FEB S'iS88
I
ALFRED
P.
WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
OVERIKWESTMENT WITH RELATION- SPECIFIC CAPITAL
Rotemberg
and
Garth Saloner
Julio
J.
Working Paper #1950-87
October 1987
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
OVERIKWESTMENT WITH RELATION- SPECIFIC CAPITAL
Julio J. Rotemberg
and
Garth Saloner
Working Paper #1950-87
October 1987
Overinvestment With Relation-Specific Capital
Julio J.
Rotemberg'''
and
Garth Saloner*
October 1987
Abstract
We consider a situation in which one party (the owner) owns a
project.
He is better informed than another party (tlie worl<er) about
the payoff this project would have if investment specific to their
Initially many workers compete to be the
relationship is undertaken.
owner's partner in the project.
If the investment is undertaken the
worker gains knowledge which makes him worth more than other workers
and which allows him to capture some of the payoffs of the project
We show that the equilibrium contract generally involves
overinvestment
We consider both the case in which the owner can
credibly commit never to undertake the project with a different worker
and the case in which he can't. In the former case tliere is always
.
overinvestment.
In the latter case, there are multiple equilibria.
Overinvestment equilibria always exist, underinvestment equilibria
never exist and efficient equilibria sometimes exist.
We would like to thank Drew Fudenberg, Oliver Hart, Paul
Klemperer, Meg Meyer, Paul Milgrom and Jean Tirole for helpful
conversations and comments, and the National Science Foundation
(grants SES 8R19004 and 1ST-85101G2) for financial support.
''"MIT.
,
1
FEB
81988
When assets arc
specific 1o a particular relationship,
the
contractual forms that are feasible for governing the relationship are
crncial in determining the ability of the parties to exploit
The importance
profitable investment opportunities.
of relation-
specific assets derives from the quasi-rents they create.
These
quasi-rents are the difference between the value of the assets
current relationship and their value
such assets are instaDed,
at
least
if
to the relationship
earns less, under any original agreement, than the
By threatening
quasi-rents.
new (more favorable)
to
Once
the relationship ceases.
one party
the
in
total
vaJiie of the
withdraw from the relationship unless
contractxial terms are agreed,
that party
may be
able to Improve his outcome.
If
the original contract cannot prohibit renegotiation,
inefficient investment in relation-specific assets
in the original
undertaken
at
contract may be distorted,
all,
efficient.
Klein,
This idea
a
is
result.
a vertically integrated
market transaction would olherwise be more
central to the work of Williamson
Crawford, and Alchian (1978) who suggest that
underinvestment
will
Prices
some projects not
and others mediated within
enterprise even when
may
result.
(1975) and
in
general
For example, Klein, Crawford, and
Alchian (1978, page 301) conclude:
"...Less specific investments
will
be made to avoid being locked in".
Several recent papers have formalized these ideas.
(1984) considers the relationship between a union and a firm
latter
must decide whether or not
to
undertake
a
Grout
where the
T-elationship- specific
-
3
Efficiency requires that the firm be reimiMirsotl
investment.
the cost of the investment
the gains from
if
Grout points out, however, that
costs.
(through
excessive share of the gains once they are
invest even
it
if
is
worthwhile.
iTivestment exceed
a
its
attempt to garner an
to
reali7,ed,
may not
the firm
on the other hand, binding
If,
contracts are possible, investment will obviously be efficient
WhUe
least
the imion cannot commit
if
binding long-term contract) not
a
llie
at
1
.
binding long-term contract ensures efficiency
this
in
several authors have pointed out that efficiency can be
setting,
obtained with simpler, less complete contracts.
2
Tlic reason
is
that
farsighted agents are able to anticipate the outcome of the
anticipated bargaining and can make transfers before in\'estment must
take place that are sufficient to yield efficiency.
example,
the parties realize that the agent
if
investment
wilJ fall
ex post
transfer of $x to that pa7-1y
in
(Notice too that
partners competing for
competition
In this
tlie
among them
who must make
will
,
it
the
they can, ox a nte, agree
is
contract of this kind,
if
there are
many
is
potential noninvesting
right to participate in the relationship,
result in an offer of $x for that right.)
mutually worthwhile.
it
to a
the contingency that the investment
way the investing party can always he induced
investment when
for
$x short of recouping the cost of the investment
in the division of the spoils
undertaken.
Thus,
In
order
to
to
make the
implement a
must be possible for the third party
enforcing the contract to observe whether the investment did
take place: investment must be a contractible activit.y.
in
fact
llolmstrom and
4
-
-
Hart (1906) provide an example (along the lines of Grossman and Hart
(1986) and Moore and Hart
(1985)) that illustrates that
underinvestment can
even
investment
is
res\jlt
if
bargaining
and
efficient
is
observable to the parties, provided investment
not
is
also contractible.
While that example shows that underinvestment can result
investment
is
in addition,
IV) shows that
noncontractible, Tirole (1986, Sec.
bargaining
inefficient,
is
underinvestment
a characteristic of the optimal contract.
must undertake
if,
necessarily
s
In his model the "firm"
(unobservable
relationship-specific investment
a
i
if
to the
other party, the "sponsor") that determines the firm's costs of
producing
a
good that that the sponsor desires.
