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working paper
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MONITORING AND COLLUSION:
"CARROTS" VERSUS "STICKS" IN THE CONTROL OF AUDITORS
Daron Acemoglu
94-9
Jan.
1994
massachusetts
institute of
technology
50 memorial drive
Cambridge, mass. 02139
MONITORING AND COLLUSION:
"CARROTS" VERSUS "STICKS" IN THE CONTROL OF AUDITORS
Daron Acemoglu
94-9
Jan.
1994
APR 5
1994
MONITORING AND COLLUSION
:
"CARROTS" VERSUS "STICKS" IN THE CONTROL OF AUDITORS
Daron Acemoglu
Department of Economics
Massachusetts Institute of Technology
02139
50 Memorial Drive, Cambridge,
MA
This Version: January 1994
JEL
Keywords: monitoring,
Classification:
D23, L22
collusion, implicit collusion, career concerns,
the threat of lawsuits
Some of
the ideas in this paper
paper on auditing.
I
am
were discussed with Miles Gietzmann while working on a
joint
indebted to him, Andres Almazan, Abhijit Banerjee, Leonardo Felli,
Frank Fisher, Peter Klibanoff, John Moore, Steve Pischke and seminar participants
helpful discussion. Naturally all remaining errors are mine.
at
MIT
for
MONITORING AND COLLUSION
:
"CARROTS" VERSUS "STICKS" IN THE CONTROL OF AUDITORS
Abstract
Monitors can be useful to the principal in controlling the agent. However, in such an
hierarchical organizational, monitors will also have an incentive to collude with the agent. We
consider a static model where an auditor is hired to monitor an empire building manager. We
start by allowing unrestricted and enforceable side-contracting between the manager and the
auditor. While this model predicts that the auditor's fees should be contingent upon her report,
in practice auditors are largely controlled
A
model does not
fit
this
auditors' independence.
It
is
static
collusion.
We
by the
threat
of lawsuits rather than direct incentives.
observation nor the established view of the imperfectness of the
also unable to answer a
number of interesting questions about
where the auditor conceals
therefore offer a theory of implicit collusion
information because of her "career concerns" which arise from the expectation of future rents.
This dynamic model predicts that the "stick" of the law combined with a flat fee is a more
effective method of control than bonuses. We also show that market structure matters for
organizational form, a large scope for monitors
may
facilitate implicit collusion
interesting multiplicity of equilibria is possible. Overall
informative to explicitly model the forces that
JEL
Keywords: monitoring,
may
Classification:
we
argue that
it
is
more
and
that an
realistic
maintain collusion as an equilibrium.
D23, L22
collusion, implicit collusion, career concerns,
the threat of lawsuits
and
1)
Introduction
most organizations, agents are not the residual claimants of the returns they generate.
In
This conflict of interest between the residual claimant (the principal) and the agent
is
often
resolved by an incentive contract. Nevertheless, the inability of the principal to perfectly monitor
the agent
costly. In
is
many
situations a third-party
is
introduced to monitor the agent; foremen
on the factory floor (Calvo and Wellisz (1979), auditors (Antle (1982, 1984)), regulation agencies
(Baron and Besanko (1984)), the judiciary system
fit
this picture since
However,
one of
as discussed
their
major roles
by Tirole (1986),
in
is
separation of powers) can
(i.e.
all
be seen
monitor an agent on behalf of another party.
to
such an hierarchical control structure, the monitor
have an incentive to make side deals with the agent. Thus, the principal has
will
to
collusion unattractive for the monitor and the agent (see for instance
to
make
Kofman and Lawaree
(1993a), Laffont and Tirole (1993), Felli (1993), also see multi-agent contracting models such
as
Holmstrom (1982), Demski and Sappington (1983), Mookherjee (1984),
Holmstrom and Milgrom (1990), Laffont (1990)
number of important problems.
collusion poses a
like? In practice,
we seldom
to
name
First,
a few).
what
Ma
et al (1988),
The study of monitoring and
will the contract of the monitor be
observe monitors being given direct incentives or being paid
according to the performance of the agent; rather most monitors have legal obligations to the
principal and are threatened
by lawsuits
1
.
Do our
theories predict this reliance on "sticks" rather
than "carrots"? Second, since legal control appears to be important in practice, are the legal
regulations
we observe
optimal in any sense? Third, Tirole (1986), following Crozier (1963) and
Dalton (1959), gives many examples of actual collusion.
Do
our theories imply
equilibrium or does
also take place such that
restricts the set
of contracts that can be used
in equilibrium,
monitors conceal valuable information? Fourth, since collusion
how do
restrictions
on
in
is
often illegal,
on collusion? Can collusion take place
explicit side-contracting impact
without explicit and enforceable side-contracts and
it
that collusion
what are the conditions necessary
if so,
such implicit collusion? Fifth, should monitors just monitor or can other tasks be delegated
them? Sixth, should monitors be subordinated
the structure of market for monitors impact
To
1
offer
What
some answers
distinguishes
to the agent or
his superior? Seventh,
to
how does
on equilibrium organizational form?
to these questions,
legal
be
for
we
will consider a simple organization; an
punishment from direct incentives
performance of the firm, the payment of the monitor
1
is
is
that
instead
of the
conditional on the decision of a court.
auditor
is
manager who has conflicting
hired to monitor the
Kofman and Lawaree (1993a)
shareholders (as in Antle (1982) or
One of our main aims
make use of
in this
paper
with those of the
interests
to
name a few
We
open the black-box of collusion.
is to partially
precedents).
will thus
the institutional details relating to auditors. Nevertheless, most of our analysis
applicable to other monitoring relationships.
goals other than those of the owners
is
An
is
important factor in managers' ability to pursue
the extent to
which he possesses more information about
the corporation, therefore the attestation of the manager's reports can be valuable and an auditor
may be
hired for this purpose.
We will thus consider a hidden information principal-agent model
but the qualitative features of our results would also translate to a hidden action model where
the auditor
would report about
We
the effort level of the manager.
between the
will first consider a static setting with unrestricted side-contracting
manager and the
auditor. This
model predicts
that the auditor should not
the performance of the firm and that her rewards should be based
of legal punishment
is
counter-productive
when
on her
reports.
is
The
to
possibility
the monitor can conceal both favorable and
unfavorable evidence. In the case where she can only conceal bad evidence,
for legal punishment but this role
be paid according
quite limited. Although
it
we can
derive a role
can be argued that monitors'
reputation thus their future payments depend upon their previous reports
(i.e.
whether they
"blow-the-whistle" on bad projects), the predictions of this model do not seem to adhere well
with the observation that most monitors are regulated by law or disciplined by the threat of being
fired.
Further such a
static
model
is
not well-suited to answer the other questions posed above;
for instance, since unrestricted contracts are possible, the scope of the monitor's other duties or
whether she
We
is
the agent's subordinate or his superior are irrelevant for collusion.
will therefore argue that a
Williamson (1975), suggests
dynamic model
is
needed. Tirole (1986), following
that long-term relationships are
also emphasizes the concept of reciprocity
more conducive
to collusion
and
from Gouldner (1961), while lawyers and auditors
emphasize the importance of career concerns as a threat
to auditor
independence2 rather than the
2
Gormley (1981), Chapter 3, DeAngelo (1981). In particular, Dunn (1991), p.20, "It is
impossible to overcome the fact that auditor receives a fee for the audit. This creates an
immediate and pressing need for him to make sure that he does not endanger this source of
income.". Schandl (1978) goes even further; "It is interesting to observe the hypocrisy of the
professional accounting bodies and the security exchange regulations dealing with the problem
of independence... Ownership of a share by the auditor, by his wife, by his partner or by the
employer of the auditor disqualifies him from rendering an opinion. But they close their eyes
presence of explicit bribes. However,
would be no reason
to
if
side-contracts
were unrestricted and enforceable, there
between the short and the long-term.
to expect a difference
open the black-box of long-term relationships. With
we develop
aim,
this
It is
thus useful
a theory of implicit
collusion. Auditors cannot sign a side-contract with the manager, and yet they receive rents in
Therefore to be reemployed
their relationship with the firm.
they
the
may
find
it
profitable to conceal
manager must have a credible
some
(i.e.
due
to their career concerns),
useful information. For this to be an equilibrium,
threat to fire the auditor
not be interpreted as a bad signal by the shareholders.
and the
Our
firing
of the auditor should
analysis will derive the exact
conditions for such an implicit collusion equilibrium to exist and relate these conditions to the
An
questions posed in the opening paragraph.
alternative approach to collusion in the absence
of enforceable side-contracts would be based on reputation and cooperation
applying ideas developed by Kreps et
see Tirole (1990)). In this paper,
because
is
it
al
(1982),
leads
to
repeated
games
Cremer (1986) or Fudenberg and Levine (1989),
we have chosen
simpler to analyze,
in
an approach based on the credibility of threats
and emphasizes
clear predictions
institutional
determinants of collusion.
