Circulation of ideas: Firms versus
Markets
Thomas Hellmann (Stanford GSB) and Enrico Perotti
(University of Amsterdam)
Abstract
We study the comparative advantages of di¤erent environments for generation and implementation of ideas. We describe
early stage ideas as incomplete concepts requiring further feedback from agents with complementary expertise. We show that
open exchange systems are good for matching, but may fail to
reward idea generation. Hierarchical organizations can reward
idea generation, but restrict their circulation. This identi…es a
basic trade-o¤ between protecting the rights of invention and the
free circulation of ideas. When …rms and markets compete, the
possibility of leakages reduce optimal …rm size.
Introduction1
1
The role of innovation in economic growth has become central in the
literature on endogenous growth (Paul Romer, 1990). Yet the process of
the generation of innovative ideas is still a novel …eld. A recent literature
has studied the incentives for the generation of ideas, recognizing that
ideas may be easily appropriated once shared (Anton and Yao, 1994).
To satisfy novelty and non-obviousness requirements, patent protection
requires a completed concept. This paper is concerned with a prior stage
in the innovation process, where ideas are still half-baked. Speci…cally,
we ask what environment promotes the development of vague concepts
which still need to be completed through a process of screening and
elaboration, when communicating them creates the risk that they will be
stolen from the inventor. We advance the notion that the free circulation
of ideas may be at least as critical for innovation as their protection.
Schumpeter suggested that new ideas are original combinations of
existing elements (1929). While most combinations are useless, valuable
1
We are grateful for comments by Amar Bhide. The usual disclaimer applies.
1
ideas are combinations which ”…t” together, aggregating the component
resources in a novel and functional way (Biais and Perotti, 2003).2 We
study this process at an early stage when the idea itself is an incomplete
concept which misses some essential component. If the concept has some
merit, it will become implementable once completed with the feedback
of complementary expertise. Yet because the concept is novel and incomplete, it is ex ante uncertain who may be able to complete it. Then
the circulation of ideas is necessary to search for their necessary complements and is therefore critical for the process of innovation. In her work
on Silicon Valley, Saxenian (1994) suggests the term "cross-pollination"
to highlight the innovative potential of open random matches. This is
consistent with a notion that an open circulation of incomplete ideas
allows maximum scope for any concept to …nd a complementary match
for elaboration and implementation.
Yet there is a fundamental problem with the circulation of ideas,
namely that information cannot be sold as a conventional good (Arrow,
1964?). 3 Put simply, once an idea is communicated, it can also be stolen.
Innovating entrepreneurs are indeed extremely concerned with con…dentiality issues. Yet sharing ideas is necessary, especially at an early stage
when they must be matched with some complementary expertise to be
screened and completed. We assume that agents cannot be bound to
cooperate on an idea without revealing to them its content, but be too
vague for an independent patent o¢ce to grant exclusive property rights.
Exchanging ideas may thus require some form of contractual governance
to create a viable arrangement between the inventor and potential partners that may have complementary information.
This paper studies how alternative governance structures o¤er different trade-o¤s between the need to circulate ideas and to reward their
generation. In our model, an individual who generates a novel but vague
idea needs to …nd another agent with a set of complementary skills, in
order to screen, and if valuable, implement the idea. We assume that
only individuals with the right match of complementary information can
assess whether the idea is good or bad. If the idea is good, the complementor can o¤er useful feedback which completes it and allows implementation. Alternatively, a complementor could give negative feedback
and seek to implement it with someone else. 4
2 The
notion of innovative ideas as novel combinations of pre-existing elements is
implicit within the combinatorial theory of innovation in Weitzman (1998)
3
Arrow states that none would agree to pay for information before its content
(and thus its value) is revealed. But once one has been told the information one no
longer needs to pay for the idea.
4
Since ideas may be described verbally, they may be written down in a contract.
Yet any potential partner who reads the contract containing a no compete clause
2
We …rst examine a so-called open environment, which we view as a
pure market environment with many agents where the only constraining
institutions are voluntary contracts, and anybody can talk to anybody
else. We show that the open environment provides the maximum scope
for circulation, which ensures that good ideas always …nd a match to be
developed, but does not provide any mechanism to avoid idea stealing,
because no ex ante contractual commitment is possible without sharing
the idea. As a result, often the inventor does not receive the bene…t of
the idea, as it can be easily appropriated by others. Indeed, we show how
an idea circulates freely as it gets appropriated by a sequence of agents,
until someone …nds a match of complementary skills. Only at that stage
the idea is either dismissed as nonviable or else developed further. While
this may appear a pure theft, it is important to recognize that many new
concepts at a preliminary stage need much elaboration to be of any value.
In many cases, the ingredients added by later contributors to the idea
dramatically improves the original concept. So from a social perspective,
it is in fact desirable to let ideas circulate freely while they are so vague.
However, we can easily show that markets fail when the expected direct
reward to the generation of an idea is too low because it is stolen too
often.
We conceptualize …rms as closed exchange systems, and examine
how they may emerge in response to idea appropriation in the open
exchange system. The productive means in our model are intangible
ideas generated and thus initially controlled by individuals. Unlike in
the “property-right” theories of the …rm, pioneered in Grossman-Hart
(1986), where …rms are de…ned by residual control rights over real assets,
our …rms are centered around individuals, or human capital, and our …rm
boundaries consist of restrictions to the set of people that employees can
interact with. Moreover, unlike patents, these intangible assets are not
directly controlled by the …rm but by their authors. Although the …rm
has a claim on such ideas, it can capture their value only indirectly.
We suggest that …rms restrict the circulation of ideas in order to
reward their origination and control their implementation. Speci…cally,
by creating a boundary which blocks any transaction with the outside
world, a …rm forces internal completion and transform ideas in projects
on which the …rm can claim ownership. It also allows …rms to reward
idea generation. In this arrangement it is possible to target distinct
rewards to the inventor and to her implementation partner. Firms can
on the idea learns its content and thus may not sign the contract. In addition, we
assume that none would commit to any restriction or obligation relative to an idea
whose content they have not seen, as this may restrict their future opportunity or
expose them to blackmail.
3
thus be viable when markets fail. The drawbacks of …rms are the costs
of monitoring and the fact that the set of possible matches is restricted,
so good ideas may not be completed and implemented. The optimal
…rm boundary thus trades o¤ a greater chance of adding more ideas and
more complementors against higher monitoring costs.
When a close and open environment coexists, …rm employers may
attempt to take an internally generated idea outside the …rm, to be able
to reap a larger reward.5 This competition from markets forces …rms
to adjust their internal reward system, increasing the rewards of the
agents with the greatest incentive to leave. As the ability to escape
increases,6 the higher cost of providing incentives to retain ideas reduces
the pro…tability of employing agents, and induces a reduction in …rm
size.
In our extensions we discuss partnerships and networks as special
governance structures for idea exchange. We de…ne a partnership as a
…rm which restrict idea circulation and project implementation within its
boundary but does not rely on explicit monitoring, saving on monitoring
costs. The drawback is an inability to reward directly the generation of
ideas. The partnership’s equal sharing rule however ensures that over
time each partner receives the average value of ideas generated internally.
We show that a partnership may be viable in cases where markets or
…rms fail, but its ability to reward invention directly dissipates fast as
the number of partners grows. We also present a stylized idea of a
network of free agents as an intermediate solution between a close and
an open system, and contrast it with reputational models of cooperation.
We highlight in particular the looser discipline imposed by a network,
which is to be traded o¤ against a larger number of participants and
thus of potential matches.
The theme of the optimal allocation of control over innovative ideas
is already analyzed in Aghion and Tirole (1994); Ambec and Poitevin
(2001) study the case where the innovator needs to communicate reliably
private information. Prior work has recognized the problem faced by
an inventor in talking to potential partners in an unstructured market
environment. Anton and Yao (1994) show that the inventor can avoid
idea stealing and secure some rents by threatening to transmit the idea to
competitors. Cestone and White (1998) and Baccara and Razin (2002)
5
According to Bhide’, over 70 % of the founders of …rms in the Inc 500 list of
fast growing young …rms replicated or modi…ed ideas encountered in their previous
employment. Gompers, Lerner and Scharfstein (2003) show how a very high number
of new entrepreneurs in Silicon Valley and Massachussets left larger …rms and started
their …rm thanks to contacts in the venture capital network.