Aftei- tlie
investment
has been made, only the sponsor learns the value of the good.
parties then bargain (under incomplete information) about
firm should be paid
if
it
produces.
how
The
mvicli
the
Since mutually beneficial
opportunities are typically foregone when bargaining occurs under
incomplete information, the firm anticipates thai
full
benefits of
its
investment and so invests too
In contrast to Tirole
adverse selection
it
in
(1986)
which one
will
not reap
little.
we focus instead on
of the parties
value of the relationship prior to the time
1lio
situations of
(the "owner")
when the
knows the
relation- spe cific
investment must take place but the other (the "worker") does not.
Such an asymmetry
tlie
worker finds
project.
it
of information
more
would arise,
foi-
example, whenever
difficult to evaluate the quality of the
Then projects which
the owner would
know
to
ho
rliffei'ent
would be viewed as identical by worl<ers
seems
to characterize
many
relation -specific capital
is
An
.
of the cases in
an issne.
asymniolT-y of inforniaiion
which investment
in
For example, General Motors
might have had better information than Fisher Body about the payoff
making
their joint venture; a firm considering
investment may be better informed of
individual worker with which
considering installing cable
to the
bargaining;
TV may know
Defence, which knows how
of
new
capital
value than the union or
its
a
municipality
moT-e about
community than potential providers
Department
into a
is
it
a
the ultimate value
and the
of the service;
eacli
piece of hai-dware fits
weapons system and how weapons systems combine
defence network, has better information about the value
to
form
them
to
a
total
of
each individual project than any of the contractors bidding for the
contract.
This asymmetry of information
realized value of the project
itself
is
is
inconsequential
contract ible
case an efficient long-term contract can
simy^ily
.
Foi-
specify
of the spoils as a function of the realized value.
the
if
in
tliat
llu>
division
In practice,
however, there are numerous reasons why the outcome may not be
contractible
point which
.
Tirole (198G) contains an extensive discussion of this
we
shall not
more obvious reasons.
in
other projects
it
repeat here.
First,
if
payoffs of his various projects.
accrue
in
We merely mention three
the owner
may be impossible
to
to
is
of the
simultaneously involved
separate the costs and
Second, the payoff may
in
part
nontangible benefits that are difficult for an outsider
to
evaluate, sucli as the cffert on
of thp parties.
tlie
firms rppvitatioii or
this is
utiJitiGs
an outsidor may not know tho opportunity
Finally,
cost of funds or other inputs the parties commit to
if
llio
common knowledge
to the parties
even
project,
tlie
themselves.
With the exception of adverse selection the situation we study
is
the canonical one in this literature.
participation of the worker
ventvire.
order
in
The events unfold
in
to
The owner requires the
carry out his proposed
three stages.
In
owner bargains with the worker over the terms
tho first stage,
the
of an e x ante contract.
Once hired, however,
that
makes him superior
any replacement and which therefore, ex po st,
to
worker acquires training
endows him with some leverage.
the second stage,
the owner must decide whethor to undertake a
gains from the investment are realized and,
ex post bargaining ovpt
We
in
the third stage,
there
tiiose gains.
restrict attention to the case which w(^ believe to be of
bargaining position ex an te.
we assume
that the
We formulate
complete-information setting.
(198,3)
is
conducive
In the second,
the stronger
ways.
at the first
jinte identical.-^
discussion that this ass\miption
in
is
this in two
owner can bargain
many workers who are ex
Takahashi
he does so, the
If
most practical importance: where the informed owner-
first
that
With the specific worker in place, in
particular investment he has under consideration.
is
knowledge
ot-
In the
stage with
Recall from the above
to efficiency in the
as
in
Sobel and
and Fudenberg and Tirole (1903), the owner makes
take-it-or-leave-it offer to a specific worker- before investment takes
a
-
7
place.
Examples where the
When
are
workers
a firm is hiring
many workers with
Ex post
first
to
formulation
work
similar skills
in a
appropriate abound:
new
factory, e x ante tliere
who are competing
for the job.
however, the workers acquire specific human capital which
,
allows them to acquire some rents which
the plant.
partner
is
to
depend on the productivity
of
consider the case of an inventor who needs a
Similarly,
supply inputs.
Ex ante there may be many
potential such
suppliers but only one inventor.
Particularly in this case of ex ante large numbers, the
formalism of the three stage model neglects
Such
feature of real world contracts.
a
a
potentially important
model implicitly assumes thai
the owner and the worker are able to form an exclusive relationship
in
the sense that the owner can credibly promise that he will not engage
in the project
because
in
in
our model
incorporates bolii
a
it
is
relationship,
Where
it
lump-sum payment
is
This
generally optimal to design
whether he invests or not) and
investing.
any other worker.
the future with
a
to the
payment
n
is
important
contract that
owner (independent
that
is
of
contingent on his
impossible to specify an exclusive
the "noncontractible projects" case, an incentive
is
introduced for the owner to abscond with the lump-sum payment and then
solicit
an offer anew from another worker.
owner may find
it
Indeed an
ini
scrupulous
profitable to go into the business of colJecting
lump-sum payments without ever investing.
This would be a
particularly attractive option for an owner with
a
very unprofitable
8
-
investment opportvinity
There are
contractible.
An example
similar businesses
which
a variety of
is
and where
circumstances
in.
Investment by
wlvirli
it
manufacturing process might be
way
in
from other projects the owner
particular
in a
in
is
new engine
this category.
however, the project may be contractible.
not
is
several
in
difficult to specify the
is
GM
project
a
where the owner operates
a particular project differs
involved
in
other cases,
In
For example
a
project to
provide a cable television service to a city or the automobile bodies
for an automobile
producer are easily definable.
venture one partner may be able
specific line of business will be
Our focus
is
to
promise thai
Similarly in a joint
all
conducted via the
his efforts in a
joint
venture.
mainly on the contractible projects case,
Our
formalized by the three stage model.
result in this case
unambiguous: the optimal long-term contract leads
relation -specific capital.
to
is
overinvestment
This results despite the fart that
it
in
i^s
possible to structure a contract that leads to efficient investment.
