
paper
optimal
is
the
threat
in our model,
it
of
is
In
being
the cost
Our result is also similar to Stiglitz and Weiss
termination
Their
that
firm pays a fixed amount and is not monitored.
of not being refinanced.
that
specifies
the investor monitors the firm and confiscates all the
monitored and having all assets confiscated;
who
firm meets its
the creditor receives the entire
debtor
the
If the
profit is privately observed by the firm, but can be observed at a
model,
cost
face value of debt.
This is a standard debt contract.
financing.
contract
the
it is refinanced.
firm,
the
as
tt
threat
differs
can
from
be
our
used
in
to
two
improve
respects:
first-period
they
do
not
contracts and they consider a different incentive
problem, namely the choice of project riskiness.
2.2
Extensions
Other Agency Problems.
problem.
in
It
is not
The above model focuses on a particular agency
the only type of agency problem,
the simplest possible way.
but it makes our point
We believe that the refinancing threat is a
12
useful
device
incentive
for
how
exhibits
following example
wide
a
variety
basic
this
agency
of
idea
extends
problems.
to
the
The
familiar
effort-elicitation model of agency.
Suppose
there
periods
two
are
of production and in each period the
manager can "work hard" or "shirk". If the manager works hard, he increases
the probability that profit is
7r2
rather than
ir-,.
Working hard reduces the
manager's utility by some fixed amount. Managers are risk neutral and
protected by limited liability.
and
The limited-liability constraint makes
it
infeasible to sell the entire firm to the manager (which is otherwise the
optimal
solution
problem when
moral -hazard
the
to
manager
the
is
risk
neutral)
To prevent the manager from shirking the manager must be rewarded for
good
and
perfoirmance
will
be
compensated
excess
in
of
his
reservation
Therefore the manager bears a utility cost if the firm is not
utility.
-refinanced.
Moreover,
when profit
is
manager who
shirks
if the creditor threatens not
the
low,
than
effect
of
who
one
refinance the firm
threat will be
this
not
does
to
since
the
greater
on
the
probability of
low
profit is greater in the former case. Thus the threat of not refinancing
the
By using the refinancing threat,
firm makes shirking more costly.
investor
is
able
greater
induce
to
effort
at
lower
cost.
The
the
optimal
contract resembles equity with the feature that if performance is poor the
investor has the right to shut down the firm.
In this sense the financing
to preferred stock in which the holder of preferred stock
is very similar
is given control rights if certain dividend requirements are not met.
Correlation
agency models,
(firm's)
in
Profits
the principal
profitability
.
In
this
(investor)
(ability)
over
model,
unlike
many multi-period
does not learn about the agent's
time.
Here
gross
profits
are
13
identically and independently distributed.
case where profits
the
serially correlated;
are
strengthened in this case.
conditional
first-period
on
correlation,
Let
E(7r|7r2)
>
jt
and
it
/Sj^
is
- 0, ^2 =
^1 "
1>
,
It
positive
is
1^2-
Accordingly,
it has
serial
straightforward to
is
the optimal contract is such
E(7r|7r2).
Other things being equal,
more profitable for the investor to invest in the firm.
The firm's
2
is
now greater when first-period profit
more
to
lose
second-period surplus in period
is
>
ir-^
^^d R2 -
our results are
fact,
there
> E(7r|7rn).
E(7r|7r2)
^^l-
If
tt^.
establish that if 6F + (l-6)E(7r 1^2) that
in
be expected second-period profits
E(7r|7r.)
profits,
extended to
The model can be
if
it
is
not refinanced.
This
reduces its incentive to underreport profits and the investor can extract
more rent from the firm in period
Renegotiation
this
In
.
model,
if
^-i
=
there
0,
the firm exits when first-period profit is
inefficiency;
is
efficient to continue operation.
1,
after
first-period profit of
incentive
9
1.
tear
to
up
the
is
an
even though it
n-i
It is natural to ask whether,
is
n-,
realized,
contract
original
at date
two parties have
the
an
a
mutually
> F,
the most
renegotiate
and
ex-post
beneficial arrangement.