6
For instance, due to increasing availability of external resources or factors weakening the monitoring technology.
4
also study how the threat of competition can deter information leakages.
Anton and Yao (2002) considers partial disclosure of ideas. Biais and
Perotti (2003) study how an inventor needs to contract with specialized
experts who must appraise various aspects of the idea. They show that
implementation of new ideas may be feasible only when the experts’
incentive or ease to steal the idea is not too large, and that this depends
critically on the complementarity of their information. We pursue this
notion of complementarity in idea assessment further, by allowing the
agent with the right complementary information to elaborate the idea.
Hellmann (2000) studies the sequence of resource commitments in
an open bargaining setting when potential partners can add information. Ueda (2002) examines a trade-o¤ of talking to uninformed agents
(banks) that cannot appropriate an idea, versus informed agents (venture capitalists) that can. Another important contribution is Rajan and
Zingales (2001), who suggest that hierarchy may address the problem of
idea-stealing. Granting selectively access to the technology to employees
with relation-speci…c investment may avoid defection.
In section 2 we explain the base model. In section 3 we contrast open
systems (markets) and closed systems (…rms). In sections 4 and 5 we
extend the model to allow for potential and actual mobility across …rm
boundaries. In section 6 we consider further discuss further extensions,
including partnerships and networks. It is followed by a brief conclusion.
2
The Base Model
2.1
Ideas
Ideas are the sole productive asset. They are generated by agents at some
cost, and initially need to be screened and elaborated before they are
productive. Speci…cally, a good idea needs to be matched with an agent
with the right complementary skill to produce any output. However,
as it is not ex ante known what is the complementary skill required,
ideas must circulate among many agents in order to …nd their match.
Ideas are initially so vague that they are not patentable until they are
completed. Finally, we assume that agents cannot commit ex ante to
cooperate on a speci…c idea unless they sign a no-compete contract in
which the idea is clearly identi…ed. Thus it is not possible to avoid idea
stealing contractually.7
7
While this is an assumption, it seems extremely realistic. We maintain that ideas
may be contractible: if they can be described verbally, they could be written down
in a contract. Yet, any agent who is asked to sign a non-compete clause on the idea
will learn its content, at which point he may choose not to sign the contract. In
5
2.2
Firms and Markets
An open exchange system o¤ers agents with an idea the opportunity of
unrestricted matching with any other agent in the market. We refer to
them as free agents as they are not subject to any governance structure.
Since we assume that there is no contractual commitment possible, in
an open exchange ideas can be stolen with impunity.
A …rm is a set of "bound" agents, who (i) are constrained by a boundary that restricts the circulation of ideas (more generally, constrains
agents to transact only with …rm members) (ii) have an owner that captures the output of all members and (iii) compensates them according
to an employment contract. The monitor maintains the boundary of the
…rm and keeps track of the internal generation of ideas.
Since the hierarchical …rm is the classic Coasian counterpart to a
market exchange system, in the model we mostly focus on the contrast
between such …rms and free markets (open exchange systems). Later we
will discuss partnerships and networks.
2.3
Stage game
The model describes an in…nite sequence of dates in which agents interact. Assume there is a unit mass of agents. At the beginning of each
period, an agent may decide to generate an idea at a private cost Ã.
An idea comes with probability °. It may be good, with probability p,
or bad. Ideas are incomplete and need to be completed before they are
productive. Ex ante, it is not known what the complementary piece is,
so ideas must circulate among many agents to …nd their match. The
choice of matching depends on the governance arrangement. To seek a
proper partner, the carrier of the idea incurs a search cost c.8 After an
agent with an idea has presented it, the listener receives a private signal
on the quality of the idea and gives a report. Finally, the idea is either
implemented, or dropped, or taken to another listener next period by
one or both agents. Agents’ discount factor is ±:
Many listeners receive an uninformative signal, so we refer to them as
clueless listeners. With probability 1¡Á the listener is clueless. Although
he has no insight, he may have an incentive to steal the idea and try to
complete it with the help of someone else next period. Thus, a clueless
addition, no one would easily commit to any obligation relative to an idea whose
content they have not seen, as this may restrict future opportunities or expose them
to blackmail. Under these circumstances we believe that no speci…c contractual
commitment is possible without sharing the idea. An incomplete idea must thus be
necessarily shared with potential partners before they commit to cooperate.
8
For instance, (s)he needs to expend some e¤ort to avoid being matched with
agents with no chance of having any related skill.
6
listener may become a talker.
With probability Á the listener has the right complementary expertise
to assess the idea. The signal received by this complementor is always
correct. If the idea is good, the complementor knows how to complete
the idea. He can choose to deliver this information, which establishes his
type and thus reveals the idea to be good. Since two agents are always
needed to implement an idea, the complementor can engage the talker as
a collaborator. The type of agreement they may strike depends on the
governance arrangement. The complementor may also steal the idea.
If a complementor recognizes the idea as bad, he does not want to
pursue idea alone, and gives negative feedback. However, a negative report by a complementor cannot be distinguished from that of a generic
(”clueless”) listener. Thus a negative feedback may be correct, or be covering idea stealing. Under a condition derived below (called the discouragement condition), the talker stops pursuing the idea after a negative
report.
When two teams implement the idea simultaneously, we assume that
they engage in Bertrand competition, so both teams get zero returns.
Moreover, once the idea has been implemented in one period, everybody
knows about it the next period, so no one else tries it again.
We now specify the matching mechanism. In an open exchange
system people match at random. We assume that after having been
matched two agents do not meet again in the period immediately following the match. This simply prevents the possibility that an agent
takes a stolen idea and bring it back to the agent he stole it from. Note,
however, that it is possible that a stolen idea returns to the agent after
a few periods of being stolen. A closed exchange system allows the ”ordering” of matches. A rotation mechanism ensures that people get to
see everybody in the …rm, before talking to the same person again. 9 Finally, agents can only carry one idea from one period to the next. They
can thus talk about one idea of theirs at most. And they can listen to
one idea at most, namely that of their matched partner. This structure
allows us to treat talking and listening as independent activities.
Throughout the paper we denote the per period utilities of agents
with lower cases u and v, and the lifetime utilities (i.e., the net present
value of the current and all future per-period utilities) with upper cases
U and V . u and U pertain to agents in the open system, while v and V
pertain to agents inside …rms.
9
One easy way of ensuring this is that everybody gets a number, all even people
talk to f + 1 in the …rst round, to f + 2 in the second round, etc., up to f + (f ¡ 1)
and then back to the beginning.
7
3
Analysis of the open exchange system (markets)
In an open exchange system, there are no restrictions about who can talk
to whom or what they can do thereafter. Consider …rst the bargaining
between a complementor and the agent that told him the idea, and who
is now a potential collaborator. If the idea is implemented, it generates
an expected value z. On his own, the complementor could gain z0 from
the continuation game, where he …nds another partner to implement
the idea with. The original talker cannot produce anything without
z ¡ z0
the complementor. Using Nash bargaining, the talker gets az =
2
z ¡ z0
z + z0
and complementor gets az = (1 ¡
)z =
. To compute
2z
2
z0, note that the original talker does not want to take alone the idea
further. He knows that the complementor will pursue the idea, and he
does not want to end up in competition. The complementor thus takes
the idea to somebody else. With probability Á the complementor …nds
another equally skilled complementor. Since they could both implement
the idea with anyone else, they always want to cooperate and split the
z
surplus equally. Thus, with probability Á the complementor gets .
2
With probability Á, the complementor …nds a partner that is clueless.
z
In this case, he can again bargain for az. Thus z0 = ±(Á + Áaz ¡ c).
2
±(z ¡ c)
After simple transformations we obtain z0 =
, and thus
2 ¡ ± + ±Á
1
±
z ¡c
a = (1 ¡
)
2
2 ¡ ± + ±Á z
Standard comparative static calculations reveal that the bargaining share
of the talker (a) is larger when the complementor has higher relative
c
search costs (higher ), when the complementor is more likely to enz
counter another complementor (higher Á), and when the complementor
is more impatient (lower ±).
1c
1
Straightforward calculations reveal that
< a < , so that the
2z
2
share of talker is also always less than half. This shows how the open
system favors the complementor rather than the generator of an idea.