When
the contract
undertaken when
undertaken yields
it
is
is
structvired so that projects are only
efficient to do so,
the average project
a positive payoff to the relationship.
Since
bargaining yields some of this surplus to the worker, competition
at
the first stage forces workers to offer a lump-sum to the owner for
the right to participate in the relationship.
However, since workers
cannot distinguish owners with good projects from those with bad, this
lump-sum payment must be paid even
to
an owner who
in
fact
has
a
bad
who has no
project and
intention of investing.
particularly attractive to an owner
who
has
fact
in
outcome
Sucli an
a
is
not
good project
since he shares some of the potential spoils with his unattractive
Indeed, such an owner would prefer a lower
counterparts.
payment and
higher payment made contingent on investment (which he
a
intends to undertake)
this kind,
lumpsum
they
.
Since workers are happy to oblige an owner of
will offer
the preferred contract.
But then the
higher investment -contingent payment induces overinvestment.
Althought the focus of the paper
on the contractible
is
projects case,
we
We model
by extending the horizon beyond three periods and
this
briefly examine the noncontractible projects case.
enabling the owner to offer the project anew to
previously contracting with another.
a
worker
aftoi'
Not suprisingly, multiple
equilibria arise in this case.
We are able
underinvestment cannot arise
in
show, nonetheless, that
to
equilibrium and provide sufficient
conditions for tho outcome to involve strict overinvestment.
The second formulation
bargaining power
is
where he
offer to a specific worker.
of Sobel
is
\u
which the owner has relatively more
able to
In the
make
absence
a take-it -or-leave-it
of discounting,
tlie
models
and Takahashi (1983) and Fudenberg and Tirole (1983) feature
such take-it-or-leave-it offers from the informed
to the
In this case there are again multiple equilibria.
Of these, one
yields the efficient outcome while the others
overinvestment.
by the owner
all
uninformed.
involve
Moreover, those with overinvestment are
to the efficient equilibrium.
all
preferred
10
We are
not
tlie
first
to
demonstrate that relation-specific
capital can lead to overinvestment.
this
is
possible in his model
if
Tirole (198G,
investment
is
Sec.
V) shows that
observable.
This
occurs because investment alters the parties' relative bargaining
strength.
The
Idea that investment alters bargaining strength
central to the analysis of Grossman and Hart (1986).'^
also
is
Crawford's
(1982) model has the same ambiguity in that both under- and
The ambiguity there
overinvestment are possible.
arises for a
he considers risk -averse workers who
completely different reason:
wish to intertemporaUy smooth consumption and may therefore dislike
the contract that gives efficient investment.
In a
Webb
arid
paper addressed
to a
rather different question De Meza
(1987) also derive an overinvestment result.
an investing firm which must borrow to finance
its
Tliey consider
setting differs fundamentally from ours in that the investment
specific,
and
in
Their
investment.
is
not
that binding contracts can be signed before
investment takes place.
Indeed the faUuro
that drives their results
is
in
the financial markets
the presence of limited liability and the
impossibility of observing the true value of the project, even ex
post
.
Despite this large contextual difference, their model
somewhat
similar to ours in that there
is
is
adverse selection and that
the financial institution (which corresponds to the worker in our
model) expects to earn more on projects that are
in
fact
good.
this expectation that leads the financial institution to offer
contracts that are sufficiently attractive that even poor quality
It
is
11
projects are undertaken in equilibrium.
However, their result
in
some
sense derives from the fact that they do not allow for the possibility
of
payments which are not contingent on investment actually taking
As discussed above, we consider such
place.
in ovir
analysis and they
turn out to play an important role.
The paper
is
organized as follows.
the case where there are large
Section
of potential
1
Ex ante large numbers
workers while
in
of
Section
We begin by
the payoffs.
workers
recalling the timing structure,
The owner has
a project
an amount K
and by describing
which yields G
if
if
owner can enter
into a contract with a particular worker.
is
second stage, investment specific
ends.
K
is
expended.
If
In the third stage,
verifiable
We
III.
participates and
if
in
Contractible projec ts
(i)
place
we analyze
we examine take-it-or-leave-it offers by the owner.
11
present our conclusions
I
numbers
In Section
by
a third
invested.
to thai
a
worker
In the first stage the
owner and
1h;il
In the
worker lakes
investment doesn't take place the game
G
is
learned by the worker (but
is
not
party) and the owner and worker bargain over
its
division
The outcome
of this
game depends on what
be contracted on at each stage.
First,
is
known and what can
we assume throughout
thai
the
third stage payoff cannot be contracted on in the first stage so that
ex post bargaining (we use the generalized Nash bargaining solution)
12
is
The
the rule.
due
to a
inability to commit to third stage payoffs could be
One
variety of factors.
activity the
worker
is
that the actual
carry out cannot be specified
to
is
possibility
advance so
in
the worker can threaten to hold out after the investment takes place.
Second, we assume that the contract can be made contingent on the
owner/worker
specific investment taking place.