Note that although it is efficient to produce because
the investor can receive from the firm is
be possible
In contrast,
Thus,
if
jti
<
F,
it will not
negotiate around the contractually specified inefficiency.
to
if
the surplus of
ttt.
tt
tt
n-,
> F,
the investor and the firm will negotiate to share
- F that is created when the firm operates.
contract that originally specifies
•k
/3-i
-
,
Therefore, a
cannot be implemented ex-post.
This implies that the most the investor can induce the firm to pay in each
period is
One
might,
tti
since the threat of not refinancing the firm is not credible.
however,
argue
that
if
the
investor
is
long-lived with many
14
arrangements
financial
similar
have
may
it
an
incentive
to
develop
a
reputation for not renegotiating contracts.
Internal Finance
the
firm may be
able
generated funds.
712,
The analysis so
.
the possibility
ignores
far
finance second-period production with
to
second period the firm will be able to invest the difference
in the
may not be possible
it
F,
second period.
implies
This
prevent
to
raise
to
any capital;
the
If
n-,.
Thus,
»r
if
»r2
-
firm from producing in
the
that the most the
firm to pay in the first period is
able
internally
If the firm reports profit of wi, when in fact profit is
between its earnings and its first-period payment, ^2 >
that
investor can require
<
n-,
the
the
firm will not be
the
F,
ti
inability to discipline the
firm ex post
freezes the firm out of the capital market.
This illustrates quite dramatically the effects of incentive problems
created by
Jensen
"free-cash
[1986]
among
flows"
others
inside
the
there
that
firm.
may
be
It
has
been argued by
substantial
reducing the amount of internal financing by firms.
benefits
to
Our model provides a
simple example and formalization of this idea.
Bargaining
power.
Power
In
.
model,
the
the
firm has
all
the
bargaining
Above, we discuss the circumstances under which this is reasonable.
It is straightforward to show that if
ir-,
<
F,
assigning all the bargaining
power to the firm does not change the results substantially.
^ie(0,l);
that
is,
the
firm will
first-period profit is
ir-i.
bargaining power, then
;9t
the firm nor the
even though
n-,
>
exit with positive probability
In contrast,
- ^2 ~
^
^"^
if
its
if wi > F and the firm has all the
R^-R
-F, i-1,2.
investor has all the bargaining power,
F.
In this case,
When neither
in general ^i
<
1
The basic character of our results is not sensitive to
our assumptions on the bargaining game.
15
Capacity Expansion
expansion parameter.
profits
amount
contingent
plan
are n-,
In
)9jF.
That
the
as the probability
firm's
first-period
performance.
firm is given funds to increase
then the
addition,
expected profits increase by
framework will also set
;9i
<
l§,,^]
/92
as
An
.
a
Under this
/S^Jr.
but
can be
fi-
contract
optimal
If
capacity by an
interpretation there is no longer the constraint ^-£[0,1],
assumed to lie in some interval
capacity-
a
is
fis
investor commits to a staged capital-
the
is,
on
fi^
interpretation is that
An alternative
of refinancing.
expansion
We have so far interpreted
.
this
in
way of inducing the firm to reveal
profits truthfully.
3.
Predation and the Optimal Contract
In this section we model explicitly the interaction between the firm's
financial
assume
policy
that
product-market
and
firm A
competition.
discussed above,
As
we
financed with internally generated funds and that
is
firm B must raise funds from the capital market.
suppose the investor and firm B do not take into account the
To begin,
existence of firm A when designing an optimal financial contract. That is,
they
take
the
contracting
stochastic
process.
described in Section
In
2.
structure
this
case,
profits
of
financial
the
as
exogenous
contract
will
to
be
the
as
Consider the case where firm B is forced to shut
down when its first-period profit is low.
(This is case (ii) of Proposition
1.)
This opens up the possibility of predation by firm A.
take
actions
If firm A can
its
advertising
expenditure) that lower firm B's expected first-period profit,
then it can
(such
as
reducing
its
price
or
increasing
increase the probability that firm B exits. Firm A will engage in predatory
behavior if the costs of taking such actions are outweighed by the expected
benefits of acquiring a monopoly position.