Our model of
competitive
possibility
is
implicit collusion also offers a
the audit market,
the
of collusion does not only
more
likely is collusion.
restrict the
by the shareholders, for implicit collusion
we would be making
when
is
more
is
our model, the
may
lead to
Thus, as
to
we
be possible there
delegate additional
likely
when
the monitor
is
is
make
subordinated to the
implicit collusion
a more effective form of control than bonuses.
because the auditors must be earning rents for implicit collusion equilibrium
possible,
and
fired.
she has less authority. Fourth, the conditions that
possible also imply that the legal punishment
This
in
collusion easier. Further, because the threat to be fired
(career concerns) are important, collusion
agent and
Second,
since the firing of the monitor should not be
needs to be other reasons for which auditors could be
tasks to auditors,
insights. First, the less
pay-off set of the shareholders but
some valuable information being concealed. Third,
interpreted as too bad a signal
number of new
and while bonuses will increase these
try not to see the
rents,
legal
problem of much greater importance: the
much more
threat of losing the client
if
the
and Dalton (1959)
closely to a situation in which the career concerns of the monitors are
compromise. The importance of reemployment concerns are also
Acemoglu and Gietzmann (1993).
the key reason for their
discussed in
be
punishment would potentially
client dislikes the auditor's opinion". Also, the accounts of Crozier (1963)
correspond
to
decrease them. Optimal control
result,
in contrast to the static
may
thus involve a flat fee and the threat of punishment.
a
problem with unrestricted side-contracting, a dynamic theory of
collusion based on career concerns predicts the form of control that
Finally, in a
As
we
observe
in practice.
model of implicit collusion, the optimal behavior of a monitor may depend on how
other monitors are expected to behave, hence a multiplicity of equilibria arises. However, this
multiplicity is different in nature than the large
number of equilibria
games.
in repeated
It
arises
because the credibility of the manager's threats depend on the actions of other auditors.
The
recent paper by
Kofman and Lawaree (1993a)
also analyzes
how
the possibility of
collusion constrains the set of possibilities for shareholders. Nevertheless, they
the interaction between private contracts and litigation nor
implicit collusion,
assuming
that the risk-aversion
shareholders,
may be
the possibility of
can always be written. While
that binding side-contracts
of auditors
do they analyze
do not deal with
we show
important for the mix of controls that will be used by
Kofman and Lawaree assume
risk-neutrality.
The seminal paper by
does not discuss nor formally model implicit collusion, although
of long-term relationships and reciprocity
3
.
it
emphasizes the importance
Tirole also studies whether the agent
punished or rewarded as a result of the monitor's report but does not discuss
direct incentives in monitoring contracts. Finally,
Tirole (1986)
is
likely to
why we do
be
not see
by developing a model of implicit collusion,
our paper obtains a number of new results such as the possibility of multiple equilibria
depending on other auditors'
behavior, the link between market structure and organizational
form, and the importance of the scope of the monitor's duties and of her authority.
The paper
is
structured as follows. In section 2,
we
present a model in which, without
the possibility of collusion, auditing has a welfare increasing role for shareholders. In Section
3
we
develop a simple model that enables us to study monitoring and collusion
in the
presence
of enforceable side contracts and investigate the role of a range of instruments ("carrots" and
"sticks") in controlling the extent of collusion. Section
the paper.
It
4 constitutes the most important part of
develops a model for the analysis of collusion in the absence of enforceable side
contracts and discusses the questions posed above.
The paper concludes with Section
5 while an
appendix contains the proofs.
3
Tirole's
more
game framework,
discussed already.
recent paper (1990) contains a model where collusion
but this
is
different
may
arise in a repeated
from the model considered here due
to the reasons
2)
Auditing Without Collusion: The Basic Framework
Consider a manager running a firm on behalf of a group of risk-neutral shareholders who
only care about final returns. At date t=
assets of the corporation will
1,
be liquidated
a continuation decision has to be made. Either the
shareholders only want the project to be continued
assume
two
that there are
states
of nature, good
with probability p and 1-p respectively. In state
success equal to
assumed
It is
q
if
.
expected returns are greater than L.
and bad
(g)
(i
i
or the project will continue 4 Therefore,
=
g or
(b)
which are expected
b), the project has a
to
We
occur
chance of
with associated return equal to y. If unsuccessful, returns are equal to zero.
that
qy>L>q#
(CI)
thus shareholders
would only
good
like to continue in the
state.
Also
pq^-p)qy>L
(C2)
so
L
at a value
when
they have no information about the true state of the world,
it
not profitable for the
is
shareholders to discontinue the project. Since shareholders are disperse, they do not have
accounts of the company
sufficient incentives to invest time
and resources
and will not observe the true
of the world directly. Nevertheless, before the continuation
decision, they receive a
state
summary
financial statement
company's performance was good or bad
or bad. This report
summarized
in
may
Figure
or
may
in investigating the
in the
from the manager, reporting whether the
most recent period,
not be truthful.
i.e.
whether the
The sequence of events
interests that differ
receives control rents from continuation and
is
would
is
like to undertake the project in both states
in general
be solved
if
offered an incentive contract based on the returns of the company. However,
To
such incentive schemes are often expensive and introduce inefficiencies.
a very simple
model
from those of the shareholders. Specifically, he
of nature (e.g. Baumol (1959), Williamson (1964)). This problem could
manager
this
good
1.
The manager has
the
in
state is
way we adopt
the assumption of Hart and
Moore
capture this idea
(1990): the manager
is
in
an
absolute empire builder in the sense that he derives infinite control rents from continuation. This
4
As
the shareholders are disperse, an alternative interpretation
decides what their reservation price for the shares
is
and
if this
price
is
is
that each shareholder
sufficiently low, a raider
takes-over and liquidates the company. Shareholders will also have other methods of control than
auditing such as debt, incentive contracts, threat of takeover, etc.
methods only work imperfectly and as
work
at all.
it
However,
can be verified quite simply,
in
in
general these
our case they do not
assumption of unidimensional preferences for the manager considerably simplifies our analysis
by implying
manager
that there exist
Given
to shareholders.
Proposition
1
The manager
no contract or mechanism
we
this specification
by the
that will insure truthful reporting
can
state the following result.
(Overoptimistic Managerial Reporting)
will
always report the
This outcome
is
state
of nature to be good and the project will be continued.
obviously inefficient from the viewpoint of the shareholders and
it
can
be asked whether another agent attesting the validity of the report of the manager would help
(See Gormley (1981) Chapter 4 and Mednick (1986) on the role of auditors to attest reports and
make
also to
t=0 an
financial forecasts). Let us suppose that at
the accounts of the firm and if the
auditor
is
hired
manager prepares an overoptimistic
auditor discovers this with probability
1-r.
We
can think of
who
financial report, the
this situation as follows;
performing sample audit work, the auditor receives a signal about whether the
is
B
is
equal to zero.
or G. The probability that the project
P(G),
is
—
The
.
is
also studies
state
after
of nature
good conditional on message B, denoted by P(B),
probability that the project
is
good conditional on signal G, denoted by
Therefore even when the auditor finds no sign of overoptimistic reporting,
p+(l-p)r
the state of nature
r is in
may be
bad. Since auditors decide
the state of nature to be bad, the
change
at
thoroughly to investigate the accounts,
general endogenous. Assuming r constant will not however change the main features of
our paper. Note also that since there
of
how
in
our analysis
if
is
a positive probability,
manager
will
r,
that the auditor will not discover
always issue a good report and nothing would
the auditor were hired at
t= 1,
after the report of the
manager
instead
t=0.
We can
into a report.
summarize the decision of the auditor with a function
Our
a(.)
which maps her
task is to determine a(B) and a(G). Let us start with the case
signal
where
the
auditor always behaves truthfully (the extreme case of auditor independence in which the auditor
has no desire to collude with the management) which would entail
irrespective of her rewards.
bad and she discovers
it,
As a
result, if
an auditor
is
auditing, shareholders
hired,
whenever the
state
of nature
is
she will save the shareholders the difference between the expected
return of the project and the liquidation value.
independent auditor
is
a(B)=B and a(G)=G
Thus
the benefit to shareholders of hiring an
equal to (l-p)(l-r)(L-qb y). If this amount
would
is
greater than the cost of
hire an auditor and discontinue the project
whenever she claims
the
will
manager has produced an overoptimistic
assume
is
number of
However, the
(1991)).
message B.
In
what follows we
gain to be large. Thus shareholders will hire an auditor to solve the incentive
this
problem. This result
helpful in a
report, i.e sends
of course not surprising as
we know
situations (e.g. Vickers (1985),
crucial issue here
is
how
that introducing a third-party
is
Fershtman and Judd (1987) or Katz
to ensure the
independence of the auditor while
also minimizing the cost of control to shareholders.
Control of the Auditor and the Role of Legal Institutions
3) Collusion,
In this section
we
will relax the assumption that auditors can
not to collude with the management. Instead
restrictions
bribe equal to
reward the auditor
m
in other
and model
ways
the
more
in the introduction,
we
interesting cases need a
The
by u*. This
audit market
is
instruments as
is
We
this as
assume
that the
will
manager can pay a
a monetary bribe. In general, managers can also
by cooperating with them, by making
Although these show
interpret the bribe as a
dynamic framework
their
similarities to the reciprocity idea
monetary one
like the
in this section,
one we introduce
because
later.
competitive and the auditor receives her reservation return denoted
a very important assumption
it
will also
in
comparing the
relative efficacy of different
enables us to impose the participation constraint of the auditor and treat the
problem a constrained cost minimization 5 In the next
.
receive rents and additional issues will arise.
utility
upon
which there are no
will analyze a situation in
too; for instance
financial records easily available, etc.
mentioned
relied
on side-contracting between the manager and the auditor and such side-contracts
not suffer from enforceability problems.
maximum
we
be automatically
The
section, collusion will require auditors to
total cost to
shareholders will depend on the
function of the auditor and the variability in her returns.
risk-averse with a utility function u(.). Risk-aversion
is
We
assume
that the auditor
is
a plausible assumption: since most audit
firms face the risk of large lawsuits, they are unlikely to act in a risk-neutral way.