This
possible
is
can be verified (by the Courts) that the owner invests K
specific capital.^
The
and central assumption,
third,
is
if
it
the
in
that the
owner knows G exactly while the worker only knows the distribution
F(G) from which G has been drawn.
owner
in
is
many
assumption
make
In
is
that the
owner.
that emerges between
workers when
we suppose that they make offers
of them,
at the first stage.
willing to
final
a better bargaining position than the
To capture the competition
there are
The
owner
to tlie
These offers specify payments the worker
is
exchange for becoming involved with the owner.
With contractible projects and investment there are two such payments
that can be made.
The
first
owners who actually invest.
The second
which the owner promises never
different worker."
is
Thus
to
investment
in
and V
is
is
a
a
payment L
in
to
exchange
undertake the investment with
general an offer
in
an amount paid by the worker
later takes place,
payment V which accrues only
a
is
to the firm
is
whether or not investment
contingent payment that
for the equilibrium offers.
problems of this kind, we solve
it
a
!L,V}, where L
a pair
is
made only
fact takes place.
We now solve
for
As
is
usual for
by backwards induction.
If
the
if
13
third stage
reached, there
is
bargaining
is
information:
iindei- full
sunk and the surplus G must be divided.
capital costs are
The
generalized Nash bargaining solution to this bargaining problem
mazrmlzes Pq^""?^" (where Pq and P^^ are the payoffs to the owner and
worker respectively) subject
payoffs
restricted to equal G.
is
sum
to the restriction that the
The
'
of the
third stage payoffs to the
owner and worker are therefore (l-a)G and aG respectively."
Now
consider the second stage and suppose that the owner has
accepted an offer of {L.Vj.
independent
of
is
received by the owner
whether investment takes place, the owner finds
investment worthwhile
will
L
Since,
if
and only
(l-cx)G
if
V
+
>
K.
Thus the owner
undertake any investment for which
G
Thus an
>
(K-V)/(l-a)
=
gV.
offer of {L,V] that
G^, such that only investments
cutoff are undertaken.
(1)
accepted results
is
is
The higher
Is
the lower the cutoff.
V,
is
received
in
In
the event that
undertaken the more projects are undertaken.
Consider the
and suppose that an accepted offer
first stage
Then the amount
involves a contingent payment of V.
expects
a ciitoff,
that yield a return higher than the
other words, the higher the payment that
investment
in
to receive in the continuation
f
[aG-V]dF(G)
G^
=
f
gV
game
aGdF(G)
is
-
that the
worker
given by:
V[1-F(gV]
Since competition between workers ensures zero profits for the
workers,
(2).'
it
must be the case that L
is
given by the expression in
We can thus characterize the contracts by V with L being
(2)
14
determined by (2).
Furthermore, we can restrict attention
from (1), this
since,
is
V<K
an implication of nonnegative G.
Of the possible values of V, which one (with
L from
to
To examine
(2)) will be offered in equilibrium?
corresponding
its
this question
consider a proposed JL,V! equilibrium contract and an owner for
G>K under
Since such an owner
that contract.
the worker wishes to enter into a relationship,
that there
prefer.
fixed,
is
most-preferred contract amounts
to V,
subject to (1) and (2).
d0/dV
implies that
low.
I,
is
+
1
-aGVf(GV)dGV/dV
=
[K-GV]f(GV)dGV/dV
will
negative.
selecting his
maximizing i^(V)=L(V)+V with respect
=
Extremal solutions, which
and since K and G are
,
Thus
L+V.
owner would
aii
This gives:
dL/dV
=
to
sucli
L+V-K + G(l-a)
his preferences are increasing in
whom
must be the case
it
no other breakeven contract which
Since such an owner earns
the kind with
is
whom
-
[1-F(gV)1
+
+
Vf (GV)dGV/dV
F(gV).
+
1
(3)
be considered below, arise when (3)
This can happen, for instance, when
by equating
Interior solutions are obtained
(.S)
to
a
is
zero which
gives
[K-gV]
=
Since the right-hand-side
overinvestment
F(GV)(l-a)/f(GV).
is
positive,
(4)
we have K>G^: there
is
in equilibrium.
The second-order-condition
for a
maximum
is:
d20/dv2=[K-GV]f'(GV)[dGV/dV]2 + f(GV)dGV/dV-f(GV)[dGV/dV]2<O, or
[K-GV]f'(GV)-(2-a)f(GV)<0.
15
In
order
to interpret
and the overinvestment result
(3)
let
us
consider a proposGd [L,V| equilibrium contract and suppose that a
worker wishes
to
improve upon
the worker wants to
In particular,
it.
design a contract that, compared to the proposed fL.Vi contract, has
the effect of inducing the marginal investment not to be undertaken
whUe
not affecting the Inframarglnal investments.
the amount of investment that
undertaken
is
contract will have to have a slightly lower
same time,
at the
inframarginal,
to
thai
order to reduce
new
equilibrium, the
V than
before.
In order,
be as attractive to an owner whose investment
owner must be kept as
the decrease in
this,
in
In
well off as before.
is
To do
V must be matched by an exactly equal increase
in L.
So consider the effect of increasing L by
by
|f
$1.
There are two effects:
(GV)dGV/dV
I
when V
First,
is
decreased by $1,
Note however that, by definition, the owner
breaks even on the marginal projed
This moaTis thai the efficiency
.
gains that result from the abandonment of marginal projects
to the
first
worker.
term
in
These gains from the decrease
(3).
The second
effect
is
would not have undertaken the project
The probability
thus an Increase
V
whiJe reducing
The marginal such
fewer projects are undertaken.
project loses [K-G"].