16
We model predation as follows:
from
for a cost c > 0,
firm A can increase
to n the probability that firm B earns low profit,
6
in period 1.
n-,,
If firm B exits, firm A becomes a monopolist and its second-period expected
profits are n
profits
are
If instead firm B remains in the market, firm A's expected
.
jt
.
given the contract
Thus,
benefits of predation are
i^Jl-e)(n'^-n^)
(^i-6)
for any
firm A will prey if (^2
,
^2
"
1
>
«
)
(tt^-tt^)
,
if A < 1.
financial contract of firm B,
'
/S^) (/J-^)
(t^-t^)
> c or
{;9-i,
investors
firm
of
B
ignore
Ri
> A.
()92-/3^)
the benefits of predation depend on firm B's financial contract.
when the
expected
the
It will choose to prey provided
).
> c, or defining A ^ c/(/i-
More generally,
R2),
(n^-n
-
p-,
,
•
Here,
Note that
possibility of predation,
the
/So
they
maximize the benefit of predation to firm A, since Pj ~ P\ i^ largest when
=
^2
arid
1
maximizes
=
/Si
.
incentive
the
contract
The
to
that
To
prey.
minimizes
make
the
agency
analysis
problems
interesting,
also
we
assume for the remainder of the paper that the parameters are such that if
y92
~
1
To
arid
/9i
- 0,
analyze
it is optimal to prey,
the
effect
of
the
i.e. A < 1.
contract
financial
on
product-market
equilibrium we need to make two further informational assumptions.
First,
we assume that the predatory action by firm A is not observable by a court.
This is a reasonable assumption in view of the difficulties legal scholars
and
economists
have
encountered
in
defining
predation.
Given
that
predation is not verifiable by a court, the contract between firm B and its
creditors
cannot
be
made
contingent
on
the
predatory action of firm A.
Notice that we do allow for the possibility that firm B and its investors
can observe firm A's predatory actions. This distinguishes our model from
explanations
of
predation which
rely
on
signaling
(Milgrom and Roberts
[1982]) or signal jamming (Fudenberg and Tirole [1986]).
17
Our second informational assumption concerns the observability by firm
A of the contract between firm B and its
observe the contract,
i.e.,
reducing the difference between
the
investor reduces the gains from predation.
(^2
~ ^l) predation is deterred.
~
commitment
of
""
fi\
the predator
can
then the investor can use the contract to influence
first-period profit,
setting ^2
If
By reducing the sensitivity of the refinancing decision
firm A's actions.
to
investors.
^>
•
For small enough values of
firm B a
from which to finance
resources
^i
In the extreme, predation is deterred by
investor gives
^^^
^""^
fij
"deep pocket",
investment.
The
i.e.
a
assumption
that the contract is observable implies that the contracting parties cannot
secretly
renegotiate
Commission requires
their financial
no
their
that
all
contract.
Securities
The
disclosure requirement.
Exchange
publicly-held firms disclose information on
In privately-held companies,
structure.
and
however,
it may be more
For such firms,
there is
reasonable to
We therefore consider
assume that financial contracts cannot be observed.
the two cases of observable and unobservable contracts.
3
.
Observable Contracts
1
If
contracts
are
observable,
the
investor can ensure that predation
will not take place by writing a contract that satisfies the following "no-
predation constraint"
(y92-^l)(/i-5)(7r"'-7r'^)
That
the
is,
investor
can
< c
,
or
deter predation by making
sensitive to firm B's performance. As discussed earlier,
this
has
is
to
give firm B a deep pocket; ^2
often been suggested
as
a
rational
""
^i
~
1
response
•
the
contract
less
one way of doing
Although this solution
to
predation,
we
argue
18
below that it ignores an important cost of such a policy, namely the effect
of guaranteed financing on the firm's incentives.
To determine the efficient contractual response to predation, we first
analyze the optimal contract that deters predation.
contract to the optimal contract given predation.