5
Although in practice auditors are hired and incentive contracts are determined by managers,
problem as though shareholders hire the auditor. The justification is that if the
manager does not hire an auditor or does not sign a collusion-proof contract with her, the
we
treat the
shareholders will either not hire the manager or will decide to liquidate the project. This stage
can be explicitly modelled by giving the manager a choice to hire an auditor and offer her an
observable contract after he finds out about the state of nature and then impose a signalling
Cho and Kreps (1987)'s Intuitive Criterion. This is not done in the paper so
crowd the argument even further (for a similar structure see Acemoglu (1993)) but all
our results can be shown to hold with this modification.
refinement such as
as not to
We
model the
legal system as follows. If the auditor does not find the report of the
manager overoptimistic
shareholders can
(i.e.
reports a
good
state)
and subsequently zero returns are
a lawsuit against the auditor for not defending their interests. This
file
modelling assumption
is
intended to resemble the following stylized facts. Shareholders do not
observe whether auditors have performed effective audits. However,
shareholders believe that there
Gormley (1981), Chapter 5
a
if
When
is
if
the investment collapses
performance from the auditor,
after a favorable report of previous
(makes zero returns) shortly
court.
realized,
a high probability that auditors performed inadequately (see
for details of liability of auditors to clients) and decide to
go
to
sued in court, auditors are found liable with a probability 7 and fined an amount
the state
is
bad and never
truly
if
the state is good. Alternatively, this assumption can be
reinterpreted as stating that ex post, shareholders have access to an independent fourth-party,
no cost
the court, at
Kofman and Lawaree
(1993a)). This fourth-party can be quite effective in determining the state
of nature (7 can be large).
the monitor. Yet
the auditor
may
show
will
thus appear that this
that
is
a very attractive method of controlling
when shareholders cannot commit not
may be
at finding out
may
why
More
importantly, investigation by the court
by the auditor and as we
Thus an arrangement
in
Second, what happens
if
and
not replace the auditor with the
not be feasible because although the court
whether the auditor has misreported or not,
auditor's duties.
to file a lawsuit
counter-productive.
questions need to be asked at this point. First
court? This alternative
that
It
risk-averse, the threat of lawsuits
is
Two
we
our court plays a similar role to that of the external auditor of
(thus,
it
is
may be
quite competent
could not undertake
likely to
of the
all
be more expensive than
will see, in equilibrium, the court will rarely need to interfere.
which the court
is
the fourth-party
the shareholders bear
some of
is
likely to
be socially optimal.
the cost of lawsuits? If this cost
is
small
enough, our analysis will go through (but see Corollary 2, below) and
if it is high,
correspond to the case with cx=0, since the shareholders will never
a lawsuit. In general,
if
file
this will
shareholders also observe a signal of the state of nature, they can condition their decision to
file
a lawsuit upon this signal. Since in our model there
is
no such
signal, costly lawsuits
do not
enrich the analysis though such an extension looks promising for future work.
As a
result
of our assumptions, when the auditor discovers the
bad but purposely reports
it
to
state
of the world
be good, she faces a probability (l-qb)7 of being
to
fined. If she
does not discover the state of nature to be bad, she faces the smaller probability X(l-q b )7
she will be found liable, where
X=1-P(G)=
r
\
?'
r(\~PYP
8
is
be
that
the probability that the state of nature
is
bad conditional upon not discovering anything
auditor
found
is
a
liable, the fine
is
We
G).
(i.e signal
assume
also
paid to the shareholders (we thus ignore
all
that if the
costs of legal
proceedings- see the discussion above and Corollary 2).
If the shareholders
a would
court,
and auditors could write contracts conditional upon the decision of the
not matter at
all,
since private contracts
on the
would increase or reduce
However, the court considers the global
effect
Hence damages would take
any such pre-existing contracts6
into account
the contract of the auditor cannot be
or not, but
it
The
we
will consider
The
it
is
bad,
two
may
also be
We
important.
will
Case
1:
Shareholders can
We denote the bonus
by
/3
lie in
when
the bad state
when she claims
assume
that
a(B)=G
is
good
possible.
the bribe
is
payments
paid by the manager and so
7
.
both states
that the auditor receives for reporting the state of nature to be
bad
(reward to "whistle blowing"). The salary of the auditor when profits of the firm are zero
and when the return of the firm
denoted by
to
be non-negative, hence the auditor cannot be paid a lower salary when the firm
s
is y, this
salary
is
After the filing of a lawsuit, the responsibility of the auditors
Gormley (1981) Chapter
to ignore the possibility
in the case
7
it is
the report to be
is
6
that
analyze the consequences
will interpret the bribe as a financial one, the funding source of bribe
shareholders will not care about the size of the bribe
a)
To
is
it
overoptimistic she needs to back this up with evidence, thus only
we
assume
thus
are possible.
auditor can only misreport in the bad state because
Since
We
different cases of "misreporting technology";
a(G)=B and a(B)=G
both
i.e.
.
conditional upon whether she has been found guilty
auditor can misreport in both cases; she can claim that
and good when
2)
plaintiff in finding against the defendant.
can be contingent on final returns and on her report.
of the legal framework,
1)
made
as desired.
it
14. Also,
fits
is
it is
auditors takes the form of
m
successful
potentially criminal, see
to sue the auditors
unsuccessful.
often suggested that actual collusion between the
management consultancy
This would however imply that the management
assumption, thus
is
assumed
not possible for the auditor and the shareholders to agree
funds.
An
earlier version
is
management and
contracts or lucrative fees for other services
paid to subsidiaries of the auditing firm (Simunic (1984),
company
is
well with case in which the manager rewards the auditor in the form of
cooperation. However,
using the
is
of lawsuits because shareholders cannot commit not
where the project
This also
it is
equal to s+z; z
Gormley (1981), Chapter
not paying
showed
that all
m
out of
its
own
our results hold
if
2, p. 32).
resource but
we change
can be interpreted as coming out of shareholders' resources.
is
this
and the manager can hide the
(for instance, because the auditor
any bankruptcy constraints
that
may be
we assume
We
are also ignoring
binding the firm or the auditor; the firm
have sufficient reserves to pay the auditor and the auditor
her by the court. Finally,
returns).
that the
is
is
assumed
to
able to meet the fine imposed on
manager makes a
take-it-or-leave-it side-contract
offer to the auditor.
The
constraint that needs to hold
first
the auditor tells the truth in the bad state, i.e.
is
a truth-telling one, (Al). This makes sure that
a(B)=B.
If she claims the state to
receive s+|8. If she claims the state to be good, the project will
her basic salary
s
go ahead, and she
will receive
plus a bribe that can be as large as m. Also with probability q b the project will
be successful and she will get an additional bonus
project will be unsuccessful and with probability
will
be bad, she will
be fined a. Therefore, for a(B)=B,
we
However, with probability
z.
7 she
will get detected to
(l-q b ), the
have misreported and
require
u(s+p)>q b u(s+m+z)+(l-q b )(l-y)u(s+m)+(l-q b )yu(s+m-a)
(Al)
Secondly
we
need a
truth-telling constraint
when
the auditor's signal
is
G,
does not discover any signs of overoptimistic reporting by the management. In
project
may
still
.
when
she
this case, the
be bad with probability X and she will be fined a with probability \(l-q b )7.
Also conditional on her signal G, she will get the bonus with a
X)q,+Xq b Thus
i.e.
for
a(G)=G, we
total probability
of
(1-
require
u(s+0)*{(l-X.)q +hi b }u(s+m+z)
g
H(l-k)(l-q yX(l-q b )(l-y)}u^m) + X(l-q b )yu(s + m-a)
g
Next we need
expected
state
utility to
to write
the participation constraint of the auditor. This requires her
be greater than her reservation return, u*. With probability
of nature will be bad; in
lie (i.e.
down
this state there is not
(Al) holds), thus she will
tell
(l-p)(l-r), the
a sufficiently large bribe to make the auditor
the truth and receive u(s+/3).
With probability p+(l-p)r,
she will not discover any signs of the bad state and she can be bribed. However, as the manager
is
making a
take-it-or-leave-it offer,
the participation constraint
he can just offer her alternative return, u(s+/3). Therefore,
is
(PC)
u(s+p)*u*
Shareholders would like to offer a contract to the auditor which satisfies
conditions and minimizes their total cost;
TC=s^l-p)(l-r)^{pqg+ (l-p)rq }z-(l-p)r(l-qb )ya
g
10
all
these three
when
Shareholders only pay
is
paying
a back
to the shareholders with probability (l-p)r(l-q b) (since in equilibrium, the
auditor will be truthful, this
the truth)
the auditor claims the state to be bad. Also note that the auditor
is
the probability that she will be fined conditional
and the expectation of
this
amount
is
subtracted from the total cost above.
auditor claims the state of nature to be good, she
management
in the
form of bribes. This implies
the auditor to receive bribes
However,
We
in the
now
can
static
telling
When
the
receiving part of her payment from the
that shareholders are
happy
in
equilibrium for
independence.
to relinquish her full
problem, the auditor will never conceal any evidence.
ask whether z will be set different from zero, or in other words, whether the
auditor's salary will be conditioned
Proposition 2 (Case
When
is
from the management and thus
equilibrium of this
upon her
upon the performance of the firm.
Auditor Fees Are Independent of Firm Performance)
1:
her payment
misreport in both states,
the auditor can
is
on the
not conditioned
performance of the firm.
In this set-up increasing z has
two
effects. First,
a direct negative effect as costs increase
RHS
but also a beneficial indirect effect since increasing z would push up the
enabling a reduction in
s
and a
rise in 0. In the
appendix,
we show
that the indirect effect never
dominates the direct effect and profit-maximizing shareholders never
auditor to the performance of the firm. This result
compared
to
an increase in
/3,
is
is
form of bribes irrespective of the value of z
shareholders must be bearing the cost.
z<0
We
(i.e.
when
if
and a correspondingly higher value of
total costs to shareholders.
in the
Next we turn
However when a=0,
to the interaction
is
is still
uncertain.
paying
all his
However,
resources
it
z,
the
in the
s
were possible, the shareholders
as long as
a>0.