$1
that the
owner
in the
payment
is
in
to a
Any owner who
any case receives
of this type is
accrue
V are given by the
distributive.
in
all
F(gV).
$1 more.
There
is
noninvesting owner of $F(G^)
.
If
[K-GV]f (G^)dG^/dV exceeds F(G^) then the worker gains from the change
since he can induce every investor to accept his
new contract.
16
With this Intuition in mind
(3)
why
-
is
it
easy
to see directly
from
the equilibrium contract cannot involve only efficient
Investment.
In the efficient case
vanishes and we are
$1 while increasing
left
L by
K=G^
with F(G^)
$1 has a
efficiency of investment that
.
so that the first term in
At the point K=G, reducing V by
second-order effect on the
undertaken.
is
However
order effect on the lump-sum payments that are made
owner who does not invest,
(3)
In other
has
a first-
to the
type of
it
words, resources are sqviandered
on the kind of owner whom the worker does not wish
to attract in the
Although increasing V induces some inefficient
first place.
investment, this has the effect of enabling the worker continue to
attract owners with good Investments
sum payment.
because
it
The reduction
In
whUe
offering them a lower lump-
the lump-sum payment
is
desirable
applies not only to owners with good investments,
but to
those with bad investments as well.
We now show
that the above equilibrium
renegotiation between the
robust to
signing and the undertaking of the
At this point the owner has already received L so that
Investment.
when
initial
is
the payoff
is
between
G^ and K
both parties
to the relationship
could be made better off by agreeing not to go ahead with the
Investment.
The gain from cancelling the contract
gain
in
is
split
worker a(K-G).
therefore,
the usual way,
To implement
the owner must net
is
K-G.
If this
(]-a)(K-G) and the
the outcome of this renegotiation,
the worker must offer the owner (l-a)(K-G) not to invest.
This would require the worker to know G, however.
If,
as
we
17
have assumed, G
is
unobservable, the worker mvist offer an amount
the owner not to invest thai
is
AU noninvestors would now
to
Suppose the worker
independent of G.
Then investors would receive
offers M.
before.
-
as mvich as they received
receive an additional M.
This
would have exactly the same effect on investment decisions and on the
payoffs of the worker as increasing L in the original contract while
leaving L+V unchanged.
Since the
worker could not improve
that the
has no effect on the outcome.
initial
optimal contract ensured
his lot in this way,
renegotiation
This occurs essentially because
owners accept the contract so that
Its
all
acceptance yields no
information that can improve the allocation.
This argument demonstrates that our original equilibrium
robust to renegotiation.
equilibrium even
fact that
It
also implies that this
when renegotiation
is
is
the only
is
This results from the
allowed.
were there any other equilibrium with renegotiation, the
worker coul offer our equilibrium contract instead, knowing
would be accepted by an investing owner and
Ihal
it
that
i1
would be robust
renegotiation
We now consider the
effect of an increase in a,
the share of
the ex post benefits that accrues to the workers, on the efficiency of
investment.
Intuition would suggest that such an increase
makes
overinvestment more severe since efficiency obtains when a
Indeed, when the second order conditions obtain, there
relation
between
a
and eqviilibrium G^ (assuming
can be obtained by differentiating (4):
it
is
is
is
a
zero.
monotone
interior)
which
to
18
dG^/da
Up
=
[K-GV]f(GV)/{(l-a)3d2,^/dv2i.
now we have considered
to
possible that di^/dV
is
of the form
is
[0,V'i
witli
is
In this
associated
Combining
.
(1)
given by:
G'' Is
(2),
it
has L equal to zero because more attractive contracts
it
with negative L's will not be accepted by noninvestors
and
Yet,
positive even for L equal to zero.
case, the equilibrium contract
cutoff G'';
interior solutions.
\
a[G-G''']dF(G)
[1-F(G'''][K-G"1
-
=
(5)
G"
Since the first term
smaller than
K
in
so there
also apparent that
G
'
is
positive,
is
(5)
the cutoff value
overinvestment.
falls
when
a
must be
G''
Differentiating (5),
it
is
rises so tiiat the extent of
overinvestment diminishes.
might be asked under what circumstances extremal solutions
It
are likely to emerge.
In other
words when does
(3)
imply that L
negative so that nonivestors are unwilling 1o participate.
occurs
F(G'')
if
is
Indeed,
G''.
is
there are a great
in this
effort,
case (3)
that,
is
likely to
contrary
to
is
very costly
be positive even for
all
so that F(0)
individuals
of a worthless project
is
will
which
G^
Then
(3)
equal to
witho\it
is
Then, as long as
1,
is
choose to become owners of such projects
arbitrarily close to one and f(x)
arbitrarily small.
worker.
to the
endogenous and that essentially any individual can,
become an owner
so that
our assumption, ownership of projects
indistinguishable from worthwhile projects.
positive
This
projects with G loss tiian K,
high, and any lump sum transfer
Suppose
itself
many
is
is
positive for
all
foi-
x positive
positive
G^ and
is
tlie
19
thp unique equilibrium.
Is
{0,V'''}
distributed
,
it
is
If,
G
instead,
uniformly
is
straightforward to show that the interior solution
when more than
applies
-
half the projects are worthwhile while the
boundary solution applies otherwise.