We then compare this
The investor chooses the
contract with the higher payoff, provided it earns non-negative profit.
The optimal predation-deterring contract solves the following program:
max
-F + ^[R^ + ^^(w^-F)] + (1-<?)[R2 +
fi2^''l-^^^
>
subject to
(IC)
TTj
- R2 + ^2'^^"^!^ >
(LL)
'fi
^ Ri
(NPC)
(^2-^l> - ^•
This
Section
2
-
?r2
Rj^
+ fii(n-n-^),
.1=1,2,
maximization problem
is
identical
to
the
problem analyzed
in
except for the constraint (NPC) which ensures that no predation
Note that predation would never occur in the
occurs in the first period.
second period, since it is the last period.
As shown in Proposition
1,
if ^F + (l-^)7r <
tt^
<
,
^2 ~
/^j^
=
1
.
This
contract will also be the optimal predation-deterring contract because firm
A will not prey under these circumstances.
+
(l-d)n
>
TT-j^
>
solution is ^2 =
violated.
/32
the
!•
^1 =
the
f*-
(NPC)
constraint
is
the
ignored,
optimal
Firm A will prey and the (NPC) constraint is
This implies that at an optimum the constraint must be binding:
- ^1 = A.
fact
If
0.
The interesting case is when ^F
The remainder of the analysis focuses on this case.
that ^2 ~ P\
"^
^
^"'i
'^he
observation that
R-^
"
"^l
>
Using
^^^ binding
19
(IC)
constraint becomes R2
into the objective function,
-F +
max
Aw +
•=
Substituting these equalities
(1-A)7ri.
the maximization problem becomes:
+ A(l-^)(w-F),
fi-^(n-^-F)
where the restrictions that ^2 ~
~ ^> P2 - ^'
fi\
^"*^
/5t
<
imply
1
/9i
< 1-A.
The following proposition now follows easily.
Proposition
2
If
:
it
optimal
is
sign
to
*
*
contract, and if inequality (*) holds, ^i ~ fi
If
(i)
profits are
(ii)
2(7r-[^-F)
If
profits are
<
TTi
ttj^
then
> F,
7r-|
= 1-A and
fi-i
+
A[5F +
F,
then
-
(l-5)7r
=
yS-,
- F + (l-^)A(7r-F)
n-^]
and
(when
give
firm
the
a
tt-,
> F)
(partial)
probability)
to continue
reduces
incentive
the
investor;
rather
for
"shallow
+ (l-A)n-, < n.
The investor's expected
.
.
/So
=
The
A.
investor's expected
2
differ fundamentally.
deep
pocket.
By
committing
This comes
+ (1-A)7r, <
(when
pocket",
the
< F)
tt-.
,
opposite
to
leave
(with
positive
the
at a
positive
investor
cost to
the
high,
the
is
jr.
the optimal contract is to give the
of
a
deep
probability)
if
Rather
pocket.
committing not to exit when first-period profit is low,
commit
(with
even when profit is low,
firm A to prey.
AJr
In the
optimal predation-deterring strategy is to
than receiving n when first period profit
In the second case
a
-
Att
.
operation,
investor now receives only
firm
the
,
1
-=
/So
The two cases discussed in Proposition
first case
Ro ~
1
predation-deterring
a
profit
it
is
is
than
optimal to
high.
This
reduces the benefit of predation because there is now a greater probability
that the firm will exit even if firm A does not prey.
20
These different responses to predation can be understood as follows.
A marginal reduction in ^2 ^^^ increase in
have the same effect on the
^-i
constraint and the same effect on the (IC) constraint.
(NPC)
But raising
or reducing the likelihood of refinancing implies that the investor is more
or less likely to get
tti
- F in the second period.
Investor increases
if
n-^
Section
In
2
0-,;
if
TTi
it
is
that
we
can
commitment
a
if
ix-,
>
F,
the
the investor decreases Pj-
interpret
to
scale
a
The implication of Proposition
second period.
is that
F,
argued
we
expansion parameter;
<
Thus,
2
fi-
of
as
a
capacity-
operation in the
under this interpretation
< F it is optimal to deter predation by committing to expand
less when first-period profit is high.
