1.Department of Economics, University of Ottawa, P.O. Box 450, STN. A, Ot tawa, Ontario, K1N 6R5, Canada,

gatallah@uottawa.ca.

R&D cooperation with asymmetric spillovers

February 2004

Gamal Atallah1

University of Ottawa and CIRANO

Abstract

This paper analyzes the impact of technological cooperation in R&D when firms have asymmetric

spillovers. Two firms producing a homogenous good invest in R&D in the first stage and compete

à la Cournot in the second stage. The introduction of asymmetric spillovers introduces new results

regarding the desirability of R&D cooperation. It is shown that the change in R&D by a firm

following cooperation is proportional to the gap between the spillover rate transmitted by that firm

and a critical level of spillovers. In consequence, cooperation increases total R&D investments

when the average of firms’ spillover rates is sufficiently high. This constitutes a generalization of the

known res ult that cooperation increases R&D when the common spillover rate is sufficiently high.

Whereas with symmetric spillovers cooperation is always beneficial to firms, with asymmetric

spillovers only a very limited range of spillovers make cooperation beneficial to both firms.

Regarding innovation policy, privately profitable cooperation is also socially beneficial when

spillovers are close to being symmetric, or are very asymmetric, with one firm transmitting high

spillovers and the other firm transmitting low spillovers. When spillovers are asymmetric and

intermediate, there may be a conflict between maximizing total welfare on the one hand, and

maximizing effective cost reduction (and consumer surplus) on the other hand. Such a conflict did

not arise in the R&D model with symmetric spillovers.

Keywords: R&D, R&D cooperation, Research joint ventures, asymmetric spillovers, spillovers

JEL codes: D43, L13, O33, O38

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1. Introduction

R&D investments generate technological externalities which benefit many agents in addition to the

innovator. The literature on R&D investments has generally assumed that spillovers are symmetric between

firms, that is, the degree of leakage of technology is the same for all firms in the industry. Even when

asymmetries between firms are allowed, these asymmetries relate generally to initial costs (Baerenss, 1999,

Röller et al., 1997), or R&D approaches (Kamien and Zang, 2000), but generally not to spillovers.

Exceptions are Amir and Wooders (1999, 2000), De Bondt and Henriques (1995) and Jarmin (1993) who

allow for asymmetric spillovers.

There are many reasons why R&D spillovers will differ from one firm to another. Firms differ in

their absorptive capacities of the technologies of their competitors (Cohen and Levinthal, 1989). Some

technologies leak out more easily, so that firms using those technologies will have higher outgoing spillovers.

Some firms may be engaged in more basic research, while others are closer to development activities, and

we know that the former give rise to higher spillovers than the latter. Firms may belong to different

industries, and it is well known that spillovers can differ between industries. Some firms may be more

successful in protecting their know-how through secrecy. Firms may be operating in different countries, and

therefore subject to different regimes of intellectual property rights protection. As Jarmin (1993:1) notes:

“Geographical location, research and development expenditures and other idiosyncratic firm characteristics

are likely to affect how individual firms learn from the experience of their rivals.”

The goal of this paper is to analyze the impact of asymmetric spillovers on the consequences of,

and the incentives for cooperation. The paper presents a model which builds on the archetypal

D’Aspremont and Jacquemin (1988) model, where firms invest in R&D in the first stage and compete in

output in the second stage. Firms are identical except for the fact that they have different levels of spillovers.

This minor alteration of the model has major consequences as to the private profitability of R&D

cooperation, and to the impact of cooperation on R&D.

The paper presents three main results. First, the standard finding that cooperation increases R&D

when spillovers are sufficiently high (usually higher than 0.5) needs to be qualified. It is shown that what

matters for the effect of cooperation is not the spillover of each firm, but rather the average spillover rate

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of all firms. Namely, as long as the average spillover rate is greater than 0.5, cooperation will increase

R&D. This occurs because, as will be shown, the change in R&D by a firm is proportional to the difference

between the spillover generated by that firm and the critical threshold, 0.5. Hence, when the average

spillover rate is greater than 0.5, the increase in R&D by the firm generating a high spillover, outweighs the

decrease in R&D by the firm transmitting a low spillover (when R&D expenditures move in opposite

directions following cooperation). This implies that cooperation between two firms, one leaking out a high

level of spillovers, while the other leaks out very little, may still increase R&D.