The extremal
occurs for two reasons.
equals -l/(l-a)
is
(5)
a low a
First,
Second,
holds, K-G*^
zero L implies that
If
This also tends
small.
is
if
(3).
to
is
a
equal zero,
it
important
is
which the incentive for the owner
to
to
consider
abscond with
rise to an infinite horizon
that achieves this
is
to
to invest,
in
general, include
payment and an investment-contingent component.
assume that
the game
This gives
a
lump-sum
Here, however, the
lump-sum component does not automatically create an exclusive
relationship. ^^
is
lump-
game with no discounting but with complete
As above, contracts can,
interest
a
an offer anew from another worker plays a
solicit
second stage the ownei' decides not
Our
a
unambiguously positive.
is
begins again with workers making new offers to the owner.
recall.
zero so
reduce the
Indeed, for
so that (3)
not contractible
is
The simplest modification
at the
when L
Noncontractible Projects
sum payment and
role.
in
K equals G"
the project
a setting in
means that dG^/dV, which
low n means that,
a
importance of the negative term
(ii)
This
a is low.
small in absolute value so the negative term of (3)
is
relatively small.
that
when
solution also tends to arise
not
equilibria that can arise.
in
fully characterizing the possible
Rather, our concern
is
with the
-
20
conclusions that can be drawn about the amount of investment that can
occur
The
in equilibria.
underinvestment
point to note
first
in equilibrium in the
sense that an owner whose G
exceeds K must eventually Invest. H.
Suppose,
to the
The reason
is
the following.
contrary that, the best project actually undertaken
has a payoff G" which
to
that there cannot be
is
is
Define, for any equilibrium,
above K.
be the net payoff of the projects which
Z(t)
be undertaken after
will
the t'th round of the game but which have not yet been undertaken by
Then, Z(t)
the t'th round.
Therefore, for each
This means that
at
t,
T
is
there
is
obviously nonincreasing
a
T such
the owners of
expect a payoff no higher than
all
that Z(T)
t^^
smaller than
at
T, there exists
owners whose project yields less than G" who would prefer
the offer {0,aKj to continuing with the original equilibrium.
such an offer,
if
z.
projects can collectively
Therefore,
e.
is
in
to
accept
Yet,
Thus there
accepted yields profits to the workei-.
cannot be an equilibrium with G" greater than K.
Our remaining findings
contract which nets an owner
rely
who
offer
is
accepted.
{0,V'''l
the observation that
tio
actually invests less than V'' will
actually be accepted in equilibrium.
an offer
oti
To
see this,
suppose that such
Since the owner could Instead have accepted the
which workers are always willing
to
make,
it
must be the
case that the owner intends to earn more than {0,V''j by absconding
with the lump-sum component of the offer.
Thus workers would
not
this offer.
This observation has two consequences.
First
It
Implies that
make
21
when
the solution
is
!0,V'''l
(the extremal case)
are noncontractible.
it
is
in
the contractible projects equilibrium
also the unique equilibrium
The reason
is
that,
when projects
there
this case,
in
no
is
contract which nets more to an investing owner while letting workers
break even.
The second
implication
contractible projects equilibrium
parameter values for which
all
that,
is
is
interior,
previous section implies that there
which
is
V larger than aK
is
equal to aK
is
range
of
some {L.Vj combination
(since overinvestment
preferred to fO.V] by investing owners.
is
a
Interiority of the solution in the
guarantee that the contract {L',aK! where
isn't,
there
in the
the equilibria without contractible
investment feature overinvestment.
positive L and
even when the solution
preferred to [O.V'l; Indeed
L'
it
is
witli
assured)
is
This does not
V
given by (2) with
often
is
When
not.
it
equilibria with noncontractible projects involve
all
overinvestment. This occurs because, to obtain efficient investment,
owners would
L' + aK is
lets
liave to accep^t contracts
lower than
V,
there
workers break even that
Thus
is
will
whoso V equals aK
no offer whoso
be accepted
prefers the SL',aK] contract to the
To
equilibrium.
The range we have not considered
interior solution in the three stage model
in
equals aK and which
for a wide range of parameter values there
overinvestment.
show that
in
V
this
when
Yet,
.
is
is
strict
where there
is
an
and the investing owner
iO,V''=}
contract.
range the efficient equilibrium
is
It
is
easy
sustainable.
to
-"^^
gain some understanding of the relative importance of these
22
ranges we consider the case
mentioned above (0,V'j
is
in
which G
is
then the most attractive contract
{0,V'''!
so that
preferred to [L'.aKj
is
if
we are not
and only
if
less
if
Even when more than
than half the projects are worth undertaking.
half are worth undertaking,
As
uniformly distributed.
in
the extremal case,
less than two thirds of
the projects are worth undertaking.
Ill
Tak e- it-or-leave-Jt offers by the owne r
A
workers
different method for eliminating the bargaining power of the
is
to
put the informed owner
it-or-leave-it offer to the uninformed
particular,
of
B
the owner offers to invest
This method
to him.
is
in
the position of making a take-
worker
if
attractive
at
when the workers are
cannot be a lump sum payment such as L.
sum payment by the firm
firm makes
is
if
it
The
is
will
rejected
If
simply be turned down.
it
the offer
level of transfer,
in
some
any
for such a
B, that the owner
to the
is
lump
Tlie offer the
is
payable only
accepted, investment takes
We analyze the pure strategy
signalling game.
in
doesn't.
from the worker may signal something
value of G.
is
In
There thus
Any request
thus a request for a transfer R whicli
investment takes place.
place,
unable
is
carry out the project with some new worker.
to
stage.