Because
event of her being fined,
the optimal value of z
can be chosen to be negative (see equations (5)-(6)
it
increase in
(A2) holds as an equality), therefore, the
can also see that
corresponds to providing insurance to the auditor
reduce
An
introduces additional variability in the auditor's return because
receiving her reservation return and the manager
would prefer
relate the salary of the
also quite intuitive.
conditioning on her information, the performance of the firm
auditor
of (A2), thus
is
it
this
would
zero even
in the appendix).
between the "stick" imposed by the legal structure, a, and
the "carrot", 0, (having already established that the other type of carrot, z, will not be used).
We
will
show
that in this case, total costs to shareholders are increasing in a,
11
implying that the
ex post possibility of lawsuits makes shareholders worse-off.
Proposition 3 (Case
When
1: Possibility
of Litigation
the auditor can lie in both states, total costs,
The proof
is
An
provided in the appendix.
a goes
up,
the
demonstrate that
is
RHS
of (A2)
falls
are everywhere increasing in a.
a from
a
has two effects: a direct effect
the auditor and an indirect effect that
always dominates the direct
effect.
The
a
again that the manager and the auditor are as well off as before and an increase in
the variability of the auditor's return in the
have therefore shown
the cheapest
way
that,
good
state;
contract, they
only.
/3
would choose
a=0
shareholders have to bear this cost.
Thus
if
We
and
z,
shareholders were to set a by
(despite the fact that
y can be
as large as
because bonuses induce the auditor to report her information without introducing as much
1)
variability in her return.
not to
file
However, when a
is set at
a positive level by law, they cannot commit
a lawsuit ex post, and the auditor demands
Case 2: The Auditor can only
b)
We now
lie in
the
bad
more compensation ex
ante.
state
turn to the case in which the auditor needs to furnish evidence of actual over-
optimistic reporting
by the manager and thus cannot claim the
state to
be bad unless she finds
such evidence. Hence irrespective of her rewards, the auditor will report truthfully
is
intuition
increases
of the three instruments available to control the auditor, a,
to achieve control is to use
means of a private
we
needs to be reduced. In the appendix,
thus
this time, the indirect effect
TC,
increase in
that reduces the cost to shareholders as they receive
as
Harmful)
is
G,
i.e.
a(G)=G. Therefore,
the only incentive
to hide such
evidence when the state of nature
we
left
are only
is
we
need to give to the auditor
indeed bad. (A2)
now becomes
is
if
her signal
for her not
irrelevant and
with (Al). Crucially, the participation constraint of the auditor will change too
because she no longer receives u(s+j8)
in
both
states. Instead
when her
signal
is
good, she will
receive her payoff specified by the contract. Also since (Al) holds, she will never receive any
bribes in equilibrium.
nr^
Thus
(l-p)(l-r)u(s+P)+<pq +(l-p)rqb }u(s+z)
g
-W-qgH^Py(l-q
b
)(l-y)Msy(l-p)r(l-qb )yu(s-a)>u*
12
Proposition 4 (Case 2:
When
Possibility of Litigation Is
Not Always Harmful)
the auditor can only lie in the bad state, there exists an intermediate value of legal liability
which minimizes
To
is
The
total costs.
why
see
straightforward
appendix,
we
it
8
.
would never be optimal
Also, cost minimization requires (Al) to be satisfied as an equality. In the
analyze
how
and
s
shown
total costs are also
in the
to decrease in a.
was a sure payment
(PC). Before
o
vary as
of a are harmful as
that high values
pay the auditor more than her reservation return
to
tends to infinity and z
is set
equal to zero.
a
previous subsection. However, as
The
tends to zero,
and increasing
was a
cheap way
relatively
of compensating the auditor for her services. However, here, the auditor only receives
probability (l-p)(l-r).
introduces too
much
When a
On
risk.
is
which,
to rely
at
the other hand,
low values of a,
when a
may
it
Two
Corollary
The
to this discussion
any
level of
a
intuition of this corollary relies
high level of
a reduces
compensated for
it.
neutral the size of
that conditional
g
concavity of u(.)), this also allows
it is
from zero, but a would
By
still
the
same
be positive.
can also be stated (proofs omitted);
and
Further
z are equally effective.
on the discussion of the main
results
of
is
paid back to the shareholders,
not matter. Similarly, the reason
why
z
was
when both
sides are risk-
less efficient than
upon the information of the auditor, z introduced more
not an issue, the two types of bonuses are equally effective.
Since there
is
no issue of the auditor having limited resources, we
not always the case, paying a third-party
necessary to avoid collusion
when
more than her
13
finally
have (see
may be
Acemoglu (1993),
reservation return
the third-party has limited resources (e.g.
Besley and McLaren (1993)).
was
variability than 0. Yet
is
is
this section.
the auditor's return in one state of nature and the auditor needs to be
However, since a
a does
is efficient.
risk-aversion
This
not optimal
1:
If the auditor is risk-neutral
when
(i.e.
exists an optimal level of a.
also be optimal to have z different
immediate corollaries
becomes more
increases, her return
beneficial. Therefore in this case,
on one instrument too much and there
argument,
A
is
with
has to be set high in order to satisfy (Al); this
equal to zero,
variable but by virtue of the risk-aversion of the auditor
a reduction in
see
be obtained by comparing (PC) and
intuition can
to the auditor
We
Kofman and Lawaree (1993a)
for a similar result in a slightly different context);
Corollary 2:
always more costly to use non-pecuniary punishments rather than pecuniary ones.
It is
Thus
if
additional to a, there are litigation expenses and costs to applying to court, legal
punishment becomes a
see
less attractive
Acemoglu and Gietzmann
legal stick is
The
even
method of control, even without
(1993)). Since in practice legal costs are quite substantial, the
less attractive than suggested
implication of this section
by our analysis above.
is that in
a hierarchical organization form,
optimal to pay the monitor a salary independent of the outcome
conditional upon her report, because, in equilibrium, her report
information (which
that
we want
risk-neutrality (on this also
(z=a=0),
is
just rewarding her
9
.
We have also
depending on the precise assumptions, there may be a limited role for legal
monitor (auditor) and
In practice,
agent.
Our
if this is
we seldom
showed
liability
of the
the case, legal liability should be set neither too high nor too low.
observe monitors being rewarded according to the performance of the
analysis thus suggests a possible explanation for this.
predictions of this
may be
a more accurate signal of her
deduce) than the performance of the firm
to
it
model are not as
However,
the rest of the
plausible; although rewards to "whistle-blowing"
monitors are not often paid according to their reports).
It
can be argued
may
exist,
that, especially in the
case of auditors, their reputation thus their future payments will depend on
how
tough they
appear, hence indirectly on their reports. Yet casual observation as well as established views
(e.g.
Gormley (1981), Dunn (1991))
the monitors and a static
also suggest that the legal stick
model does not
fit
this
model and the practice may have a number of different sources.
we
observe
inefficient.
Second, report contingent pay-offs
a static model with unrestricted side contracts
situation.
try to
Motivated by
this last observation,
9
may
we
Strictly speaking,
we
when z=a=0,
and lying. In this case we assume
be marginally positive.
First, the legal
may
arrangements
not be possible. Third,
not be capturing the salient features of the
next turn to a dynamic model in which
open the black-box of collusion and analyze
monitors direct incentives. Further as
important in controlling
observation very well. This discrepancy between
the
may be
is
its
predictions on whether
will see, a
model of
it is
we
will
optimal to give
implicit collusion will enable us
the auditor will be indifferent between telling the truth
that she
behaves as
14
we want
her
to.
Alternatively, z or
a can
to offer
some
tentative answers to the questions posed in the introduction
model was
silent.
4) Implicit
Collusion and Auditor Behavior
The previous
on which the
section has a major omission: there will often exist legal limits to the side-
contracts that can be written between the
manager and the auditor and
as a result enforceability
problems associated with these side deals will also be quite serious. For instance
of auditing,
all
transactions between the auditor and the
SEC and AICPA
regulatory agencies (e.g.
13).
in the
management
is
we
yes,
our example
US, see Gormley (1981), Chapters
This leads us to ask the following question; suppose there
possible? If the answer
in
are closely monitored by
is
no
refer to this as implicit collusion.
There
2, 5
and
possibility of side-
contracting via direct financial transfers between the manager and the auditor,
is
is
collusion
still
nothing that forces
the auditor to collude; but along the equilibrium path, the auditor suppresses
in
static
some information
order to increase her payoff. This, rather than a situation in which auditors receive explicit
bribes, also
seems
to
be more
in line with the
view among lawyers, accountants and sociologists
about the imperfectness of the independence of the auditor and,
references in footnote 2).
collusion can arise.
Our
We
will investigate the circumstances
analysis will suggest a
(4.1)
A
(4.2)
The manager should have a
(4.3)
The
number of
under which such implicit
conditions;
firing
credible threat to fire the auditor.
of the auditor should not be interpreted by the shareholders as sufficient proof
bad
-
this will require that auditors
And/or there should be a positive probability
have a secondary role
that the next auditor
find out about the state of affairs or is willing to cooperate with the
(4.4)
of monitors (see
long-term relationship must exist between the auditor and the manager.
that the project is
fail.
in general,
The
threat of being fired should
be damaging
some
When
now
hired does not
to the first auditor so that she is willing to
first
auditor should be
positive rents in future periods.
such collusion
is
possible,
it
can again be prevented by the threat of
by an appropriate incentive scheme for the
threat is
is
which they can
management.
collude implicitly in order to avoid being fired. In other words, the
expecting
who
in
different
and the
"stick" is
We
auditor.
much more
litigation or
will see that the role of the litigation
effective relative to the "carrot" than in the
previous section.