With this, we can compute the return to generating and stealing an
idea. Conditional on having an idea, the utility of the talker is
uT = Ápaz ¡ c
The expected period utility of an idea generator is given by
uG = °uT ¡ Ã
8
Part of the expected bene…t of being a listener comes from the chance
of becoming a complementor, as captured by
uL = Ápaz
Below we derive the total bene…t of being a listener, which also includes
the bene…t of stealing the idea.
We now introduce an intuitive assumption that allows us to maintain stationarity of the process of idea circulation. Namely, we identify
some condition under which a talker receiving negative feedback would
abandon the idea. We call this the discouragement condition.
To derive it, consider the continuation game after negative feedback.
Áp
With probability
the reported negative signal was honest, so the
Áp + Á
utility of pursuing the idea for one period will be ¡c. With probability
Á
the negative signal was dishonest. If the talker pursues anyway,
Áp + Á
he always incurs the search cost c. With probability Á the original talker
…nds no match, and gets no bene…ts. With probability Á2 both the
talker and the clueless listener …nd their respective match, each getting
the Bertrand payo¤, which is zero. And with probability ÁÁ the talker
…nds a match, but the clueless listener does not. In this case the talker
gets paz. Thus the expected return for the talker from pursuing an
Á
idea one more period after negative feedback is
ÁÁpaz ¡ c. The
Áp + Á
discouragement condition ensures that an agent prefers to generate a
new idea, rather than pursuing an old idea on which he has received
negative feedback. Formally, the condition is given by
2
ÁÁ paz
¡ (°Ápaz ¡ Ã) > c.
Áp + Á
Throughout the analysis we assume that this condition holds.
To derive the steady state properties of the open system, denote by
s the fraction of agents who just stole an idea and by s those without
any (stolen) ideas. The number of people who have an idea are all those
who stole an idea (s), and those who did not but generated one (s°).
Thus the number of people talking is given by t = s + s°. Naturally,
this is also the number of people listening.
We can thus establish the following. In any period, tpÁ projects
get implemented, and tpÁ projects get stopped because a complementor
realizes they are bad and discourage the talker without taking them
further. Finally, in any period, tÁ projects get stolen. Thus s = tÁ.
9
°
° ¡ °Á
and s =
. It is easy
Á + ° ¡ °Á
Á + ° ¡ °Á
to see that the rate of talking (t) and stealing (s) both increase with the
probability of generating an idea (°) and both fall with the probability
of …nding a complementor (Á).
Consider now the ex-ante utility of an agent in such a system, assuming that everyone invest in generating new ideas. With probability
s the agent steals an idea, and gets uT :With probability s°, the agent
has a new idea and also gets uT :With probability s°, the agent has no
idea and gets nothing. In addition, with probability t, an agent becomes
a listener and gets uL. We get10
Using t = s + s° we get t =
suG + suT + tuL
1¡±
Note that U is increasing in p; z; ±; Á and °, which is all very intuitive.
The open exchange system generates e¢cient outcomes. In particular, ideas circulate until they …nd their complementary match. They are
then either implemented if good, or dropped if bad. The above expression for U also shows that the payo¤ for an agent in the open system
is exactly the net present value of generating ideas. In the open exchange system each agent on average receives a payo¤ equal to his per
capita quota of ideas. But the agent does not receive the payo¤ from his
own ideas. Instead one large fraction of his returns stem from being the
complementor to other people ideas. And another fraction stems from
circulating ideas that were stolen from other agents.
The main issue is whether agents have an incentive to generate ideas.
So far the calculations assume that agents want to generate ideas. We
now examine for what values of à this is true. Let the critical cost
threshold is given by
U=
ÃM
·
1
±
z¡c
´ °uT = °(Ápaz ¡ c) = ° Ápz (1 ¡
)¡c
2
2 ¡ ± + ±Á z
¸
Proposition 1 Consider an open exchange system.
² For à < à M , the system achieves a …rst-best outcome, where ideas
circulate until they are either implemented if good, or dropped if
bad.
10
To see the derivation, denote the lifetime utility with a stolen idea by UT and
without a stolen idea by U G, then UT = u T + tu L + s±UG + s±U T and UG = u G +
tuL + s±UG + s±UT . Using U = sUG + sUT , we rewrite this as UT = u T + tuL + ±U
and UG = uG + tuL + ±U , so that U = s(uG + tuL + ±U ) + s(u T + tu L + ±U) =
su G + su T + tu L + ±U .
10
² For à > ÃM , the expected reward of generating an idea os too low
because of idea stealing. No ideas are therefore generated.
² Markets are more likely to fail
1. if …nding an idea is rare (low °),
2. if the idea is unlikely to be good (low p),
3. if ideas have little value (low z),
4. if …nding a right match is rare (low Á),
5. if it is costly to search for a match (high c),
6. and if the complementor is su¢ciently patient (high ±).
This results echoes Grossman and Stiglitz (1980), who derive the
impossibility of perfectly informative …nancial prices in a frictionless environment, also because there are no incentives to generate information.
Here, the problem with generating ideas is that a large fraction of the
returns are appropriated by the complementor, not the generator of an
idea.
4
Analysis of a closed exchange system (…rms)
We now consider the …rm as a possible solution to the weakness of the
pure open system. We de…ne the …rm as a closed exchange system with
three essential properties. First, the …rm captures the value of projects
implemented by its employees. Second, the …rm imposes a …rm boundary
to prevent the leakage of ideas. And third, the …rm has an internal
system for tracking and rewarding idea generation and completion.
Speci…cally, we assume that each …rm has a monitor (or boss). She
chooses the size of the …rm by choosing the number of employees F .
The total (lifetime) cost of monitoring is given by M (F ), where M > 0,
M 0 > 0 and M 00 > 0. We assume that the monitor can perfectly control
the external boundaries of the …rm (we relax this later). She can also
register the generation of ideas inside the …rm, and assign rewards to
their generation and completion. Let b be the compensation for the
generator of the idea, and B for the complementor. We restrict our
attention to stationary compensation and employment policies.11
Concretely, we suppose that an inventor ”registers” the idea with the
owner, who, although never able to complete it, assigns to the inventor
the task to try to …nd an internal match (i.e., act as an internal "champion" for the idea). The inability to escape the boundary of the …rm
11
We assume that employees are wealth constrained, so that the …rm cannot recover
the cost of providing incentives by making employees pay for them in advance.
11
allows the champion to obtain reliable feedback from all matches within
the …rm, and abandon the idea if none are found. We assume that the
size of the …rm is constant so it will not hire another agent to complete
an individual idea.
We denote the per period utility by v and the lifetime utility by
V . These utilities always consist of two components, the utility from
listening to other people’s ideas (vL), and the utility from generating
and talking about one’s own ideas (vG and vT ). Since
vL = ÁpBz
then the per-period utility from listening is simply given by vL times the
probability of listening to an idea. This may depend on the number of
ideas currently circulating in the …rm. 12 The expected utility of being a
talker in any period is given by
vT = Ápbz ¡ c
To calculate the lifetime utility, we need to take into account how long
an idea has already circulated. Let VG denote the agent’s utility when
he does not have an idea, and thus needs to generate a new one. Let f
be the f th round of talking about an idea, so VTf is the lifetime utility
of an employee who is about to talk to the f th listener. For any f with
1 · f < F , we have
VTf = vT + Á±VG + Á±VTf+1
12
In steady state we can calculate the probability of listening to an idea as follows.
Let qf be the fraction of agents in a …rm with an idea which is f periods old.
Let q0 be the number of agents without an idea. At the end of the …rst period,
q0 ° agents tried but did not …nd a new idea, q0 °Á found an idea and completed it
by …nding a complementor, and q0 °Á = q1 generated an idea that they could not
complete, so that they take it into the next period. In the second period, q0 °ÁÁ get
resolved, and q0 °ÁÁ = q2 ideas get taken into the next period. In the f th period,
f¡1
f
q0 °Á
Á get resolved, and q0 °Á = qf ideas get taken into the next period. Thus
the number of agents that have an idea is given by 1 ¡ q0 = q1 + q2 + ::: + qF ¡ 1 =
q0 °Á + q0 °ÁÁ + ::: + q0 °Á
F ¡1
q0 =
1 + °Á
. Simple transformations yield
1
X i=F ¡2
i=0
f
Á
i
and qf =
1 + °Á
°Á
Xi=F ¡ 2
i=0
Á
i
With then note that the probability of listening is the same as the probability of
talking. The only agents that do not talk are the q0 ° agents that failed to generate
a new idea. Thus the probability of talking, or listening to an idea is given by
1 ¡ q0 (F )°. Naturally, this is increasing in F .