the worker makes a transfer
sense already employed by the firm and the owner
event
first
tlie
willing to accept
worker about the true
equilibria of this
Although there are multiple equilibria, several
properties that any equilibrium must satisfy can bo readily
if
-
23
established
First,
if
B
aK the offer
>
an owner offers aK, G must equal
lose
by making the
to
at least
earn aE(G|B)
expectation of G given an offer of B.
at least
K and
B, where E(G|B)
-
Thus,
if
is
offer of
the
B equals aK, E(G|B)
owner wUl never
of this result is that the
ask less than aK since he can be sure to gain more by asking aK.
second consequence
he
will
is
that there cannot be underinvestment
By asking aK, an owner can earn (l-a)G
always undertake an investment for which G
There exist other signalling equilibria.
between
G''
and K, there
investments whose
is
G exceeds
given G' in this range
These offers as
is
the worker has nothing to lose by accepting the offer.
The consequence
equilibrium.
If
K, for otherwise he would
On the other hand by accepting an
offer.
B the worker expects
be accepted by the worker.
will
is
+
in
Therefore
aK.
K.
>
Indeed, for
a signalling equilibrium in
which
all
G'
all
The equilibrium
G' are carried out.
supported by offers equal
well as smaller offers are accepted,
A
to
for a
K- (]-a)G'.
larger offers are
rejected
To
see that these are indeed equilibria,
owner who makes an equilibrium
a)G', which
Is
positive
if
He earns (l-a)G
offer.
and only
G
if
consider first the
> G'.
So,
-K+ K-(l-
owners whose G
exceeds G' benefit by making these offers and gain nothing by making
smaller offers.
On
the other hand owners with G<G' will
offers which will be rejected.
make larger
Therefore
a
worker who accepts the
K
+
(]-a)G'.
offer of K-(l-a)G' earns aE(G|G>G')
-
This gain
is,
24
-
given (5), nonnegative as long as G' >
It.
exist,
G'''.
worth noting that, not only do overinvestment equilibria
is
they are extremely desirable from the point of view of the
owners whose bargaining power
assumed
is
to be strong.
Specifically,
owners prefer equilibria with higher transfers so their most preferred
equilibrium
the one where
is
all
projects whose
G exceeds
are
G''
undertaken.
We now
briefly consider what would
happen
if,
instead of
giving the owner the right to make take-it-or-leave-it offers in the
first stage,
we endowed both players with
more closely resembles that
difficult to
there
is
know what outcome
to predict
bargaining strength that
stage of our game.
It
is
suggestive
is
to
is
from such bargaining since
a dearth of extensive form models analyzing this case.
possiblity which
stage,
in the third
a
imagine that, even in the
One
first
the two parties are trying to divide the benefits of the
relationship with a fraction a going to the worker. This can be
achieved by letting V equal nK
is
The owner then invests
.
positive so that efficiency prevails
importance of the change
in
^'^
.
if
(l-a)(G-K)
This points to the
bargaining strength between stage one and
stage three for our overinvestment results.
IV Conclusions
Our main conclusion
is
that adverse selection creates a
tendency towards overinvestment.
investment
is
Moreover
in
the important case where
contractible and there are ex ante large
numbers
25
overinvestment characterizes the unique equilibrium contractual
relationship.
That optimal contract has the feature that
sum payment
model
is
it
requires a lump-
for the exclusive right to the particular project.
correct we ought to observe such payments.
In
many
such as cable television franchises and military procurement,
uncommon
of the
we would argue are characterized by our assumptions,
situations which
not
our
If
to see substantial
supply the good
in
question
.
is
it
lobbying efforts for the right
to
Provided the granter of that right
Municipality or the Defence Department in these examples
beneficiary of these efforts, then the
initial
-
is
-
the
a
lobbying can be
interpreted as the lump-sum (noncontingent) payment in our model.
Besides the wining-and-dining that
rent-dissipation process,
is
usually part and parcel of the
such benefits might also include
uncompensated design work,
feasibility analysis,
and consumer surveys
performed by the lobbying firm.
In order to higlilight the effect of adverse snloction on
overinvestment, we have made some strong assumptions.
our discussion
in
Section
II
suggests that the asymmetry
bargaining power may be necessary for the result.
in
For example,
in
initial
Similarly,
Grossman and Hart (198G) or Tirole (1986), investment
if,
as
itself is not
contractible a countervailing tendency towards underinvestment arises.
Finally,
our assumption of efficient bargaining
is
clearly important.
Suppose, for purposes of Illustration, that bargaining dissipates some
fraction,
say
t,
of the gains
from
a project.
Then we should replace
26
G by tG
in
our analysis.
example,
it
is
-
In the contractiblo projects case,
then immediate from equations
could be underinvestment in equilibrium.
as
T
approaches unity there
and
(1)
This
be no investment
will
that there
(4)
fairly
is
for
obvious since
Thus
at all!
while
the presence of bargaining leads to overinvestment, costs of
bargaining move the outcome
We
close with a
in
the opposite direction.
comment on the implications
if
the costs of organizing economic activity are
different within the firm than
arms-length contracting
integration
1"^
.
our analysis
That analysis
for the traditional aniysis of vertical integration.
asserts that
of
is
markets then situations
in
inefficient
may give
which
in
rise to vertical
This raises the question of the incentives for
One common way
vertical integration in our model.
this is issue is to
of thinking
suppose that the firm faces a trade-off
in
vertical integration decision.