To model
this situation in the simplest
way,
15
we
maintain the basic structure
set
up
in
section 2 but also introduce
thus
assume
We are
On
one of
the returns are realized, a
manager
is
again assumed to be an absolute empire-builder
is
this project for as
the project will yield
project will
abandon
come
to
good project has probability
q, of success while this
an end and yield
this project, shareholders
to discounting
game both
we
final return.
its
when
Because the manager never wants
also need to modify assumptions (CI) and (C2).
qy>L>
to
Namely
qy
T
Thus the expected net present value of a good project
1-5(1-0)^
is
higher than the liquidation value but that
is less.
ipqg+{ l-p)qb}
<C4)
-±-y>L
This condition states that unconditionally, the project
is
Since the firm consists of a number of projects,
and
uncertain
it is
the auditor and the shareholders discount the future at the rate
1-5(1-0)
the time
q b for a bad
cannot induce him to report truthfully and the auditor can
(C3)
of a bad project
However,
is
return. In particular, in each period there is a probability 6 that the
its
again be useful. In this
long as possible.
good with probability p and bad with probability 1-p and when
We thus have a structure very similar to the static model.
project.
is
need a dynamic framework and
time and consists of a number of projects.
he always wants to continue with
cost,
Unconditionally, the project
Due
we now
these. Shareholders are not sure about the probability of success of
the other hand, the
and whatever the
5.
features. Firstly,
that the firm is infinitely lived in discrete
interested in
this project.
some new
this auditor will also issue
on average
it
profitable.
needs to have an auditor employed
all
a statement each period reporting whether the manager
overoptimistic about the project in question.
Here we make a number of additional
assumptions, which will be discussed in more detail as
we go
along. First
the firm faces
,
switching costs in the audit market, thus pays a fee higher than the marginal cost of auditing.
In particular, each period, the auditor receives a
marginal cost. Second
,
there
is
minimum payment
a small probability
e that
the auditor will
R
of
(rent)
fail
above
its
in her duties
associated with other projects. Yet these duties are quite important (e.g. internal fraud detection,
see
Gormley (1981), Chapter
replaced.
3.7) and if the auditor fails in these duties, she needs to be
Whether she has done so or not
over the auditor
is
is
delegated to the manager.
hired in the following period.
We
unobservable by the shareholders, thus authority
When
will later analyze
16
the auditor
how
is
dismissed a
new
the results change if the
auditor
new
is
auditor
is
brought immediately. Third the auditor
,
risk-aversion introduces important effects.
now assumed
is
However,
it
to
be risk-neutral. As argued above.
also complicates the analysis and
crucial for the
mechanisms we are investigating
true state (i.e.
r=0) but she obtains two kinds of evidence; with
probability
10
it
.
Soft evidence in contrast
report
it
and
if
she reports
is
if
verifiable
is
n hard and with
probability
and the auditor
unable to conceal
is
may choose
hard or soft
is
a with
three possible reports for the auditor: good, G; bad with soft evidence,
First,
a(BH)=BH
to describe the case in
(G,
true
is
by
definition.
We
Thus there now
possible and
situation
information and
we
(for
exist
BS and bad with hard
we
by the management or not and
are also assuming that side-contracts
cannot be written between the auditor and the manager, implicit collusion
The
game
will use the term implicit collusion
the auditor has been discharged
decide whether to continue with the project. Since
is
also
which a(BS)=G. Each period, shareholders observe the auditor's report
BS or BH) and whether
collusion that
we
an independent event from whether the
is
brevity ignoring the failure and success of the auditor in the other tasks).
BH.
will just
it
probability 7. For simplicity,
auditor failed in her other duties. Figure 2 summarizes the sequence of events in this
evidence,
not to
the auditor conceals her soft evidence and the project fails, she
whether the evidence
that
the auditor always observes the
to the shareholders using hard facts;
it
again found out to be guilty and fined an amount
assume
,
unverifiable by the shareholders; the auditor
she cannot prove
it,
be her opinion". However,
is
Hard evidence
soft evidence.
l-fj.
here. Finally
not
is
we
we
will investigate
are considering
now
under what circumstances
corresponds to a dynamic
is
it
game
use the concept of Perfect Bayesian Equilibrium.
the only type of
may
arise.
with incomplete
According
to
this
equilibrium concept, shareholders' beliefs must be derived from the equilibrium strategies of the
manager and
10
As we
the auditor
by Bayes'
rule
and
at
each stage of the game, given these beliefs, the
will see later, the auditor will only conceal not to be discharged
Therefore even
if
by the manager.
she had the possibility of concealing hard evidence, she would never do
Thus our assumption
that hard evidence cannot
be concealed
is
so.
purely to simplify the discussion
in the text.
11
The assumption
However, the
that
distinction
r=0
between
only serves to simplify the expressions that will follow.
soft
and hard information
hard information, the manager would not find
have a credible
threat. If
to tolerate collusion.
The
we
it
is
more
substantive. If
we
profitable to fire the auditor and thus
only had
would not
only had soft information, the shareholders would be less willing
distinction
between
soft
and hard evidence
is
made by Antle
(1984),
among others, but none of these papers discusses the interplay
between non-verifiability of information and collusion via career concerns.
Tirole (1986) and Jewitt (1992)
17
s
must be best-response
strategies of each player
model
equilibria of this
to the strategies of other players.
such as
satisfy stronger equilibrium concepts
Also the
Cho and Kreps (1987)s
Intuitive Criterion.
The
not
12
,
first
thing to note
the auditor
if
to
manager has the
the threat of the
is
R
per period, from being employed by
in other
this firm.
words, she has career concerns. Also note
right to fire her claiming that she failed in her other duties. Therefore
to fire the auditor is credible, he will
way he
interpreted
Provided that
be reemployed or
manager
her to report in the
dismissal
irrespective of whether the project in question continues or
expecting future rents,
is
Thus the auditor wants
that the
is that
desires. This credibility will
have some scope
in forcing
depend on whether the auditor'
by the shareholders as a bad signal about the quality of the firm.
this threat is credible, the auditor will
compare
the return to collusion with the
return to being honest and getting fired. If she prefers the former,
we
will
have an implicit
collusion equilibrium where auditors conceal their soft information and managers fire auditors
who
refuse to collude.
truthfully.
Our
The
alternative
a no collusion equilibrium where auditors always report
strategy of analysis in the rest of this section
implicit collusion equilibrium to exist
As we
is
collude
(i.e.
We
derive conditions for an
and then globally characterize the equilibria of
will see, the behavior of the auditor
behavior of other auditors.
is to
may depend on
this
game.
the structure of audit market and the
will first suppose that all auditors are believed to implicitly
a(BS)=G).
Proposition 5 (Optimal Continuation With Implicit Collusion)
In the equilibrium in
which auditors
auditor provides hard evidence that
Our
first result states that
of an auditor
is
implicitly collude, the project
it is
when
manager keeps
never abandoned
an
bad.
not interpreted as a bad signal which will in turn
is
until
auditors are believed to implicitly collude, the dismissal
manager a credible one. The proof of
underlying idea
is
this proposition is
the threat of the
again in the appendix. Yet, the
sufficiently important to deserve discussion in the
firing auditors, this is not interpreted as a
make
main
text:
bad signal and the project
12
In general, the auditor would receive less rents when one of her projects
which could increase her incentives to implicitly collude.
18
even
is
if the
is
not
abandoned
abandoned. In an equilibrium
not colluding. Therefore,
in
which auditors are expected
all firings
would be no use
auditors
in
who
never fired for
are interpreted as due to auditor incompetence and do not
constitute bad signals. If an auditor has
it
to collude, they are
no hard evidence but
for her to claim so because she only has
are actually fired for incompetence
would
is
because of incompetence,
fired
non -verifiable
soft
evidence and
all
also have a similar incentive and thus
equilibrium they will not be believed unless they possess hard evidence. In other words.
denoting failure by the auditor in assisting the manager by
collusion equilibrium,
F and no
failure
by
S; in the implicit
a(G,F)=a(BS,F)=BS and a(G,S)=a(BS,S)=G. Thus
BS when
deviates and sends message
interpreted as a(.,F)=BS.
As a
her signal
is
BS and
the
manager
is
very
be
fires her, this will
result, in the implicit collusion equilibrium, soft
not adversely affect shareholders' beliefs. Since this result
an auditor
if
information does
much dependent on
the
secondary role of the auditor (condition (4.3)), collusion will be more difficult when the scope
of the responsibilities of the auditor
collusion can be prevented
(e.g.
if
is
narrowly defined. In our simple example of
the secondary duties of the auditor are delegated to another party
employ another auditing firm
for the other projects)
the authority to fire the auditor, the auditor will have
less incentive to collude. In
this section,
13
.
Also,
if
the
manager does not have
weaker career concerns and thus
our model, the manager
is
assumed
to
have the right
will
have
to fire the
auditor because shareholders cannot observe her performance. But in general, the principal
should prefer not to
make
the monitor the agent's subordinate. In fact, in
most hierarchical
organizations, although the agent can always complain about the monitor, the monitors are not
under the direct control of the agent and have higher authority than the people they supervise
In a
model with unrestricted contracting, there
13
is
no reason
to expect such an
14
.
arrangement.
would still be an Perfect Bayesian Equilibrium but would fail
any other refinement of PBE. Also obviously, other sources of noise
will lead to a similar result. But our general claim, that the narrower is the scope of the monitor,
the smaller is this noise and thus the more difficult is collusion, would hold.