If
n-,
>
F,
the optimal predation-
deterring strategy is to commit to more aggressive expansion even if the
firm does poorly in the first period.
It remains
deterring
an open question whether it is optimal to sign predation-
contracts.
The
benefit
probability of low profit is
<
1
so
< m-
6
of
deterring
predation
is
The cost is that ^2 ~ ^i
that
the
i^ equal to A
that the investor can extract less surplus from the firm.
Whether
the benefits of deterring predation outweigh the costs depends on a number
of
factors;
there
is
no crisp
characterization of when it is optimal
to
deter predation.
Inspection of the investor's payoffs reveals that it will be optimal
to deter predation provided
(i)
(ii)
(l-fi)A > 1-n
A(^F +
if
il-6)7t-n-^)
where recall that A =
JTj^
>
c/(7r"'-?r
< F;
(/iF
+ (l-fi)n-n-^)
)(/i-5)
if
is itself a
n-^
> F,
function of
A number of comparative statics follow easily.
/i
and
6.
21
An increase
(i)
in
benefit of predation,
cost of predation,
the
- n
n
c,
and a decrease
in
the
make predation deterrence more attractive.
,
This is because the costs of predation deterrence decline;
^So
-
need not
fi-\
be reduced by as much to deter predation.
since
predation,
extreme
the
In
(ii)
this
case
would
where
require
c
-
0,
setting
fin
it
never
" P\
pays
to
which has
deter
extreme
negative incentive effects.
(iii)
If
/i
- 1,
it always pays to deter predation,
since otherwise the
firm would always earn low profit.
To complete the analysis,
the
if
firm is to produce at all,
profitable of the two contracts must earn non-negative profit.
of whether
the
yield
will
contract deters predation or not,
optimal
expected
lower
profit
for
investor.
the
If
the more
Regardless
both contracts
tti
<
this
F,
reduction in profit may be large enough to prevent entry altogether.
Thus,
it is possible that the threat of predation upon entry can prevent the firm
entering
from
in
the
first
place,
even
if
ex-post
optimal
the
contract
between firm B and its investor is such that predation is deterred.
3
.
2
Unobservable Contracts
The assumption that contracts are observable may inappropriate in some
circumstances. There are no financial disclosure requirements for privately
held firms,
firm's
so
it
contractual
may be
impossible for outsiders to actually observe a
relationship
with
its
creditors.
12
Thus,
we
also
investigate the case in which firm A cannot observe the contract signed by
firm B and the investor.
Instead,
firm A must make a rational conjecture
about the contract chosen in equilibrium.
When
contracts
are
unobservable,
predator play a simultaneous move game.
it
is
as
if
the
(We can ignore
investor
and
the
firm B because its
22
actions follow trivially from the contract chosen by the investor.)
A's
strategy
set
composed of two pure strategies:
is
strategy set is essentially a choice of a pair
ignore Ri
The investor's
^2^ ^ [0,1]
2
.
(We can
and R2 since firm A is only concerned with the probabilities of
refinancing,
To
i^-^,
which we
"prey,"
denote by P, and "do not prey," which we denote by NP.
Firm
and ^2
fi-,
characterize
the
Nash equilibria of the
identify three
we
game,
cases
pF +
(i)
(ii)
Case (i)
/iF
JTj^;
n-^
< BT + (l-5)Jr;
+ (l-M)'r < ^F + (l-e)7r <
If
:
>
+ (l-M)'r <
ti¥
(iii)
{\-^l)'^l
/xF
+
(l-/i)7r
>
tt,
,
(0,1)
given any strategy by firm A,
investor;
A's best response to contract (0,1)
is
ttj^.
a dominant strategy for the
is
contract (0,1)
to choose P.
optimal.
is
Thus,
Firm
in this case,
contract (0,1) and predation form a unique Nash equilibrium.
Case
(ii)
pF +
If
:
equilibrium in pure
(l-p)7r
strategies.