The second result pertains to the private profitability of R&D cooperation. In the literature, R&D

cooperation between symmetric firms is always profitable. It is shown that this is due to the assumption of

symmetric spillovers. When this assumption is dropped, cooperation is not profitable for a wide range of

spillover values. Cooperation is more likely to be profitable to a firm when it induces: a) a reduction in its

R&D while its spillover is sufficiently high so that this hurts the other firm; or, an increase in its R&D while

its spillover is not too high, so that this increase does not benefit the other firm too much; and/or b) a

reduction in the R&D of its competitor, while the spillover rate of the latter is not too high; or, an increase

in the R&D of its competitor, while the spillover rate of the latter is sufficiently high. R&D cooperation is

profitable to both firms when the spillover rates of both firms are close enough (in a precisely defined way)

to each other, or when the average spillover is close enough to 0.5. This means that in most cases firms will

not agree on cooperating, because cooperation reduces the profits of one of them. In addition, it is found

that cooperation reduces the gap between firm’s costs (which are initially different because of asymmetric

spillovers), hence reducing market concentration, except when spillovers of both firms are sufficiently high.

The third results pertains to the social desirability of cooperation. In the model with symmetric

spillovers, cooperation increases welfare (defined as the sum of producers’ and consumer surplus)

whenever it increases effective cost reduction, as long as there is no overinvestment in R&D. With

asymmetric spillovers, this link between welfare and effective cost reduction is broken. It remains true that

cooperation will be socially beneficial when the spillover rate of at least one firm is sufficiently high. But it

is only consumer surplus that moves in the same direction as effective cost reduction. This means that there

are spillover values such that cooperation reduces innovation, effective cost reduction and consumer

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surplus, but increases total welfare because of its effect on total profits. Moreover, the spillover range for

which R&D is privately profitable (it increases the profits of both firms) and is also socially beneficial is

extremely limited. This means that most instances of R&D cooperation, where cooperation is of the type

studied in this paper, are not socially beneficial.

Most of the literature on R&D and R&D cooperation has assumed symmetric firms and symmetric

spillovers. A few papers have assumed that firms have different production costs. There is an analogy

between asymmetric costs and asymmetric spillovers, because asymmetric spillovers lead to different

production costs.

Baerenss (1999) develops a stochastic model with R&D competition and cooperation where firms

have different production costs. He shows that cooperation may not be socially beneficial when firms are

very dissimilar, as it preserves the near-monopolistic position of the low-cost firm. In addition, there is a

wide range of cost levels such that firms fail to agree on cooperation because it is not beneficial to at least

one of them. Here it will be shown that, contrary to asymmetry in costs, asymmetry in spillovers in general

reduces the gap between firms’ effective production costs. However, in the spirit of the results of Baerenss,

it is found that agreement on cooperation is more difficult with asymmetric spillovers.

Röller et al. (1997) develop a model where firms differ in their production costs and test it using

American data. In their model there are no spillovers when firms compete in R&D, while spillovers are

perfect under cooperation. They find that, theoretically as well as empirically, firms tend to form Research

Joint Ventures (RJVs) with other firms of similar size, that is, asymmetries between firms reduce the

incentives for R&D cooperation. This is consistent with the results obtained here, where asymmetric

spillovers make agreement on cooperation more difficult.

Closer to the present paper, some studies have explicitly considered asymmetric spillovers. Amir

and Wooders (2000) present a general model where spillovers are unidirectional, the firm transmitting the

spillover being more advanced in its research program than the receiving firm. While the model developed

in the current paper is less general, a richer range of spillovers is considered (both firms can have spillovers

ranging from 0 to 1), and the impact of cooperation is more explicitly analyzed.

De Bondt and Henriques (1995) analyze the case where firms have asymmetric spillovers. They

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identify a unique equilibrium where the firm absorbing large spillovers is the leader and the firm receiving

small spillovers is the follower. The current paper assumes that R&D decisions are taken simultaneously.

Arguments are provided as to why firms may not always have the latitude of adopting sequential R&D

investments.

Amir and Wooders (1999) develop a model which is close to their 2000 model mentioned above,

with two differences. First, they derive endogenous innovator and imitator roles, in the same spirit as De

Bondt and Henriques (1995). Second, they study more explicitly the role of cooperation, considering

different modes of cooperation, such as a joint R&D lab and an R&D cartel.

In the literature on learning by doing, Jarmin (1993) allows for differences in spillovers between

firms. He shows that with asymmetric spillovers, spillovers may increase market concentration, which is not

possible under symmetric spillovers. Hence asymmetric spillovers create a tradeoff between industry

performance and market concentration. In the model studied here, asymmetric spillovers increase market

concentration by inducing cost asymmetries between firms, but cooperation generally reduces these

asymmetries, except when spillovers of both firms are sufficiently high.