12
This says that in the f th round an agent has an expect per-period return
of vT . With probability Á the idea is resolved (the idea is either implemented or dropped) so that the agent can start afresh, generate new
ideas and get VG. And with probability Á the idea is still unresolved,
the agent continues to circulate his idea, and gets VTf +1. At f = F , the
agent has no one left to talk to, so
VTF = VG where V G = ¡Ã + °VT1 + °±VG
Clearly, these utilities form a recursive system. The following lemma
characterizes their solution.
Lemma 1:
(i) VG = ¿ vT ¡ ½Ã where
Xi=F ¡2
(Á±)i
¿=
Xi=F¡2
1 ¡ [°± + °(Á±)F¡1 + °Á±
(Á±)i ]
i=0
1
½=
Xi=F ¡2
1 ¡ [°± + °(Á±)F ¡1 + °Á±
(Á±)i ]
°
i=0
i=0
(ii) VG is increasing in F .
(iii) VT1 > V T2 > ::: > VTF ¡1 > VTF = VG.
The proof is in the appendix. ¿ is the discounted number of times
that an employee has an idea to talk about. Naturally this is also the
discounted number of times an agent gets to listen to an idea. And ½ is
the discounted number of times that an employee generates an idea. with
this, we readily see that VG is the discounted value of talking about ideas,
minus the cost of generating them. The intuition why VG is increasing
in F is that a larger …rm provides more opportunities to circulate the
idea, implying a greater value of generating an idea. The intuition why
VTf > VTf +1 is that having more people left to talk to (i.e., having a
fresher idea) is better for the agent, since the expected time to generate
a new idea is further out in the future.
The monitor’s net present value of pro…ts is given by
¦ = F (1 ¡ b ¡ B)¿ Ápz ¡ M (F )
The monitor’s objective is to maximize ¦, subject to the agent’s incentive constraints. For this, she chooses the optimal size F , as well as a
13
compensation package b, B. We focus only on stationary choices of F ,
b and B.
In the base model there is only one incentive constraint to worry
about. The complementor cannot steal the idea. He is therefore willing
to provide honest feedback and implement the project. His compliance
is free, so that the monitor can set B ¤ = 0. The generator also cannot
steal the idea, nor would he want to, since the …rm helps him to protect
the idea. The only incentive constraint thus concerns the willingness to
generate ideas in the …rst place, and is given by VG ¸ 0. VG is increasing
in b (through vT ). Since the monitor wants to minimize b, we get
½
c +Ã
¿
VG = 0 , b¤ =
Ápz
Substituting b¤ into ¦ yields
¦(F ) = F ¿(Ápz ¡ c) ¡ F ½Ã ¡ M(F )
where F ¿ (Ápz ¡ c) is the number of employees times how many ideas
they have, times the expected value of an idea net of search costs, F ½Ã
is the number of employees, times how many times they have to seek
new ideas, times to cost of generating ideas. 13
With this we can state the main results of this section
Proposition 2 In a closed system, restrictions on the circulation of
ideas imply that not all ideas are resolved. The probability that an idea
Xi=F ¡2
gets resolved is given by
Á(Á) i < 1. This is an increasing funci=0
tion of F .
A fundamental insight is that …rms restrict the circulation of ideas
imply. This helps to create an environment in which employees’ incentives to generate ideas is preserved. but it also implies that the full
potential of an idea will not be realized. In particular, the restriction
not to take ideas outside the …rm means that some ideas do not …nd a
match for their completion.
13
In this setting, the monitor’s pro…t function equals the social return, since he
can hold agents down to their reservation utility. This does not imply that …rms
are e¢cient, since from a social perspective it would be better to let ideas circulate
freely.
14
Proposition 3 The monitor’s optimal choice of F ¤ is
² decreasing in the marginal cost of monitoring (M 0 ).
² decreasing in the cost of generating ideas (Ã)
² decreasing in the search cost (c)
² and increasing in the pro…tability of new ideas (p and z).
The optimal compensation b¤ is
² increasing in the cost of generating ideas (Ã)
² increasing in the search cost (c)
² and decreasing in the pro…tability of new ideas (p and z).
The proof is in the appendix. This proposition generates some intuitive results about the optimal size of the …rm. The boundaries of
the …rm are determined by the di¢culty of monitoring the information
exchange among agents. Naturally, the greater the marginal cost of
monitoring an additional agent, the smaller the …rm. But the boundaries of the …rm are also determined by the fundamental properties of
ideas. The greater the cost of generating ideas (high Ã), the smaller the
…rm. This is because the marginal bene…t of having another employee
that generates is lower. The same applies to search costs (c). And the
more pro…table the agent’s ideas (higher p or z), the larger are …rms.
The comparative statics of b¤ are also intuitive. If the cost of generating an idea is greater (higher Ã), the agents need to be compensated
more. Interestingly, in addition to this direct of e¤ect, there is also an
indirect e¤ect. Higher generation costs reduce the optimal …rm size F ¤,
which in turn reduces the return to generating an idea. The change in
the optimal b¤ also takes this into account. The same logic also applies
too all other comparative statics.
Finally, note that ¦ is decreasing in Ã. We de…ne à F so that
¦(F ¤; Ã F ) = 0, where F ¤ is the optimal choice of F . Ã F is the critical
value, above which …rms are not viable. For à · ÃM , open exchange
system is feasible. Since there are no monitoring costs, and since agents
face no constraints on who to talk to, the open system is more e¢cient.
In general, we cannot say whether ÃF is greater or smaller than ÃM ,
since this depends on the cost of monitoring (which may also include
a …xed cost of setting up a …rm). If monitoring costs are high, then
15
à F < à M , and …rms are never e¢cient. But if monitoring costs are not
too high, then ÃF > ÃM .
We de…ne a system of circulation of ideas viable if it can sustain idea
generation.
Lemma 4 For à 2 [ÃM ; à F ] the closed system is feasible whereas the
open is not.
In this region we can think of …rms as an e¢cient response to the
market’s stealing problem.
5
Porous …rm boundary
So far we assumed that a …rm can perfectly prevent its employees from
leaving with their ideas. We now relax this assumption. If employees
were to leave the …rm to implement their ideas, this would pose an
existential threat to the …rm. We examine how …rms optimally react to
such a threat.
We now model an economy where agents can work both in an open
or closed system. For simplicity we assume that there is a …xed number
of …rms of constant size. We also assume that there are always more
agents available than the number the …rms would hire, so that there are
always some people in the open system who can listen to ideas and thus
o¤er an opportunity for completion.14 For simplicity, we focus on the
case where à > ÃM , so that the open exchange system does not generate
ideas on its own. Thus the only ideas circulating in the open system are
those which escape from …rms.
In this section we maintain the assumption that ideas are homogenous. In such a setting retaining all ideas is critical since the …rm is
otherwise not viable. In principle there are three types of escapes that
the …rm needs to worry about. The generator of an idea may leave, a
clueless listener may provide false negative feedback and leave, and a
complementor may provide false negative feedback and leave. We assume that employees are always committed to the …rm for the current
period, but may leave the …rm in between periods.
We parameterize the temptation of leaving by x. This is the probability that an employee escapes unscathed into the open environment,
where he can then implement an idea. With probability (1¡x) the agent
is caught. We assume that no party receives any utility in this case.
When does a clueless listener want to give false feedback, and escape
with the idea? The utility of leaving is given by ±(xÁpaz ¡ c+ U + ). This
14
We do not consider the possibility of departing employees moving to another
…rm.