<
tt-,^
< 5F +
To see this,
then the investor's best response is (1,1).
contract (1,1)
is
NP.
Finally,
can,
however,
mixed strategy.
between P and NP.
no Nash
P,
the investor's best
i^-^.
an equilibrium
in which
If firm A plays a mixed strategy,
Thus, 02 ~ ^l ~
is
suppose firm A chooses
if firm A chooses NP,
construct
there
But firm A's best response to
response is contract (0,1) since 67 + (l-^)jr >
We
(l-5)7r,
firm A plays
it must be
a
indifferent
^
Recall that if q is the probability that first period profit is n^,
then if qF + (1-Q)7r >
n-^,
the investor chooses contract (0,1), and if qF +
23
(I-Q)jr
<
contract
investor chooses
the
n-,,
which ^2 ~ ^1 ~ ^ is optimal only if aV + (1—a)Jr firm A preys with probability 7,
If
Thus,
(1,1).
contract
a
in
n-<.
a - 7^ +
(1
<i)6
.
Thus,
7 must
satisfy
[7M + (1-7)^]F + [1 - 7M - (I-tX?]^ - ^i
(**)
determine
To
(l-^)7r
<
implies
TTj^
this case
-
^-i
Case
particular values of
the
<
n-^
It
F.
- A and ^2 "
1
(iii)
If
:
+
^lF
'^
y3-i
and
observe
that pF +
then follows from Proposition
2
that in
13
(l-/i)Jr
<
^F
+
(1-6)7!
dominant strategy is to choose contract (1,1).
NP.
fi^'
<
n-^,
the
investor's
Firm A's best response is
(1,1) and NF form the unique Nash equilibrium in this case.
Thus,
We summarize these results in Proposition 3.
Proposition
if ^F + (l-5)7r >
(i)
If
fiF
3
n-^.
+
In particular,
(l-fi)n
equilibrium contract is
(ii)
If
fiF
+
firm A preys with positive probability
In equilibrium,
:
>
firm A preys with probability one and the
n-,,
(/9i,
/52)
=
(l-n)n <
TTi,
firm A preys with probability 7
(0,1);
solves (**)) and the equilibrium contract is
Finally,
contract is
if 6F + (1-8)t! <
(fi-^,
n-,,
(0-^,
(where 7
^2) " (l~^.l)-
firm A does not prey and the equilibrium
^j) = (1.1)-
In case (i) of the proposition,
(0,1) is a dominant strategy for the
investor. With unobservable contracts, there is nothing the investor can do
to
deter predation.
The predator rationally conjectures that the investor
will always choose contract (0,1). Therefore, in equilibrium firm A preys.
24
In case
investor.
contract (0,1) is no longer a dominant startegy for the
(ii),
firm A preys,
If
contract (1,1) will be chosen;
if firm A does
not prey contract (0,1) will be chosen. Thus, no pure strategy equilibrium
equilibrium,
In
exists.
A
firm
preys
with
probability
e
7
so
(0,1)
predation is partially deterred even though contracts are not observable.
4.
Concluding Remarks
central
The
idea of this paper
give
can
contracting
rise
to
Is
that agency problems in financial
predation.
financial
The
minimizes agency problems also maximizes rivals'
there
result,
is
a
incentive problems:
to
the performance
incentive
tradeoff
incentives to prey.
As a
sensitivity of the refinancing decision
firm discourages predation but exacerbates
whether
equilibrium,
In
that
between deterring predation and mitigating
reducing the
of the
problem.
contract
financial
contracts
the
deter
predation depends on the relative importance these two effects.
Our
views
theory
predation
unprofitable
predation departs
of
an
as
remain
to
attempt
in
the
to
from the
convince
industry.
In
existing literature which
rivals
our
that
model,
it
it
would
is
be
common
knowledge that it is profitable for the rivals to remain in the industry.
Predation induces exit because it adversely affects the agency relationship
between the rivals'
investors and its manager and not because it changes
rivals' perceptions about their profitability.