None of the studies mentioned here consider the interaction between the full range of asymmetric

spillovers and the dynamics of R&D cooperation. This is the gap which this paper aims at filling. The next

section presents the model and its solution. Section 3 analyzes the effect of cooperation on R&D

investments. Profitability is studied in section 4, while section 5 looks at the impact of cooperation on

market concentration. The implications for effective cost reduction, consumer surplus, and total welfare are

taken up in section 6, and section 7 concludes.

2. The model

There are two firms producing a homogenous good and competing in quantities à la Cournot. Firms

face the linear inverse demand p=A-y1-y2, with yi denoting firm i’s output. The production cost of firm i

is

ci = "-x i-$jx j, i=1,2, (1)

where " is the initial production cost, x i is the R&D output of firm i, and $j,[0,1] denotes the leakage from

2.It must be noted that throu ghout the paper R&D decisions are assumed to be simultaneous. While De Bondt

and Henriques (1995) and Amir and Wooders (1999) show that endogenous leader-follower roles arise due to asymmetric

spillovers, this implicitly assumes t hat firms can choose the timing of their investments. There are many obstacles to the

adopt ion of these asymmetric roles. Firms may be engaged in an innovation race, and delaying an investment may

weaken their future bargaining pos it ions, especially if they envisage to engage in R&D cooperation or licensing

agreements in the future. There may be uncertainty as to what the level of sp illovers will be, and this uncert aint y may

be gradually resolved only as the technological investments are made and the scientific/technological work is perfo rmed.

There may be more than two firms performing in the industry, in which case the adoption of sequential R&D investments

becomes extremely complicated, both at the theoretical level, and from the point of view of individual firms. For all these

reasons, we find it is safe to assume that firms make their R&D decisions simultaneous ly . Moreover, this assumption

has also been made by Amir and Wooders (2000) and Jarmin (1993).

5

(3)

(5)

(4)

firm j’s technology. In reality, the spillover from firm i to firm j can depend on three factors: firm i’s

characteristics (type of technology, secrecy efforts), the legal, economic and technological environment

(intellectual property rights protection, formal and informal communication networks), and firm j’s

characteristics (absorptive capacities, imitation efforts, type of technology, learning experience). The

spillover $j summarizes the net sum of these different effects. We do not assume a priori that one firm has

a higher spillover rate than the other. The cost of x units of R&D output is given by (x2. This entails a profit

of firm i equal to

Bi = (p-ci)yi-(x i2. (2)

In the first stage each firm chooses its R&D investment. Two regimes are considered: cooperation

and no cooperation. Under cooperation, R&D investments are chosen so as to maximize the joint profits

of both firms. Cooperation does not affect the spillover rates between firms. In the second stage each firm

chooses its output noncooperatively to maximize its profits.2

Solving the game starting with the last stage, we obtain the output of firm i:

Substituting this optimal level of output into the profit function, it is straightforward to derive the

noncooperative and cooperative R&D investments of each firm:

3.All proofs are in the appendix.

6

Note that the equilibrium is asymmetric: R&D investments of the two firms will coincide (given that they

cooperate, or that they don’t) only if spillovers are symmetric.

In what follows we analyze the impact of cooperation on R&D, the profitability of cooperation, its

impact on market concentration, and its social benefits.

3. Effect of cooperation on R&D

Consider first the impact of cooperation on R&D. In the symmetric model the answer to this

question is straightforward: cooperation increases R&D iff $>0.5. The answer is more complex with

asymmetric spillovers, as it now depends on both $1 and $2. First consider the impact of R&D cooperation

on the R&D investments of each firm.

Whether x1 increases or decreases following cooperation depends only on $1, the spillover given

away by firm 1. This is because cooperation induces the internalization of this externality. As expected,

x1n>x1

c iff $1<0.5. Firm 1 internalizes the impact of its R&D on the other firm through cooperation. This

internalization leads to an increase in R&D when the spillover firm 1 gives away is high enough, so that the

positive effect of the spillover on firm 2's profits is higher than the negative effect of the reduction in c1 on

firm 2's profits. The same analysis applies to firm 2.

Proposition 1.3 x ic>x i

n iff $i>0.5.

In addition, cooperation has a radical effect on the ranking of firms in terms of R&D spending.

Without cooperation, the firm with the lower outgoing spillover rate spends more on R&D than the other

firm, while this situation is reversed with cooperation (this is straightforward to verify using the solutions for

x in and x i

c given above). When the externality is not internalized, it induces its transmitter to reduce its

R&D; whereas when it is internalized, it induces the transmitter to increase it.