16
consists of the expected payo¤ from the stolen idea (xÁpaz), as well as
a continuation utility in the open system, that we denote by U +. The
utility from staying in the …rm is ±V f = ±(VTf + VL ). Note that the value
of staying in the …rm depends on how old the clueless listener’s own idea
is (through VTf ), as well as the number of other ideas currently circulating
within the …rm (through VL ). In principle the incentive to leave may thus
also varying over time. Since we focus on stationary strategies, the …rm
needs to be viable all the time, including at the beginning, when no
ideas have yet been generated. We therefore consider the most binding
condition that ensures that no one leaves the …rm. This implies using the
lowest possible value of V f . Using Lemma 1, this is given by VT = VG
and VL = ¿vL. A clueless listener will therefore never escape as long as
±(VG + ¿ vL) ¸ ±(xÁpaz ¡ c + U + )
Next, consider the generator of the idea. It is immediate that if
the clueless listener does not want to escape, neither does the generator.
This is because the generator has a higher internal value of talking, given
by V Tf ¸ VG.
Finally consider the complementor’s incentive to escape. If the complementor succeeds to escape into the open system, with probability Á
z
he …nds another complementor and splits the returns, obtaining , and
2
with probability Á he extracts a share az as before. The total utility
z
from leaving is thus ±[x(Á + Áaz) ¡ c + U +]. If he stays, he gets Bz
2
from implementing the idea within the …rm, and ±V f thereafter. Again,
the lowest value of V f is given by VG + ¿ vL . Thus, the condition that
ensures that the complementor never leaves is given by
z
Bz + ±(VG + ¿vL) ¸ ±(xÁ + xÁaz ¡ c + U + )
2
We can now characterize the …rm’s maximization problem. As before,
the monitor wants to maximize
¦ = F (1 ¡ b ¡ B)¿ Ápz ¡ M (F )
by choice of F , b and B. The incentive constraint for idea generation is
again VG ¸ 0. In addition we now have two retention conditions, that
we denote by
r ´ ±(VG + ¿vL) ¡ ±(xÁpaz ¡ c + U +) ¸ 0
for the clueless listener (as well as the generator) and
z
R ´ Bz + ±(VG + ¿vL) ¡ ±(xÁ + xÁaz ¡ c + U +) ¸ 0
2
17
for the complementor.
Since in this model the open system is not viable, the continuation
utility is given by U + = 0. It is also easy to verify that the incentive
½
c+Ã
¿ as before. We need to
constraint is binding again, so that b¤ =
Ápz
consider the cases where r ¸ 0 and R ¸ 0 is binding separately. Using
VG = 0 we note that
xÁpaz ¡ c
¿ Ápz
z
±(xÁ + xÁaz ¡ c)
2
R = 0 , BR¤ =
z + ±¿ Ápz
r = 0 , Br¤ =
The optimal choice of B is naturally just given by B ¤ = M ax[Br¤ ; BR¤ ].
We can now state the main result of this section.
Proposition 5 The easier it is to escape a …rm (higher x)
² the greater the share of the complementor B
² the greater the share of the generator b
² the smaller the optimal size of the …rm F .
The proof is in the appendix. The main intuition for this proposition is that if employees can escape the …rm boundarinn h
6
6.1
Mutual monitoring mechanisms
Partnership
We de…ne now a simpler closed exchange system, a non-hierarchical …rm.
As a …rm, it has a clear border (so that all transactions are constrained
to be internal, and output may not be absconded), but has no monitoring
mechanism for individual behavior. It thus cannot control internal idea
stealing directly, nor make rewards contingent on idea generation or
completion. Since ideas can only circulate internally, they may not …nd
their e¢cient match.
We assume that the reward system grants everybody the same fraction of all …rm returns, as in a partnership. Given that employees are
symmetric, this is an e¢cient mechanism for ensuring that nobody has
an incentive to steal ideas. However, the major problem for as a partnership is that as it expands, the rewards for inventors falls rapidly, as
the returns are shared with more and more partners. Let P be the number of partners. The incentive constraint that ensure idea generation is
given by
Xi=P ¡2
¡Ã + °vPT
(Á±)i
i=0
VG(P ) =
¸0
Xi=P ¡2
1 ¡ [°± + °Á±
(Á±)i + °(Á±)P¡1 ]
i=0
z
where vPT = Áp ¡ c. It can be shown that VG(P ) is concave in P . As
P
P ! 1 we have VG(P ) < 0. The optimal size of the partnership is thus
given by P ¤ such that VG (P ¤) = 0. This ensures the largest size for a
maximum chance for internal completion, while still providing incentives
for idea generation.
De…ne à P the lowest value of Ã, so that VG(P; Ã) · 0 for all P .
Partnerships are feasible for à · ÃP , but not for à > à P .
Proposition 6 Partnerships may be feasible at intermediate idea generation costs. In particular, when markets cease to be feasible, partnerships
are still viable.
Proof. We need to show that à P > ÃM . Note that at P = 2 we
z
have VG(P ) = ¡Ã + °(Áp ¡ c). At à = ÃM = °(Ápaz ¡ c) we thus get
2
z
1
VG(P; Ã M ) = °(Áp ¡c)¡ °(Ápaz ¡c) > 0 since a < . Thus ÃM < Ã P .
2
2
¥
Thus the size of the partnership is limited by the fact that rewards
need to be shared equally among all partners, irrespective of their contribution to the innovation. For high costs of idea generation à > à P
19
it is impossible to satisfy the participation constraint, and partnerships
become infeasible.
Beyond …rms and partnerships, one can think of further closed systems. Some extreme cases are families or clans, which have a predetermined (often genetic) de…nition of membership, so that joining them is
largely impossible, and leaving them extremely costly. More generally,
the threat of exclusion may be most e¤ective to discipline idea stealing
if there is no option to join another form of close exchange and open
exchange is unreliable.
6.2
Networks
So far we have assumed that there is no way for free agents to commit
to reward idea generation. In practice, there are decentralized market
mechanisms which limit idea stealing, such as mutual monitoring. We
now move to consider such informal organizational forms to exchange
ideas outside …rms. In particular, we study the case when subsets of
free agents create self-enforcing mechanisms to share ideas among themselves. Any mutual arrangement may function only within a limited set
of agents, since there are limits to the scope of mutual monitoring.
We sketch here a stylized model of a "di¤use network", de…ned as
a completely decentralized arrangement, without any internal tracking
system nor any coordinating monitor. We take the view that a network
is a more impersonal arrangement than reputation mechanisms, where
the disciplining of idea stealing requires a direct and precise observation
of individually actions.
The network adopts the maximum punishment available in repeated
interaction among free agents: if a member is found to be violating the
rules, (s)he is excluded from any further interaction with any other agent
in the set. We assume that an ostracized agent cannot …nd another network willing to adopt him/her. Finally, we assume that agents perceive
that a failure to enforce such a threat leads to a collapse of the arrangement. We assume that the open system is not viable by itself, so that
the continuation payo¤ after stealing an idea and being banished from
the network is zero.
In addition to these classic characteristics of repeated reputation
games, we add some critical features to our de…nition of a network:
1) A network constrains individuals to trade only among members,
whose identity is common knowledge.
For simplicity we assume that the size of the network N is such that
this form of mutual monitoring can occur at no cost.
2) Di¤use monitoring by network members cannot establish whether
a talker has originated or stolen an idea, but can observe all members’
20
productive activities.
3) Participation in the network requires that agents regularly contribute new ideas to other members. Agents who just listen to ideas or
simply repeat ideas by others are expelled. Since ideas circulate freely in
the network, agents can recognize at least some of those taken by others.
Thus we view a network as too di¤use to be able to monitor idea
stealing or to provide any form of pro…t sharing on the set of ideas implemented by its members. Thus agents are not punished for taking
around ideas generated by others, as long as they share them with network member only. Instead, they may be expelled for not contributing
enough ideas of their own. It is a somewhat cynical view of the network:
it condones opportunism, as long as it achieves a long term fair share to
its members.
We assume, as in the general open system, that the discouragement
condition holds, so that if the generator of an idea receives a negative
feedback (s)he stops pursuing it and seeks another one. We will show
later that the feedback indeed contains some information.
Since a clueless agent will earn nothing from reporting her true signal,
(s)he will always give negative feedback in order to take the idea further.
Thus an idea generator earns a return only when immediately matched
with a complementor. The direct return to idea generation is exactly as
in the open system, namely
uG = °uT ¡ Ã
where uT = Áp®z ¡ c: In such a network the main bene…t of generating
ideas is to be admitted to listen to other network agents’ idea. The
expected bene…t of being a listener comes from the chance of being a
complementor, or to …nd one next period:
uL = Áp®z + (1 ¡ Á)±[Áp®z ¡ c]
Being a listener is strictly better than the return to idea generation.