Although our model narrowly focuses on predation, we believe that the
model
provides
a
useful
starting
point
for
analyzing a broader
set
of
issues concerning competitive interaction among firms with agency problems
and financial constraints. One issue that can be addressed with our type of
model is the effect of product-market competition on the incentive problem
within
the
firm.
The
conventional
wisdom
is
that
increased
competitive
25
pressure reduces managerial slack. This idea has been formalized by Oliver
Hart [1983], but as Scharfstein [1988]
the results depend crucially
shows,
on the specification of managerial preferences;
competition
preferences,
managerial
about
for reasonable assumptions
actually
exacerbates
the
incentive problem.
model,
this
In
unambiguously
negative
investors
predation,
results
the
incentive
make
even
are
effects.
response
In
decision
refinancing
the
competition
stronger:
to
threat
of
sensitive
to
the
less
has
performance and hence the manager is able to extract greater rent from the
investors.
ambiguous.
The
If
welfare
effects
of
increased
< F and contracts are observable,
tt-i
^2 i^ response to the predation threat.
competition and welfare
response is to increase
There
analysis.
lower.
is
/S-,
are
is optimal to reduce
it
contrast,
if
> F,
tt-i
the
optimal
there is less exit, and welfare is higher.
,
obviously
are
In
however,
there is greater exit due to
Thus,
important
effects
that
omitted
are
in
this
First, within any period there is no production decision made by
the firm and thus no productive inefficiency;
between periods
is
competition,
modelled
in
in the exit decision.
reduced form,
the only inefficiency arises
Second,
and hence
it
is
the competitive
difficult
to
interaction
consider how
efficiency changes as competition becomes more or less aggressive. A model
that maintained the dynamic
other
features
would
be
features of our model and incorporated these
an
important
step
towards
understanding
the
incentive effects of competition.
A second general issue raised by our analysis concerns the nature of
dynamic
early
competition
generation
of
when
firms
models
of
face
capital-market
dynamic
competition
constraints.
the
only
In
the
relevant
consideration is the total capital stock acquired by firms and not the way
26
in
which
was
it
competitive
acquired.
behavior
depends
internally-generated
through
suggests
that
an
In
important
contrast,
crucially
funds
or
on
in
our
whether
framework,
capital
external
through
was
firms'
acquired
financing.
determinant of product-market success
This
is
the
ability of firms to finance investment from internal funds. As Donaldson's
[1984]
study
shows,
corporate managers
observation
may
this
of
have
belief
large
appears
industrial
important
to
be
widely-held
companies.
implications
We
for
believe
even
that
understanding
product-market competition and corporate financing decisions.
among
this
both
27
Appendix
Lemma
Constraint (IC) is binding.
1:
Suppose
Proof:
constraints
are
to
(LL)
.
the
contrary that
We
establish
(IC)
that
slack and that the only
is
optimal
the
solution
this
to
relaxed program violates (IC).
First note that the maximization problem can be written:
maximize
R^ + fi^R^
-
fi^F
subject to
< n^
(A.l)
R.
(A. 2)
R^ + R^ <
+
TT^
7r-|^.
At an optimum to this program,
case where ^-
the
(A. 2),
it
n-,-
-=
"
and R
tt-
"'i-
This
true in
is
because given the constraint on the total payments
to shift more of the payment to the first period when
received with certainty.
will be
=
1
is optimal
it
satisfying R- + R
R-
<
R-
-=
tt-
+
(Note that given
If
-=
/9-
1
1,
any division of payments
and we may as well set R^
is optimal
tt-,
—
fi-
•=
the division of payments between R-
tt-
and
and R
has no effect on the incentive-compatibility constraint.)
The (IC) constraint therefore simplifies to
/32(Jr
-
>
TTj^)
7r2
-
w-i^
+
fi-^in
n-^)
-
It is easily seen that for all values of
Thus
satisfied.
the
constraint
(IC)
is
fi-,
.
and
the inequality cannot be
/Sn
violated at
the
optimum of
the
relaxed program, establishing the contradiction.