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(6)

Hence, the net effect of cooperation on R&D depends on the sum of the changes in x1 and x2.

When spillovers are symmetric, these changes have the same sign. Moreover, when both spillovers are

lower than 0.5 or both are greater than 0.5, the changes also go in the same direction. However, when, for

instance, $1<0.5 but $2>0.5, cooperation will reduce x1 but increase x2. The net effect on total R&D will

depend on the magnitudes of these changes.

This net effect depends on how far each spillover rate is from 0.5 It turns out that the effect of

cooperation on R&D is proportional to the gap between the spillover a firm generates and the critical

threshold, 0.5. For instance, if $1=0.4 and $2=0.6, so that spillovers are symmetric around their “central”

value, the decrease in x1 following cooperation is exactly matched by the increase in x2, implying that total

R&D is unchanged. Therefore, what determines the impact of cooperation is the average spillover rate.

It turns out that the ratio of changes in R&D expenditures depends on the ratio of the gap between

firms’ spillovers and the critical spillover level 0.5. Let )x i/x ic-x i

n and )$i/$i-0.5. Taking the ratio )x1

/)x2 yields a complex function that depends only on $1, $2, and (. Evaluating this function for any

admissible values of its arguments yields a value that is equal to the ratio ($1-0.5)/($2-0.5). Hence we have

that

Verifying (6) is straightforward: using equations (4) and (5), we evaluate the left hand side of (6). This

difference does not depend on A or " (this is obvious from (4) and (5)), but depends on $1, $2, and (. We

evaluate the expression for any admissible value of (: the choice of ( has no bearing on the result. Then,

we substract from it the right hand side of (6). The difference is 0 for all values of spillovers in the interval

[0,1].

Ultimately we are interested in the impact of cooperation on total R&D. Let total noncooperative

R&D be given by xn/x1n+x2

n, and total cooperative R&D by xc/x1c+x2

c. From proposition 1 and (6) we

have the following proposition.

Proposition 2. xc>xn iff $1+$2>1.

4.A sensit ivity analysis, available up on request , shows that none of the results that follow depend on this

particular numerical parametrization.

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Figure 1a illustrates the effect of cooperation on total R&D for all levels of spillovers. Along the

leading (negatively sloped) diagonal, the increase in R&D by one firm is exactly matched by the decrease

in R&D by the other firm. To the right (left) of that diagonal, total R&D increases (decreases). Figure 1b

decomposes the total change by indicating the effect on each firm’s R&D. Note how the lines $1=0.5 and

$2=0.5 determine the change in each firm’s R&D, while the leading diagonal $1+$2=1 determines the

change in total R&D.

[Figures 1a and 1b here]

The main result of the pre-competitive R&D literature, that cooperation increases R&D when

spillovers are high, hinges upon the assumption of symmetric spillovers. The critical value found in the

literature is a special case where $1=$2=0.5. With asymmetric spillovers, what matters for the effect of

cooperation on total R&D is the average spillover rate between the cooperating firms. Cooperation can

be socially beneficial even when one of the firms transmits low spillovers, and in fact reduces its R&D. The

increase in R&D by the other firm may (if the spillover it generates is sufficiently high) more than

compensate for that reduction, resulting in an increase in total R&D.

4. The profitability of cooperation

We now consider the effect of cooperation on profitability. The goal is to see how asymmetric

spillovers affect the profitability of cooperation. As will be seen, this is not really an issue with symmetric

spillovers, because in this case cooperation increases the profits of all firms (at least when firms are

symmetric and cooperation is industry-wide). As is usual in the literature, the analytical complexity of the

solutions prohibits us from analyzing them algebraically. To overcome this limitation, we use numerical

values for the parameters that are known to have little impact on the strategic interactions of the model:

demand, initial cost of production, and R&D cost. We use the numerical parametrization A=1000, "=50,

(=60.4

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For R&D cooperation to occur in a decentralized fashion and without side payments, it must be

profitable to all the firms involved. Hence, in this model, cooperation will arise only when B1c>B1

n and

B2c>B2

n. Therefore we need to consider first profitability form the point of view of each firm.

Figure 2a shows how cooperation affects the profits of firm 1. A + sign indicates that cooperation

increases B1, while a - sign indicates a reduction in B1. We see that cooperation is beneficial to firm 1 when

the spillover transmitted by firm 2 is sufficiently low or sufficiently high (not intermediate), with its exact

critical value depending on $1. Note how spillovers have a non-monotonic effect on the profitability of

cooperation. For instance, for a given $1, an increase in $2 changes cooperation from profitable, to

unprofitable, to profitable again, for firm 1.