Since there are no penalties, clueless agents will always steal the idea.
Thus the main incentive problem is again to reward idea generation.
Let U0 be the continuation value in network. For a complementor,
the utility from stealing is then as in the open system
z
±[(Á(1 ¡ ®)z + (1 ¡ Á) ¡ c ¡ c]
2
which is less than agreeing to complete the idea immediately with the
talker, which yields Á(1 ¡ ®)z and thus avoids discounting and search
costs. Therefore meeting a complementor in a network always leads to a
cooperative implementation. This con…rms that a negative feedback will
21
be informative, since a complementor with a good signal would report
it, and is consistent with the discouragement condition assumed earlier.
To complete the model, we assume that the e¤ort to generate a new
idea is observable, so that mutual monitoring can police the requirement
that each network member contributes his fair share of ideas. In conclusion, inventors sharing ideas within a network often have their idea
taken but are able to maintain membership and thus to gain access to
others’ ideas.
Provided agents indeed have an incentive to generate ideas, it is easy
to see that
Proposition 7 The expected payo¤ to participate in a di¤use network
is the same as the payo¤ to join a partnership.
The proof is very intuitive: over time, network agents are like partners who contribute and complete ideas with a common frequency. In
both contexts each agent receives the average per capita value of all
ideas generated within the group. The di¤erence is that in the partnership each partner receives exactly the same share from all projects, while
in a network each agent receives half of the value of all ideas which he
participate in implementing, whether as a generator, clueless idea-taker
or complementor. Over time, all agents contribute the same average
number of ideas, and have access to the same number of ideas by other
network members.
What if other agents could not observe this e¤ort ? An alternative
mechanism to ensure an incentive for idea generation is that the network
members records over time whether each agent contributes his/her fair
share of own ideas.
Speci…cally, the rule has to ensure that any agent who did not take
an idea from the last period has an incentive to attempt to generate an
idea. With probability ° this leads to an idea, with probability (1 ¡ °)
it does not.
Network participation would then require that each agent over time
presents an idea with a minimum probability µ, where µ equals the
chance to have taken an idea last period plus the chance of not having taken an idea but having attempted to generate an idea. The chance
to have taken an idea last period equals the chance to hear an idea on
which the agent is clueless. Thus µ = (1 ¡ µ)° + µÁ which implies µ =
°
.
°+Á
Thus the rule states that an agent must presents a new idea to other
network members with frequency µ in order to be admitted to participate
further. For this rule to be self-enforceable, it must be optimal to comply,
22
which requires that the capitalized value of remaining in the network as
an active idea generator be positive, namely
U0 = µuT ¡(1¡µ)°Ã+(1¡µ)uL = µ[Áp®z+(1¡Á)±[Áp®z¡c¡c]¡(1¡µ)°Ã+Áp®z ¸ 0
and that it would exceed the gain from a deviation from the network
norm. Here the best deviation would save idea generation costs by free
riding on the ideas circulating in the network, which implies that the
agent would have an idea to talk about only with probability µÁ. If we
de…ne t as the period over which such a deviation would be detected,
then the network is viable if the potential loss of network participation
is greater than the gain from saving on idea generation costs:15
t
± U0 >
t
X
i=o
± i(1 ¡ µ)°Ã
A special version of this threat would be to assume that an agent
who presents ideas more often is sought more often as a listener by other
agents in the network, which is attractive since it reduces the number of
periods without a new idea. This produces an equilibrium in which all
agents would choose the same degree of idea generation e¤ort.
The type of network we have outlined is only one of many possible
mutual monitoring mechanisms. It is a particularly weak form of governance, as it does not attempt to control idea stealing nor to capture
output to reallocate it. It simply predicates that all bilateral deals must
take place among members of the network and that all members must
present their f t9 Tc (f) Tj 5.25 0 TD -0.168 Tc (t0.336 Tc (l) Tj 3 0 TD 0 Tc (a) Tj 6 0 T
monitoring costs. More likely, such precise monitoring may not be feasible except in small, geographically localized circles. Our de…nition of
network is probably a description of a more di¤use, if also less precise,
form of peer monitoring.
6.3
6.3.1
Ideas for further extensions
Costly search and better matching
We have so far assumed that search costs are just as high in an open
as in a close exchange system. It may be that …rms actually reduce
such costs, e.g. by centralizing information; on the other hand, there are
fewer possibilities for good matches within …rms.
There may be in fact a structural trade-o¤: in the open system people
seek better matches (high Á), and are willing to accept higher search
costs (high c). In contrast, in closed systems agents may be matched by
authority, which may result in lower search costs. Yet it seems possible
that the inventor may be the better individual to seek a match, and that
hierarchical matching would result in a lower chance of completion, i.e.
a lower Á. It seems straightforward to extend our model to account for
this trade-o¤. The relative performance of the open system depends on
the bene…ts of better matches versus their higher cost.
6.3.2
Simple and costly ideas
We have seen that the open system may not create incentives for idea
generation when the cost of producing an idea are too large. This may
suggest a sort of specialization based on this comparative advantages.
We have so far assumed that search costs are just as high in an open
as in a close exchange system. It may be that …rms actually reduce such
costs, e.g. by centralizing information or enforcing proximity; on the
other hand, there are fewer possibilities for good matches within …rms.
There may be in fact a structural trade-o¤: in the open system,
agents are free to seek better matches (high ), although this may involve accepting higher search costs (high c). In contrast, closed systems
may lower search costs, but their constrained matching process would
result in a narrower set of options, i.e. a lower average . It would
be straightforward to extend our model to account for this trade-o¤.
The relative performance of the open system depends on the bene…ts of
better matches versus their higher cost.
Suppose that ideas may come in various combination of cost and
return. Then free agents may specialize in creating ideas that are simple,
"cheap to produce", i.e. with low Ã, (or high p), and low z. In contrast,
closed systems are best to produce ambitious ideas, i.e. with high à (or
low p), and high z.
24
To see this, use uG = °(Á®pz ¡ c) ¡ Ã
Áp
±
z¡c
= ° z(1 ¡
) ¡ °c ¡ Ã
2
2 ¡ ± + ±Á z
Áp
±
= ° (z ¡
(z ¡ c)) ¡ °c ¡ Ã
2
2 ¡ ± + ±Á
Áp
±
Áp
±
= ° (z ¡
z) + °
c ¡ °c ¡ Ã
2
2 ¡ ± + ±Á
2 2 ¡ ± + ±Á
Áp 2(1 ¡ ±) + ±Á
Áp
±
=°
z + °c[
¡ 1] ¡ Ã
2 2 ¡ ± + ±Á
2 2 ¡ ± + ±Á
Consider di¤erent projects with variable à and z, all with °Ápz ¡ Ã
constant, i.e., °Ápz ¡ Ã(z) = con , Ã(z) = °Ápz ¡ con. We have
Áp 2(1 ¡ ±) + ±Á
Áp
±
uG = °
z + °c[
¡ 1] ¡ °Ápz + con
2 2 ¡ ± + ±Á
2 2 ¡ ± + ±Á
1 2(1 ¡ ±) + ±Á
Áp
±
= °Ápz[
¡ 1] + °c[
¡ 1] + con
2 2 ¡ ± + ±Á
2 2 ¡ ± + ±Á
±Á
(1 ¡ ±) +
±
2 ¡ 2 ¡ ± + ±Á ] + °c[ Áp
= °Ápz[
¡ 1] + con
2 ¡ ± + ±Á
2 ¡ ± + ±Á
2 2 ¡ ± + ±Á
Noting that
±Á
±Á
(1 ¡ ±) +
¡ ¡1
2
¡
±
+
±Á
2 ¡
2
[
]=
<0
2 ¡ ± + ±Á
2 ¡ ± + ±Á
2 ¡ ± + ±Á
we see that an increase in z (using Ã(z) = °Ápz ¡ con) will decrease
uG. Thus, for projects with higher à and z, it is increasingly di¢cult
for the open system to ensure a positive return to idea generation. Thus
the open system will specialize in generating lower e¤ort - lower return
projects. The closed system still works for bigger e¤ort, bigger return
projects.