If
e=0,
implicit collusion
the Intuitive Criterion or
14
See Corzier (1964, pp 42-43) about how the relationships between the agent and the
supervisor varies depending on how much authority the supervisor has. Felli (1993) offers a
different interpretation of Corner's discussion. In Felli 's model, when the supervisor has more
authority, the agent is less willing to reveal her private information, thus collusion is more
difficult.
Whereas
in
our model more authority insulates the supervisor from the influence of the
agent.
19
Proposition 6 (Managerial Behavior With Implicit Collusion)
when
In the implicit collusion equilibrium,
auditor
who
the project
is
bad, the manager will always fire an
does not collude and does not possess hard evidence.
The proof of
this proposition is straightforward
and
is
thus omitted.
shareholders described above implies that the manager will find
it
who
If
deviates. If he does not fire her, the project
interpreted
by the shareholders as due
(see proof of Proposition 5)
to auditor
and the project
is
implicit collusion equilibrium, the next auditor
is
abandoned.
The
inference of the
profitable to fire an auditor
he
fires the auditor, this
incompetence and their posterior
is
not abandoned. Moreover, since
is
is
not changed
we
are in the
expected to collude (again condition (4.3)).
Therefore, the manager will be better off by firing a deviant auditor.
Having established
would prefer
see whether the auditor
to collude will again
two kinds of
z.
manager has a credible
that the
to implicitly collude rather than to
depend on the carrot and the
variability of the auditor's returns. Since the auditor is
Proposition 7 (Incentives
To
/3,
we
fired.
now
We
we need
The
also
to
incentive
know
that
and profit contingent bonuses,
two instruments differed as they
equally effective (Corollary 1) and
be
stick facing the auditor.
carrots are possible; report contingent bonuses,
In the previous section these
When
threat to fire the auditor,
differentially affected the
risk-neutral, both instruments are
can just concentrate on the case
in
which only
/3
is
used.
Collude)
the manager's threat to fire is credible and the information
is soft,
the auditor will prefer
to implicitly collude iff
R*.
(ID
{l-8(l- €)}{9(l-qb)ya+(l-8(l-0)(l-n)(l-e))p}
l-5(l-0)(l-/i)(l-«r)
Obviously the
possibility of a lawsuit
most preferred outcome for the auditor
and
still
receive the future rents. However,
collusion equilibrium, the auditor will get fired
costs her the rents.
However,
is to
when she
be
truthful thus avoid the
when we
refuses to collude.
in return she avoids the possibility
are in an implicit
Thus being honest
of being found guilty
in the
court (a) and receives the bonus 0. Proof of Proposition 7 in the appendix compares these costs
20
and benefits and derives condition
other conditions
we
(II)
15
Note an important feature of
.
will derive; the larger is R, the
more
likely
the cost of not colluding in terms of future forgone benefits
a market with a lower
competitive
is
R can
is
more
difficult is collusion.
shared by
the auditor to collude because
greater (condition (4.4)). Since
is
be interpreted as more competitive,
the audit market, the
(II), that is
this result implies that the
more
This proposition thus establishes
an important link between the conditions of the market and organizational form: the implicit
collusion concerns
become much more important
in a hierarchical organization
monitor has market power which gives her strong career concerns
the fact that
it
may be more
difficult to fire
(in this
claim,
form when
we
the
are ignoring
an auditor with market power, e.g. a complete
monopolist).
We
can however see that the
RHS
of
(II)
depends on 0. By choosing
large enough.
shareholders can ensure that (II) does not hold and thus implicit collusion does not take place.
Next we
will
show
that
depending on the values of a and R,
"carrot" strategy and that, as
we
often observe in practice,
it
it
may be
too expensive to use this
may be
optimal to pay a
flat fee
to the auditor rather than giving her direct incentives.
Proposition 8 (No Contingent Fees With Implicit Collusion)
If
^
{l-g(i-g)Hl-M-g(i-M)(i-0)}£
{i-g(i-g)H(i-/*)flg»y}
l-8(l-n)(l-0)
02)
1-S(1-m)(1-0)
2
{(l-8(l-€)}Ui(l-8(l-n)(l-9))-8(l-n) (l-9)€}0(l-g b )ya
{l-S(l-/i)(l-0)}{l-S(l-M)(l-0)(l-e)}
then
it is
optimal for the shareholders to
The proof of
that is required.
0=0
and pay a
this proposition is again in the
ensure that the auditor does not collude
of
set
However, paying
may be
not satisfied), there
15
It is
reports
it,
assumed
is
receiving a
minimum payment,
that if the auditor reports
she suffers no punishment.
21
G
is that,
is
a
in
order to
minimum
value
too expensive for the shareholders. This
again related to the fact that, because of the switching cost
audit market), the auditor
fee to the auditor.
appendix. The intuition
(i.e. that (II) is
this
flat
and
(i.e.
non-competitive forces
R, in
all states.
later she discovers
An
is
in the
increase in
hard evidence and
constitutes an additional payment; in contrast to the previous section
went up, here the auditor will be paid
16
from the firm)
R
extract
.
As a
R
result,
contrast to the previous section,
it
may be
this
information not being transmitted to the shareholders.
the result that
it
may be
as
$
too expensive to use bonuses to control
less than full auditor
equilibrium,
in
was reduced
s
and R+/3 depending on her report (since she can always
Thus shareholders may be content with
collusion.
where
compromise
it
some
leads to
Kofman and Lawaree (1993b)
optimal to allow some collusion.
from ours, some auditors are naturally honest and
independence and
may
However
in their
in
relevant
also derive
model
differently
thus be profitable not to incur the costs
of preventing collusion.
Proposition 8 establishes condition (12) which shows
when
it
will
be more expensive
to
prevent implicit collusion. Nevertheless, the presence of implicit collusion does not imply that
auditing
is
essential.
useless. First,
we have assumed
that the other services offered
by the auditor are
Second, even when the auditor implicitly colludes, she reveals the quality of the
project with probability
willing to tolerate
When
fi.
(12) is satisfied, shareholders
some degree of
is
like to set
/3=0 thus are
collusion despite the fact that they can prevent
a high bonus to the auditors. However, even with /3=0, (II)
enough. This
would
may
not be satisfied
it
by paying
if
the sense in which legal liability, a, matters in the present model.
a
high
Thus
for
be an equilibrium we require
implicit collusion to
U-g(l-0)(l-M)(l-*)}
q<
03)
K
}
R
l-S(l-€)e(l-qb )y
should hold
i.e. (II)
when /3=0.
If
a
is
too high, implicit collusion will not be possible. Thus,
the legal system needs to be lenient for implicit collusion to take place in equilibrium.
contrast this result to those of the previous section where, without risk-aversion,
matter.
The
crucial ingredient in the
for the possibility of high fines.
at all.
However
a does
receiving
16
not
mean
is
is
we
payment of the auditor
receiving rents equal to
R
did not
to
compensate her
per period. Thus a small increase
have to pay the auditor more, because she
reservation return. Although increasing
is
R+z when
it is
successful and so exactly the
through.
22
is
already
not always beneficial
use performance contingent fees, the auditor will be paid
unsuccessful and
can
both parties are risk-neutral, such transfers do not matter
that shareholders
more than her
Similarly, if
project
When
here, the auditor
a
We
argument of section 3 was the participation constraint of
the auditor. Before shareholders had to increase the
in
is
same
R when
results
the
would go
(Proposition 8), increasing
more than her
17
is
beneficial to shareholders as long as the auditor
reservation return.
makes
collusion possible, also
auditors
a
is
receiving
follows that the presence of rents which makes implicit
It
more
the "stick", a, a relatively
method of controlling
effective
Therefore, in contrast to the case of explicit collusion where the auditor received her
.
reservation return, there
is
now
a clear rationale for paying a
system for disciplining the auditor
opportunistic
.
credible.
When
are high,
all
However,
the manager, therefore the manager's threat to fire a deviant auditor
the legal
framework
is
lenient
is
and the rents expected from continued relationship
auditors prefer to collude in this case and
is this
hold, there exists an implicit collusion
auditors are expected to collude, dismissals are not interpreted as an
all
move by
legal
18
We can thus conclude that when both (12) and (13)
equilibrium. Because
and relying on the
flat fee
also the unique equilibrium?
we have an
The answer
is
implicit collusion equilibrium.
yes.
Proposition 9 (Uniqueness of Implicit Collusion Equilibrium)
When
(12)
which
all
and
(13) are satisfied, the
To
interpret this as a
this
proposition
straightforward.
is
The argument above
What
will
happen
if the
manager
to
fire
we
in
establishes
are not in an implicit
fires the auditor?
bad signal and abandon the project. However,
have no incentive
may
Shareholders
in this case, the
manager
will
the auditor for strategic reasons and a dismissal should not be
interpreted as a bad signal. Alternatively, shareholders
life
an implicit collusion equilibrium
see uniqueness suppose that (12) and (13) hold and that
collusion equilibrium.
case, the
is
auditors conceal their soft information.
The proof of
existence.
unique equilibrium
manager would have an incentive
to
keep
do not
interpret
it
as a bad signal. In this
firing the auditors in order to
prolong the
of the project for as long as he can and hence a firing should be interpreted as a bad signal.
17
Increasing
to shareholders,
a
has two benefits;
whereas
/S
it
makes collusion
makes collusion
less likely but increases total costs.
always preferred as long as the auditor
is
necessary for implicit collusion (condition (4.4)).
18
We could
and also reduces
total costs
Thus using a
being paid more than her reservation return, which
is
is
less likely
obtain similar results in the static contracting problem of the last section,
auditor could not be paid less than a certain
the static problem, in our
model of
minimum
positive amount.
implicit collusion, there are
much
presence of rents and thus for the auditor to be controlled by the legal
23
However,
if
the
in contrast to
clearer reasons for the
stick.