Lemma
2
Proof:
R
1
-=
R
2
-=
is a part of an optimal contract.
tti
Substituting the
(IC)
constraint
into
the
yields the new objective function,
-F +
R;[^
+ Pi[R^
-
e?
-
(1-6)^] + (l-5)^2('^
-
f")-
objective
function
28
It
follows
that
/So
individual values R
2
-
Hence
1-
and R2
affects
2
constraint. Thus we can set R =
and R
.
If ^i
simultaneously
<
1,
Ri
and R
maximizes
only
tt-i
.
the
the
If
/Si
sum,
R
2
+
objective
,
and
not
objective function and the
-
1
the
(IC)
the same can be said for
will be chosen to maximize
the
R2
function
and
Ri
+ ^-iR
relaxes
R-,
since it
the
(IC)
constraint. This expression is maximized subject to (LL) by setting Ri - R
-
TTi.
This completes the proof.
29
Endnotes
1.
See,
[1986]
2.
Telser
for example,
Benoit
[1965],
Fudenberg and Tirole
[1984],
and Tirole [1988]
Fudenberg and Tirole [1986] endogenize the financial constraints
facing the firm; however, they do not address the question of how these
financial constraints might change under the threat of predation.
3.
Stiglitz and Weiss [1983] also show that the termination threat can be
an optimal incentive scheme for reasons similar to those considered here;
however, they analyze a different incentive problem.
4.
for
See
Saloner
Salop
example,
and
Shapiro
Scharfstein
[1982],
[1984],
and
These papers draw much from the early work of Milgrom and
[1987].
Roberts [1982] on rational limit-pricing.
5.
Saloner 's paper differs from ours in that he uses a signaling model to
analyze predation.
however,
It is,
similar in that the predation mechanism
operates through the capital market:
predation lowers the price at which
the prey can be acquired.
6.
This
is
similar
to
Fershtman
and
Judd
[1986]
on
effect
the
managerial employment contracts on product-market competition.
7.
In many situations,
the latter interpretation is more plausible; an
investor is often closely involved in the firm's operations, whereas the
courts are not. Irregular accounting practices can make it difficult for
outside parties to know the firm's true profitability.
8.
Note that in each case, the firm weakly prefers to announce the true
profit, when first-period profit is
firm reports
7r2,
tt,
.
When
/9-i
-
and R2
-
tt
,
if the
it will not be able to meet its first-period payment
obligation and so it will be in default.
In this case,
paid
The firm is then indifferent
rr-i
and does not refinance the firm.
the investor is
of
30
between the possible reports of
profit.
In the case when
-
^^^
We assume that it reports the true
w.
1
and R2
~
^i
indifferent between the two profit reports.
.
the firm is always
Again we assume profit is
reported truthfully.
9.
it
Obviously,
loses
creditor
less
if the firm's profits are negatively correlated over time,
if
it
extract
to
is
not
refinanced and it is more difficult for the
from
rent
the
However,
firm.
situations
in
which
profits are negatively correlated over time seem rather implausible.
10.
example,
for
See,
Joskow
and
Klevorick
[1979]
for
attempt
one
at
defining predation and a discussion of the difficulties in doing so.
11.
more
For
discussion
of
the
different
implications
of
contract
observability, we refer the reader to Katz [1987].
12.
It may be argued that although it is costly for outsiders to observe
the contract,
firm A.
it is in the investor's interest to reveal its contract to
But, as Katz [1987] points out in a related context,
if the
observed contract is not efficient, the two parties will have an incentive
to annul the advertised contract by writing a hidden contract.
13. We have identified an equilibrium in which the investor plays a pure
strategy.
However, this strategy is equivalent to mixing between contract
(0,1) and (1,1) where the investor plays the former contract with
probability A and the latter with probability
14. This
assumes
that
the
welfare
loss
1
- A.
from
less
competition
in
the
second period outweighs the potential gains from increased competition in
the first period.
15.
See Fudenberg and Tirole
[1986b]
for a discussion of the
of this assumption in dynamic oligopoly models.
importance
31
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ill I
ill"''*'"
3 c^oao
LlBB''"'^-\,
371
00^ ^^13
"1 11