On the other hand, when we have coexistence of …rms and markets,
the open system may be best at implementing also some ambitious ideas,
namely those that complementors stole from their …rms, or that …rms
chose to drop. A related possibility is that the quality of elaboration may
vary, depending on the precise …t of the complementary skills identi…ed.
If agents in the open system are more diverse, or if there are among them
more quali…ed individuals, implementation in the open system may be
not just more likely but also of higher quality.
6.3.3
Coexistence
A natural extension of the model would have some people actually manage to leave …rms in equilibrium. We sketch here a conjecture on a
stationary equilibrium with partial mobility. Suppose that ideas are
heterogenous, so that some are easier to retain than others (i.e., it is
easier to lay an ownership claim on part of their content). Intuitively,
25
some ideas are so general that the …rm cannot lay any claim on them;
others may be veri…ably …rm speci…c, as they are related to current internal processes or products. The escape probability is thus di¤erent.
For a general idea occurring escape is always possible, so that xe = 1.
But for a contextual idea escape is more di¢cult, so that xe = x 2 (0; 1).
Let » be the fraction of ideas that are general. We assume that the
probability of escape is not contractible, so that the …rm cannot vary its
rewards depending on whether an idea is general or contextual. Thus to
retain all ideas requires that agents with general ideas (the easier ones
to take out of the …rm) be rewarded enough internally so as not to wish
to escape.16
If …rms cannot retain neither general and contextual ideas, then …rms
are not a viable solution to the stealing problem. If …rms retain all ideas,
the model is the same as in the previous section, solved for xe = 1. But
now there may be an equilibrium with a small fraction » such that …rms
only retain contextual ideas, but do not attempt to capture general ideas,
as it would be too expensive to o¤er a su¢ciently large reward for a rare
event. In such a model, employees move between the open and closed
system. Thus even if the open system fails to create ideas, it may receive
ideas escaped from …rms.
Even if we take the size and number of …rms as exogenous, so that
escaped employees are always replaced, this extension is quite complex.
An internal idea may keep circulating inside …rms, since there are new
employees. Moreover, the attractiveness of escaping depends on the
return to being in the open system (and perhaps the chance of being
rehired), which depend on the number of people escaping …rms. Thus
there may be multiple equilibria, some in which agents escape because
they expect many other agents to escape.
In this admittedly hypothetical equilibrium, the open system acts as
a parasite to the closed system. All ideas are generated inside …rms,
but some of them escape into the open system, which has a comparative
advantage in implementing them as it o¤ers more matches.
7
Discussion and Conclusion
We have proposed a novel trade-o¤ between the necessity to protect idea
generation and the need to share ideas in order to screen and elaborate
them. A free circulation of ideas would thus be more e¢cient at the
elaboration of incomplete concepts, but fail to reward a costly search for
16
Proving that an idea is …rm speci…c may require a legal challenge. Without an
actual escape, it is di¢cult to verify what the probability of detection would have
been.
26
such novel concepts.
It may appear that …rms as de…ned in our model may be too ef…cient in terms of rewarding initiatives by employees relative to selfemployment. Actually, the relevant comparison is between …rms’ relative advantage in supporting long term investment in new ideas versus
the inventor’s ability to capture a large personal return once an idea is
elaborated.
The notion that markets produce poor incentives relative to …rms
for idea generation may sound at …rst counter-intuitive. Typically, the
reward to develop a new venture on one’s own are much greater than
for an employee. Yet our model is consistent with this intuition. In a
hierarchical …rm, the monitor wishes to reward idea generation, but has
no incentive to o¤er more than the bare minimum. For the agent who
can complete the idea, the di¤erence between the internal and external
reward is even greater.
More generally, our model shows how the open exchange system favors those who can elaborate and implement new ideas over pure inventors, since the former have more bargaining power. In contrast, in a
…rm all agents are subject to authority and the reward for implementing
the project may be kept down to the reservation utility. Yet …rms may
be uniquely important as a protected environment for the generation of
initial concepts, even though they may capture most of the value created by the inventor. The remarkable number of highly novel ventures
started by individuals who took an idea from their previous employment
con…rms this incubating role for enterprises, and suggest a symbiotic
relationship between …rms and open markets.
We may now summarize our implications as follows. Firms constrain
idea circulation in order to capture their value, and may reward inventors
and complementors only up to their reservation utility. So our model
is consistent with modest incentives in …rms and large incentives and
potential payo¤s in markets, coupled with higher risks.
Our approach may seem to overstate the e¢ciency of …rms in internal monitoring. Firms in fact can only prevent idea stealing indirectly,
by policing its own boundary. At the same time, our approach may
overstate the inability of agents in open exchange systems to cooperate enough to reward idea generation. Some institutional environments,
such as universities, do encourage a broad circulation of ideas, although
the best researchers often do not capture much of the value created by
their discoveries. Markets do provide strong rewards to complementors,
so it may look as if markets reward innovators entrepreneurs handsomely.
But in fact, the entrepreneurs are not necessarily the idea generators.
Of course, complementors have also a creative role in idea elaboration,
27
which may be even more signi…cant than the initial concept.
In an equilibrium with coexistence of markets and …rms, where some
employees leave their …rm to implement their projects outside, we expect
to see them reap larger rewards than what they would get inside.
A …nal interesting question is whether an open exchange system
which fails to reward the creation of ideas may thrive by attracting
ideas from the corporate sector for implementation. This would suggest
a reinterpretation of the role of …rms in highly innovative environments.
The hierarchical approach to R&D in Japan and Europe, as well as in
the large high tech companies on Route 128 in Massachusetts, is often
contrasted with the loosely organized open environment of Silicon Valley
in California (Saxenian, 1994; Aoki, 2002). The success of the Silicon
Valley model is attributed to a free movement of ideas and individuals
among small ventures assembled via informal arrangements. Yet the
intense exchange of ideas in Silicon Valley is puzzling, since California
actually has a fairly weak tradition of protecting intellectual property
(Gilson (?) and Hyde (?)), so it is not clear how idea generation may be
rewarded. Perhaps it is the interplay of large corporations and start-ups
by departing employees which has a major role in the development of
a thriving open exchange system. In practice, many new ventures in
Silicon Valley develop ideas which originated in large …rms. The open
environment in Silicon Valley thus thrives thanks to its contact with
large …rms, which are important incubators of new ideas, particularly
those which are costly to develop. The notion that the interplay of large
corporations and start-ups by departing employees has a major role in
entrepreneurial spawning is con…rmed by Gompers, Lerner and Scharfstein (2003), who o¤er evidence on the number of employees departing
from large …rms. Hellmann (2003) provides a related theory of when employees leave, and how intellectual property rights a¤ect their incentives.
According to Bhide, over 70 % of the founders of …rms in the Inc. 500
list of fast growing young …rms replicated or modi…ed ideas encountered
in their previous employment.
8
References (incomplete)
² Aghion, P. and J. Tirole, 1994, "On the management of innovation", Quarterly Journal of Economics, 1185–207.
² Anton, J., and D. Yao, 1994, "Expropriation and Inventions",
American Economic Review, 190–209.
² Anton, J., and D. Yao, 2002, "The sale of ideas: Strategic disclosure, property rights and contracting," forthcoming Review of
Economic Studies.
28
² Anton, J. and D. Yao, 2003, "Attracting skeptical buyers", Working paper, Duke University.
² Arrow, K., 1962, Economic Welfare and the Allocation of Resources for Inventions, in R. Nelson (ed), The rate and direction
of inventive activity: Economic and social factors, Princeton University Press, Princeton.
² Baccara, and Razin, 2002, "From thought to practice: Appropriation and endogenous market structure with imperfect intellectual
property rights," Working paper, Princeton University.
² Bidhé, Amar V., 2000, "The Origin and Evolution of New Businesses", Oxford University Press
² Cheung, "Property Rights in Trade Secrets", Economic Inquiry,
1992.
² Garmaise, M., 2001, "Informed Investors and the Process of Financing Entrepreneurial Projects", University of Chicago mimeo
² Hellmann, Thomas, 2001, "Entrepreneurship and the Process of
Obtaining Resource Commitments", mimeo, Stanford University
² Lazear, E., 2002, Entrepreneurship, Working paper, Graduate School
of Business, Stanford University.