Therefore
we
can see that shareholders must be using mixed strategies, but
project will not be abandoned with probability
fire the auditor to
keep the project going.
collude. This result
when
It is
the
is
It
1
that
the
threat to
follows that the auditor will prefer to implicitly
dependent on the unidimensional preferences of the manager. In general
he too
that
a yet unproven conjecture that in such a setting, the higher
of the implicit collusion outcome.
more
is e,
may
play mixed strategies.
the higher
our earlier claim
If true, this will strengthen
are delegated to the auditor and
We
means
and the manager will have a credible
manager has smooth preferences, we can see
becomes more
this
is
the probability
that as
more
authority given to the manager, implicit
tasks
collusion
likely.
next turn to the case in which (12) or (13) does not hold.
Proposition 10 (No Collusion Equilibrium)
If either (13) or (12) is not satisfied, there exists a
auditors
do not collude and always report
'
p g {l-rf(l-fl)}{
(14)
is
qf-L}<(l-p)(l-n){l-8(l-9)}{L-
abandoned immediately.
when her information
is soft
If (14) is not satisfied, the
and the project
is
intuitive.
Suppose
this proposition is
that the threat
bonus,
(12), or, the legal
project
is
punishment
first firing is
and get
Thus conditions
of
this
(12)
and
is
discontinued
fired.
(13). If e is
firing. In contrast, if e is
is
is
is
(13)
bad
falls sufficiently
to
quite
But despite
receiving a high
small and satisfies
(14), the
high enough so that (14) does
not interpreted as a sufficiently bad signal and the project
immediately abandoned. Yet, as auditor after auditor prefers
probability that the project
fires the auditor
fire the auditor is still credible.
severe enough,
immediately abandoned after a
not hold, the
manager
behave truthfully because either she
is
which
ft?)
provided in the appendix, but the argument
of the manager to
this threat, the auditor will prefer to
^^
not immediately abandoned but
in finite time as all the auditors report their information
The proof of
in
truthfully. If e satisfies
e)
i
a bad project
unique non-collusion equilibrium
is
not
be fired to collusion, the updated
and the project
is
abandoned
in finite time.
and Propositions 9 and 10 completely characterize the equilibria
game.
Despite characterizing the equilibria, our analysis leaves out an important point. In
general, the credibility of the manager's threat will depend
24
on the behavior of other auditors
(condition (4.3)). This
however does not
arise in
our analysis, again due
We can
assumption that the manager has unidimensional preferences.
by
effects
letting a
We
period.
new
thus need to have the report of an auditor
made by
threat will obviously
depend on what
When
when
nevertheless capture these
this auditor is
believed not to collude with probability
1,
do not hold, our analysis
either (12) or (13)
(who
is
not discharged) before the
the shareholders. In this case, the credibility of the manager's
is
is
our simplifying
auditor to be introduced immediately after a dismissal rather than next
continuation decision
auditor
to
expected to do. In particular,
there
will
when
they both hold, auditors will only collude
no point
is
if
the
new
in firing the first auditor.
be no different than before. However,
other auditors are expected to collude.
Proposition 11 (Multiplicity of Equilibria)
When
both (12) and (13) hold and a
new
auditor
there exist
two pure strategy symmetric
and one
which no collusion takes place.
in
The
outcome
because
intuition is straightforward,
is to tell
all
equilibria;
introduced before the continuation decision.
one
in
thus the proof
do
the truth and they can
this
when
which
is
is
auditors implicitly collude
all
omitted.
Auditors most preferred
the manager's threat
other auditors behave truthfully too. In contrast,
believed to collude, the manager's threat
implicitly.
is
if
some of
is
not credible
the other auditors are
credible and each auditor prefers to collude
This result therefore shows that auditor behavior does not only depend on the
allocation of authority, legal regulations and market structure but also
on the expected behavior
of other auditors. This also makes the multiplicity of equilibria different than those encountered
in repeated
games. Given the strategy of other auditors, the manager and the auditor have unique
best responses to each other,
however these
best responses in turn
depend on what other auditors
are expected to do.
5)
Concluding Remarks
In this paper
can arise and
how
we
it
studied a simple hierarchical organization and discussed
how
can be prevented. Section 3 analyzed the case with unrestricted side-
contracts between the monitor and the agent.
The
implication
was
that although the principal
should not pay the monitor according to the performance of the agent, he should
direct incentives.
We
collusion
argued
that this finding
still
does not adhere well with the practice
25
give her
in
which
most monitors are only indirectly controlled by the threat of the law or of being
in line
with the conventional view
of collusion
to
(e.g. footnote 2).
among
fired,
nor
is it
lawyers, accountants and sociologists about the nature
We thus argued that to understand how collusion
open the black box by modelling collusion
in
works,
we need
a dynamic context.
Section 4 developed a theory of implicit collusion in which, due to the career concerns
of the monitor, collusion takes place without side-contracts. This model predicts
the monitor without direct incentives
implications.
Collusion
is
The
more
often preferable.
may be happy
principal
likely
is
when
It
also has a
that controlling
number of important
with some valuable information remaining hidden.
the market for monitors
is
non-competitive and thus when the
monitor expects high rents from continued relationship and has strong career concerns; also
when
the monitor has
more than one
task and
when
of equilibria with different organizational forms
although collusion
is
important, a
number of
is
the monitor has less authority.
A
multiplicity
also possible. Overall this paper argues that
the predictions that follow are not realistic if
we
interpret collusion as taking place through unrestricted side-contracts. Therefore, the concept of
implicit collusion
is
an important one to analyze;
it
avoids several of these problems and has
better equilibrium foundations.
However, our analysis had number of short-comings,
assumption that the manager
at all costs. I believe
for future work.
It
new
is
an absolute empire-builder and wants to continue with the project
insights will follow
will also
the most important being the
when we
relax this assumption
which
is
a task
left
be informative to endogenize the allocation of tasks and of authority
across agents in such a context since these provide the foundations for implicit collusion. This
will also enable us to develop an analysis
and incentives
to collude are jointly
complementary
determined but
one with enforceable contracts.
26
in
to that of Felli (1993)
where authority
a model of implicit collusion rather than
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Appendix
Proof of Proposition 2:
We can
see
and (PC)
by
direct inspection that (A2)
totally evaluate this at
z=0,
and (PC) would hold as
to see
how
s
equalities. Differentiate (A2)
change when
and
we
using
start
z.
This
will give us the following system
<u \s +0)
-{1 -X(l -q„) y)u
'(i
+m) -X(l -q b )yu
'(s
+m -a) u \s +(})"
Ids'
dp)
(1)
(-{\q b +(l-k)qx }u>(s+m))
From
this
we
obtain
{\q b + (l-\)qg }u'(s+m)
dp__ds__
(2)
dz
The change
dz
dz
in total costs
{\--k(\-q h )-i }uXs+my\(\-q b )*i uXs+m-a)
TC
can be obtained by differentiating
(3)
dz
with respect to
z;
-{(\-p)r+p}^{pqg +{\-p)rq b )
dz
Thus
dTC
,
_
dz
-{(l-p)r^p}{Xq b ^(l-X)q }u (s-m)
g
{l-k(l-q b )y}u'(s+m)+k(l-q b )YuXs+m-a)
(4)
<Pqg + (l-pyq b }[{l-W-q b )y}uXs+m)
+
X(l-q b )yuXs + m-a)}
{l-k(l-qb)y}uXs+m) + X(l-qb)yuXs+m-a)
Now
noting that
{(l-p)r+p}{kqb +(l-\)q }=pq +(l-pyqb
g
g
(5)
and that u'(s+m)<u'(s+m-a) by the concavity of
u(.),
we
can write
dTC.
>{pq+(\-p)rqe }{uXs + m)-uXs+m)}=0
(6)
dz
QED
Proof of Proposition
3:
Now
set
LHS
of system (1) will be unchanged and the
(7)
z=0
and
totally differentiate
(A2) and (PC),
RHS
this
will
now be
k{\-q b )yuXs*m-a)
27
time with respect to
da
given by
s, /3
and a. The
Thus
8(l-q b )yu'{s+m-a)
<k___djl =
(8)
da
da
Change
in total cost is
{\-8(\-qb)y}u'((s+m)+8{\-qb )yu'(s+m-a)
given by
dTC
(9)
;
ds
={p+(l-p)r}^-(l-p)r(l-q b )y
(10)
da
{l-k(l-qb )yuXs+m)+X(l-qb )yu'(s+m-a)
Total costs are thus always increasing in a. Next note that
linW^=0
(11)
da
and
a=0
is
optimal from the viewpoint of minimizing the costs of control to shareholders.
Proof of Proposition
(We
will give the
4:
proof for z=0.
When z=0,
become much more complicated.)
differentiate these
'
QED
In
this
same
the
effects are present but the expressions
case (Al) and
(PC)
hold and
we
can
totally
and obtain
uXs+p)-{l-(l-q b )y}u'(s+m)-(l-q b )yu'(s+m-a)
(1 -p)(l -r)u \s
+py{p+(l -p)r(q b + (1 -qb )(l -y))}u
u'(s+P)
'(,)
(l-p)(l-r)u>(s+(3)
+(l-p)r(l-q b )yuXs-a)
(12)
'
(ds'
-(\-qb )yu'(s+m-a)'
(\-p)r{\-q b )yu'{s-a)
We would
ds/da as
a
like to
show
that
dTC/da
is
negative as
tends to zero.
28
a
tends to zero.
We thus evaluate d/3/da
and
ds _ (1 -P)(l -0(1 -q h )yu
'(s
+m)u \s +£)+(!