On
may remove
the third stage (and replace
the bargaining
authority relationship), bu1
in
its
the one hand, vertical integration
on the other hand,
,
about
Uioi-o
it
with an
may bo some
inefficiency involved in carrying out the transaction "in house".
If
bargaining
that was the case,
is
then owners for
whom
the third -stage
particularly costly would have a strong preference for
vertical integration.
These are the owner's for whom G
is
high.
An
equilibrium of a model with endogenous vertical integration and
contractible projects might therefore have two cutoffs instead of just
one:
Owners with projects
project "in house".
that
exceed the
higliei- cutoff
Those with projects below
thi.s
would do the
cutoff would offer
27
their projects In
market as
tlie
in
-
our model.
'llic
second cutoff would
divide these projects into those that are undertaken
and those that are not.
self -select out of the
remains
On
is
in
Since the owners with the best projects would
market, the adverse selection problem that
reduced and the overinvestment that results
the other hand,
equilibrium
is
less severe.
some inefficient vertical integration then coexists
with the market's overinvestment.
28
FOOTNOTES
1
Williamson (1983) shows that efficiency obtains with binding
contracts
if
(and only
if)
transfers that are valued equally by both
parties can be made.
2
This argument
contained, for example,
is
in
Hart and Holmstrom
Grossman and Hart (1986), and Milgrom and Roberts (1987).
(1986),
what WUliamson (1975) refers
3
This
4
Tirole (1987) provides an example that illustrates
is
overinvestment can arise
5
This
is
a stronger
in
to as
ex ant e large numbers,
how
their model.
requirement than requiring that investment
spending be verifiable since
it
must also bo verifiable that the
investment which took place
is
specific to this
The investment must
owner and
worker.
this
not be sucli tlial the ownoj- ran benefit
liy
excluding the worker.
6
it
If
will
this
amount L
be accepted by
is
all
positive at the equilibrium contract offered
owners regardless
of their G.
noninvestors would never take a contract whose L
means that contracts with negative
L's
is
By
contrast,
would only have payments
investors and can be lumped together with contracts whose L
With this proviso, we can view L as being paid to
7
See Roth (1982), Grout (1984).
This
negative.
all
owners.
is
to
zero.
29
8
there
imniGdiate from this that,
is
It
is
underinvestment
investment
if
In this case
.
it
is
is
noncontractible,
not possible to
make
transfers which are contingent on whether investment
first stage
actually takes place.
Yet, investment
is
the owner will only invest
So,
socially worthwhile as long as
investments for which the payoff
is
G
(l-a)G
if
K.
>
Thus,
> K.
between K and K/(l-a)
will not
be
undertaken even thougli they are socially worthwliile.
9
workers knew G, the expression
If
projects
then forces V to equal aG
10
It
.
(2)
would be aG-V for
Competition between workers
which investment takes place.
in
The owner then gets (l-a)G-K + aG
Therefore he invests
invests.
in
if
G exceeds K and
might be asked why workers ever offer
why owners do
put differently,
and then pursue
this is that
has once accepted
a
lump
to
svim
associated with a bad project.
lump sum component or,
another worker.
draw the inference
sum transfer L
The reason
that an
So,
for
owner who
payment and then not invesled
is
in fact
while the payment of L doesn't
necessarily exclude other workers in the future,
in
efficiency results.
not simply take the lump
a relationship with
workers are free
a
he
if
it
may make workers
the future more reluctant to deal with this particular owner.
11
there
This
is
riiles
out the only conceivable form of underinvestment when
no discounting.
If
the payoffs from agreements in later
rounds are discounted relative
could say that there
does not invest
at
is
to the
payoffs from the
underinvestment
if
first
an owner whose
the first available opportunity.
It
is
rovind one
G exceeds K
possible to
30
-
construct examples of such delay when the future
as L"
+
aK
In the latter case Z
all
discounted as long
V''.
any given round either some investments take place or none do.
In
12
bigger than
is
is
unaffected while in the former Z
is
falls
since
the projects undertaken have payoffs in excess of K.
13
This can be done as follows.
Workers make offers
any owner who has not yet accepted an
offer.
of !l,',aKl
Owners who accept one
G below K.
Once again, owners have no
incentive not to accept the offers and those whose
have
to offer a positive
than
L'
+
aK.
If
G exceeds K
will,
For a deviating worker to attract an owner he would
inve.st.
in fact,
a
lump sum components because
worker deviated
in
this fashion,
V'''
is
{L'.qK! to an owner
Workers would be willing
who has spiirned
owners spurn deviators.
Thus
to
He would
extend the offer
a deviating woj-kor
the owner
is
smaller
the owner would
accept the offer but would not invest regardless of his G.
then request new offers.
borause
strictly better off
all
by not
investing with deviating workers.
14
In the case in which a
discrete
number
of values,
is
one half while the G's can take only
this solution
is
identical to the one
obtained by applying the axiomatic approach of Harsanyi and Selten
(1972) and
15
Myerson (1984).
Although
literature,
it
is
this is
commonly asserted
of
They
these offers and do not invest are not extended further offers.
are viewed as having a level of
to
to
be the case
questioned by Grossman and Hart (198G).
in
the
a
31
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Crawford, Vincent: "Long-Term Relationships Governed by Short Term
Contracts"
International Center for Economics and Related
Disciplines,
London School
of Economics,
Theoretical Discussion Paper
1982
82/59,
De Meza, David and David C. Webb: "Too much Investment: A Problem
Asymmetric Information," Q uarterly Journal
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