² Rajan, R. and L. Zingales, "The Firm as a Dedicated Hierarchy",
Quarterly Journal of Economics, 2001
² Romer, P., Endogenous Technological Change, Journal of Political
Economy, vol. 98, 1990
² Schumpeter, J., 1926, Theorie der wirtschaftlichen Entwicklung,
Duncker and Humblot, Berlin.
² Schumpeter, J., 1942, Capitalism, Socialism and Democracy, George
Allen and Unwin, London.
² Weitzman, M., 1998, Recombinant growth, Quarterly Journal of
Economics, 331–360.
29
9
9.1
Appendix
Proof of Lemma 1
For part (i) consider …rst the case of F = 3 then V T2 = vT + ±V G,
VT1 = vT + Á±VG + Á±VT2 and VG = ¡Ã + °VT1 + °±VG . This is a system of
three variables and three unknown. Solving it, we …nd that VG = ¡Ã +
°±VG + °VT1 = ¡Ã + °±V G + °vT + °Á±VG + °Á±VT2 = ¡Ã + °±VG + °vT +
°Á±VG +°Á±vT + °Á±±VG = ¡Ã + °vT +°Á±vT + °±VG + °Á±VG + °Á±±VG
so that
¡Ã + °vT + °Á±vT
VG =
1 ¡ (°± + °Á± + °Á±±)
Consider next the case of F = 4, where VT3 = vT + ±VG, VT2 =
vT + Á±VG + Á±VT3, V T1 = vT + Á±VG + Á±VT2 and VG = ¡Ã + °V T1 + °±V G.
From VG = ¡Ã + °±VG + °VT1 = ¡Ã + °±VG + °vT + °Á±VG + °Á±V T2
= ¡Ã + °±VG + °vT + °Á±V G + °Á±vT + °Á±Á±VG + °Á±Á±VT3 = ¡Ã +
°±VG + °vT + °Á±VG + °Á±vT + °Á±Á±VG + °Á±Á±vT + °Á±Á±±VG =
¡Ã + °vT + °Á±vT + °Á±Á±vT + °±VG + °Á±VG + °Á±Á±VG + °Á±Á±±VG we
obtain
¡Ã + °vT + °Á±vT + °Á±Á±vT
VG =
1 ¡ (°± + °Á± + °Á±Á± + °Á±Á±±)
For the general case, it is now easy to see that
VG =
Xi=F¡2
¡Ã + °vT
i=0
1 ¡ [°± + °(Á±)F¡1 + °Á±
(Á±)i
Xi=F¡2
(Á±)i ]
Xi=F ¡3
where for the denominator we use [°±+°±(Á±)F ¡2 +°Á±
(Á±) i] =
i=0
Xi=F ¡2
Xi=F¡2
[°±+Á°±(Á±)F ¡2+°Á±
(Á±)i ] = [°±+°(Á±)F¡1+°Á±
(Á±)i ].
i=0
i=0
Naturally, this maps directly into VG = ¿ vT ¡ ½Ã where
i=0
Xi=F ¡2
(Á±)i
¿=
Xi=F¡2
1 ¡ [°± + °(Á±)F¡1 + °Á±
(Á±)i ]
i=0
1
½=
Xi=F ¡2
1 ¡ [°± + °(Á±)F ¡1 + °Á±
(Á±)i ]
°
i=0
i=0
For part (ii) we simply note that the numerator of VG is increasing in
Xi=F ¡2
F (since
(Á±)i increases with F ) and the numerator is decreasing
i=0
Xi=F ¡2
in F (since °(Á±)F ¡1 + °Á±
(Á±)i increases with F ). Note also
i=0
that for the same reasons, both ¿ and ½ are increasing in F .
30
For part (iii) we consider again the case of F = 4. To see that
> VG, assume to the contrary that VT3 < V G. Then we have VT2 =
vT + Á±VG + Á±V T3 < vT + ±VG = VT3, so that VT1 = vT + Á±VG + Á±V T2 <
vT + Á±V G + Á±VT3 < vT + ±VG = V T3 and thus VG = ¡Ã + °VT1 + °±VG
°vT ¡ Ã
< ¡Ã + °VT3 + °±VG = ¡Ã + °vT + ±VG , VG <
. But this is
1¡±
°v ¡ Ã
not possible, since V G(F ) > VG (F = 2) = T
. Thus VT3 > VG . To
1¡±
see that VT2 > VT3 , note that VT2 ¡ V T3 = vT + Á±V G + Á±VT3 ¡ vT ¡ ±VG
= Á±(VT3 ¡ VG ) > 0. For VT1 > VT2 note that VT1 ¡ VT2 = vT + Á±VG +
Á±VT2 ¡vT ¡Á±VG ¡Á±VT3 = Á±(VT2 ¡VT3) > 0. Thus VT1 > VT2 > VT3 > V G.
The proof for F > 4 is analogous.
VT3
9.2
Proof of Proposition 3
The …rst-order condition is given by ¢ ´ (¿ +F ¿ 0)(Ápz ¡c)¡(½+F ½0 )á
M 0 = 0. Note that ¿ 0 > 0 and ½0 > 0. The second order condition ¢0 < 0
is always satis…ed for M su¢ciently concave (M 00 su¢ciently large). We
dF
1 d¢
¡Ã ¡ F ½0
dF
Áz(¿ + F ¿ 0)
thus have
=
=
<
0,
=
> 0,
dÃ
¡¢0 dÃ
¡¢0
dp
¡¢0
dF
pÁ(¿ + F ¿ 0)
dF ¡¿ ¡ F ¿ 0
=
>
0
and
< 0.
dp
¡¢0
dc
¡¢0
For the comparative statics of b¤, we note that there is a direct and
@b¤
½ 1
an indirect e¤ect. The direct e¤ect is simply given by
=
> 0.
@Ã
¿ Ápz
@b¤ @F ¤
@b¤
The indirect e¤ect is given by
>
0,
where
< 0 since
@F ¤ @Ã
@F ¤
½
@F ¤
is decreasing in F , and
< 0 from the above proposition. The
¿
@Ã
comparative statics for c, p and z follow the logic.
9.3
Proof of Proposition 4
Consider ¦ = F (1 ¡ b ¡ B)¿ Ápz ¡ M (F ). Replacing b¤ =
c+Ã
½
¿ this
Ápz
simpli…es to ¦ = F ¿(Ápz ¡ c) ¡ F ½Ã ¡ M (F ) ¡ F B ¤¿ Ápz. Suppose
z
±(xÁ + xÁaz ¡ c)
2
…rst that R = 0 is binding. Using B ¤ =
we get
z + ±¿ Ápz
z
±¿Ápz
F B ¤¿ Ápz = (xÁ + xÁaz ¡ c)& where & ´ F
. The …rst2
z + ±¿ Ápz
order condition is given by ¢ = (¿ + F ¿ 0 )(Ápz ¡ c) ¡ (F + F ½0)Ã ¡
z
M 0(F ) ¡ (xÁ + xÁaz ¡ c)& 0 = 0. The second order condition ¢0 < 0 is
2
always satis…ed for M su¢ciently concave (M 00 su¢ciently large). Using
31
z
(Á + Áaz)& 0
0
2
¤
±¿
Ápz
±¿
Ápz
dF
&0 =
+F
> 0, we get
= 2 0
< 0.
z + ±¿Ápz
(z + ±¿ Ápz)2
dx
¢
For r = 0 we have F B ¤¿ Ápz = F (xÁpaz ¡c). The …rst-order condition is
then given by ¢ = (¿ +F ¿ 0 )(Ápz ¡c)¡(F +F ½0 )áM 0(F )¡(xÁpaz¡c) =
dF ¤
Ápaz
0. Again we …nd that
=
< 0.
dx
¢0
z
±(xÁ + xÁaz ¡ c)
¤
dB
R=0
2
To see that B ¤ is increasing in x we then note that
=
(¡±¿ 0Ápz)
dx
(z + ±¿Ápz)2
½
c +Ã
¤
¤
dBr=0
xÁpaz ¡ c
dF
¿
0 and
=
(¡¿ 0Ápz)
> 0. Finally, for b¤ =
dx
(¿Ápz)2
dx
Ápz
½
1
db¤
we note that
= Xi=F ¡2
is decreasing in F , so that
»
¿
dx
°
(Á±)i
½
d dF ¤
¿
> 0.
dF ¤ dx
i=0
32