+0)
>(s
\
da
jp_
da
(B)
-p)r(\ -q b )yu \s)u
(\-p)r{l-qb )yu'{s)u'{s^)-{l-p)r{l-g b )yu'{s)u\s^m)
\
(1 ~q h )(\ -P)(\ ~r)yu '{s+P)u '(j+m)
+
+ (l -p)r}(l
{p
-qb )yu '(s+m)u
>(s)
\
where
A
=(l-p)(l-r)[{l-(l-q b )yu'(s+m)+(l-q b )yuXs+m-a)}}uXs
(14)
*\P
+ (1
-P)r{<l b
+ (1
'(s)u \s + /3) + (1 -p)r{\ -q )yu \s
b
-qj(l -Y)}]«
+
l3)
-a)u
>(s
*$)
Also
^,^
da
(15)
da
+{1 .p)il -r)f.(l-P )r(l- qb )y
da
Therefore
dTC
da
(1
-p)\\
2
-r) (l
U
,
"
(l-p)(l-r)(l-q b )yuXs+m)u'(s+p)
A,
-q b )yu \s +flu
'(s)
(1
-p)\l
-r)r(l -q
+
b
)yu \s)u
>(s
+m)
\
\
(l-pftl-rftl-qJyu'is+pyuXs+m)
(16)
'
(\-p)r{\-q b )yuX5 + m)u\s)
\
\
p(l-q b )yuXs+m)uXs)
(l-p)\l-ry(l-q b )yu'{s+m)u'{s+fi)
'
Ao
\
(1 -p)r{\ -q b )y{p+{\ -p)r)u '(j+fl)u '(j)
Ao
We
is
can
now
see that this expression, (16),
negative. Firstly
remember
always positive. Then compare the second term with the third and the
these three exacdy cancel out.
sum
is
is
is
negative. Finally the
Next compare
sum of
the
that the
last
and we can see
the fourth term with the sixth and
first, fifth
denominator
we
that
see that their
and the penultimate terms
equal to
(l-p)p(l-q b )yuXs+m)uXs+P)
(17)
\
Now
compare
that their
sum
this to the
is
seventh term and noting that u'(s)
negative too and thus (16)
is
is
greater than u'(s+/3)
we can
see
negative which implies that at low values of a,
29
:
total costs are
decreasing in a.
Next we need
high value of
we
can
set
a
show
to
that at high values
of a,
total costs are increasing in a.
Take a
(tending to infinity). For such a high value of a, (Al) will always hold and thus
0=0.
We
thus obtain
(l-p)r(\-qh )yu'(s-a)
ds
(18)
da
{1 -(1 -p)r[\ -q b )y}u
'(s)
(! -p)r{\ -q b )yu
'(,
-a)
In this case using (15) above,
dTC _ (1 ~P)r(l -g»)vU -(1 -P)r(l -g»)y >{n \s -a) -u
(19)
~
da
as,
by the concavity of
Finally as
too high.
{l-(l-p)r(l-qb)y}uXs)+(l-p)r(l-qb)y)uXs-a)
u(.), u'(s-a) is greater than u'(s).
dTC/da
is
continuous in a, a
two events:
state
first,
the project
was bad but
(state
of nature
is
not fired and reports
was good which has a
low nor
This can be due
in the first period.
probability
p
(state (G,S))
to
and second, the
(BS,S)) which has a probability (l-p)(l-/*). Thus the updated probability that the
is
good
at
time
after shareholders observe firing (S)
1
^G ^
now
G
the auditor did not find any hard evidence so implicitly colluded with the
(20)
Let us
exist that is neither too
5:
Let us suppose that the auditor
manager
minimum must
QED
Proof of Proposition
project
^
\s)}
turn to the case
expected to collude,
where
all firings
=
the auditor
and a report
G
is
given as
-7T^7T—
+ (i-p)(i-m)
p
is fired.
which auditors are
In the equilibrium in
are interpreted as due to auditor incompetence. Thus there are
two possible events; the auditor was incompetent and the project was good
(state
(G,F)) which
has a probability ep and the auditor was incompetent, the project was bad and the auditor did
not find any hard evidence against
independent
-
which has probability
it
(state
(BS,F))
e(l-p)(l-/*).
-
remember
Thus
7,
Therefore, Pi and similarly p„
(22)
two events are
PiW' p+(l-p)(l-fi)
\n
(21)
as long as there is
that these
is
not affected at
no hard evidence showing
all
i
by whether the auditor
that the project is bad,
p
Pn
P+ilrvril-P)
30
is
fired or not.
we have
Thus
5
which
is
project
always greater than
is
As soon
as such hard evidence
becomes
=0
available, p n
and the
QED
abandoned.
Proof of Proposition
We
p.
7:
when
only need to analyze the auditor's decision
the state
is
bad. If the auditor announces
a bad project, she will get an additional payment 0. If she conceals this evidence, she will keep
on getting
But also
if
R
until
she
the project
fails in
her other duties. These rents are thus equivalent to
unsuccessful
is
when
it
ends, she
may have
to
pay the
.
fine,
l-S(l-e)
a which has
probability (l-q b )7 every period (starting from this period since the project can end immediately
after her favorable report).
Thus
the net benefit to implicit collusion
g( 1
R
(23)
is
-^)Y a
l-S(l-e)"l-S(l-0)(l-M)(l-e)
On
the other hand, if she
is
truthful, she receives
and obtain condition
to the return to being truthful, 0,
Proof of Proposition
We
need to compare
as to avoid collusion,
degree,
TC 2 As
.
are exactly the
cheapest
way
but also gets fired.
total costs to shareholders
under two scenarios:
TC, and second, when they accept
same and we
just need to
(23)
compare
costs
B
, =max { 0,—
when
they pay
so
that collusion will take place to
on the case where (24)
collusion will not take place
is
TC,
positive. In this case,
^r
good
when
state, costs in the
the state of nature
W
is
some
good
state
bad.
The
-g(l -g)(l -/*)(!
_ (1
a
}
{l-S(l-0)(l-/x)(l-€)}
l-5(l-f)
0=0,
first,
so as to satisfy (II) as an equality, hence
to avoid collusion is to set
(25)
compare
QED
(II).
the auditor prefers to report truthfully in the
(24) yields
thus
8:
(24)
When
We
anyway
is
we can
(see (13)), so
concentrate
equal to 0, thus
-*))*-{! S(l -Q}0(1 -q b )ya
{1 -8(1 -e)(l-n)(l -€)}{! -8(1 -e)}
In contrast, if the shareholders set
0=0
and
let
implicit collusion take place, total cost
is
TC2 =L -(1 -fi)9{qy+(l -qb)ya) -fiL
-5 J
(
(26)
-^C 1 -WftHl -**)*«> "Ml "M)(l -0)L....
TC2 -L The
cost
is that
additional cost.
With probability
With probability
is
+{l - q
^a
1-5(1 -n)(l -9)
l-S(l-M)(l-0)
the liquidation value, L,
future revenues.
L -(1 -»)9™
ft
not realized.
From
this
we need
to subtract expected
n, there will be hard evidence and the project will end at no
(1-jt),
there will be no hard evidence and the project will not
be stopped and with probability 6 the project will end
31
at the
end of
this period;
with probability
.
qb the project will be successful and also with probability (l-qb)7, shareholders will receive
compensation from the auditor because the project
by the court. With probability
to the next period
TC, when
unsuccessful and the auditor
is
(l-/x)(l-0) the project will not
where the returns are discounted by
(12) holds.
found guilty
be stopped nor end, thus
and so on.
5,
is
TC 2
will
we move
be smaller than
QED
Proposition 11:
Let the subjective the probability that the state
is
good be
The value of
p.
continuing, V(p),
is
V(p)=9pqy+0(l-p)qp+(l-6)(l-p)tfL
(27)
gp
+ {(l-0)(l-p)(l-^) + (l-d)p6}5max{F(
The
project
comes
which explains the
to
an end with probability 8 and
two terms.
first
If the state
it is
of nature
auditor will discover hard evidence with probability
receiving
report
in
L
next period. With probability
BS and
(1-jt),
1-5(1-6/)
and
this
is
av
*
believed to be good with probability p
is
bad and the project does not end, the
p and
the shareholders will abandon,
the auditor will only discover soft evidence,
get fired (a(BS,S)=BS) but also she will report
her duties and the state
J
);L} + g(l-fl)p(l-0
ep+(l-p)(l-M)
BS and
get fired
good (a(G,F)=BS). Thus updated probability
when she
will
fails
be equal
to
event will be observed with probability {(l-9)(l-p)(l-n)+(l-d)pe}
€D+(l-p)(l-/i)
After this event, shareholders will decide whether to continue or to liquidate which explains the
fourth term. Finally, with probability (l-p)(l-e),
this,
which gives us the
last
the project will never be
hence the
final
We
indifferent
term
want
is
it is
the
good
state
and the auditor
will report
term. Note that as soon as the auditor reports that the state
abandoned since
in this equilibrium auditors
the discounted value of a
to find a value
of p* which
good
if
good,
never conceal information,
project.
sets (27) equal to
between abandoning and continuing. But
is
p=p*
then,
L
so that shareholders are
)<L
V(
,
ep+(l-p)(l-^)
and the project will be abandoned yielding L. Substituting
{1-S(1-0)ML
p ,=
(28)
If (14)
is
satisfied,
—
<p*,
this
thus after the
(14) is not satisfied, after the first
abandoning,
project is bad, the auditors will keep getting fired and after
and the project will be abandoned.
QED
32
V(p)=L
^—}
lUkH
ep+(l-p)(l-/i)
abandoned. If
and solving
first
firing,
the project will be
P€
>p*, but if the
eo+(l-p)(l-/i)
a finite time pn will fall below p*
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