[Figures 2a and 2b here]

To understand the impact of cooperation on B1, we refer to figure 2b, which makes the link

between changes in profits, changes in R&D and spillover levels. From that figure we see that cooperation

increases B1 in the following cases: a) firm 2 reduces its R&D and $2 is sufficiently low, so that this

reduction does not hurt firm 1 much (regions A and B of figure 2b); or b) when firm 2 increases its R&D

and $2 is sufficiently high so that firm 1 benefits substantially from this increase (regions C and D of figure

2b). We further note that when spillovers are symmetric, cooperation always increases R&D (i.e. the line

$1=$2 is completely within the shaded regions of figures 2a and 2b). This explains why profitability is not

an issue in the literature when spillovers (and firms) are symmetric.

The shape of each region is related to the effect of cooperation on x1 and x2. Consider region A,

where cooperation reduces R&D by both firms. For a given level of $1, the increase in $2 means that the

reduction in x2 following cooperation hurts firm 1 more; and for a given level of $2, the increase in $1 means

that the reduction in x1 hurts firm 2 more, which benefits firm 1. This explains the positive slope of the left

boundary of region A. Consider now region B, where cooperation induces an increase in x1 and a

reduction in x2. For a given level of $1, an increase in $2 reduces the benefits of cooperation to firm 1,

because the reduction in x2 hurts firm 1 more when $2 is high. And for a given level of $2, an increase in

$1 reduces the benefits of cooperation for firm 1, because the increase in x1 benefits firm 1 less when $1

is higher. This explains the negative slope of the right boundary of region B. In region C, cooperation

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increases R&D by both firms. For a given level of $1, the increase in $2 benefits firm 1, because the

increase in x2 is more valuable to firm 1 when $2 is higher. Similarly, for a given level of $2, the increase in

$1 hurts firm 1, because it benefits less from increasing its R&D when $1 is higher. This explains the positive

slope of the right boundary of region C. Finally, in region D, cooperation reduces x1 but increases x2. For

a given level of $1, the increase in $2 increases the benefits of cooperation to firm 1, because the increase

in x2 is then more valuable to it. Similarly, for a given level of $2, the increase in $1 benefits firm 1, because

the reduction in x1 hurts firm 2 more when $1 is higher. This explains the negative slope of the left boundary

of region D.

Figure 3 shows spillover values for which cooperation is beneficial to firm 2. The same analysis

made for firm 1's profits applies here.

[Figures 3 and 4 here]

We now have enough information to determine when cooperation will arise, that is, spillover values

such that cooperation increases the profits of both firms. Figure 4 shows those values, which are nothing

but the intersection of the shaded areas of figures 2a and 3. We see that cooperation is beneficial to both

firms when spillovers do not deviate too much from the line $1=$2 or the leading diagonal. Around the line

$1=$2, spillovers may differ, but not by too much. Either spillovers are low and both firms reduce their

R&D, or spillovers are high and both firms increase their R&D. Along the leading diagonal, spillovers may

still differ, but they are close to the line $2=1-$1, i.e. their average is not too far from 0.5. Along this leading

diagonal, cooperation increases R&D by one firm and reduces it by the other. This is beneficial to both

firms when the firm reducing its R&D transmits low spillovers (so that this does not hurt the other firm too

much), and that the firm increasing its R&D transmits high spillovers (so that this benefits the other firm

substantially). For instance, in the region around the lower half of the leading diagonal (the south-east

shaded region of figure 4), firm 1 increases its R&D and transmits high spillovers (which benefits firm 2

substantially), while firm 2 reduces its R&D and transmits low spillovers (hence this does hurt firm 1 too

much). The converse applies on the upper half of the leading diagonal. Interestingly, there is no case where

cooperation is detrimental to both firms.

These results are reminiscent of the findings of Baerenss (1999), who finds that asymmetries in

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costs between firms make agreement on cooperation difficult. Similarly, Röller et al. (1997) show that with

asymmetric costs, the low cost firms prefers not to cooperate with the high cost firm when products are

highly substitutable and the cost difference is important.

The requirement that cooperation be profitable to both firms is valid when side payments are not

feasible. The picture changes when side payments are allowed. Numerical simulations suggest that

whenever cooperation is beneficial to only one firm, side payments can resolve the problem: the increase

in profits of one firm is always larger than the decrease in profits of the other firm. The gaining firm can thus

always compensate the losing firm, allowing cooperation to take place. Therefore whether side payments

are feasible or not may explain to a large extent whether cooperation occurs or not. Moreover, the impact

of cooperation on total R&D or even individual R&D is not very informative about the profitability of

cooperation. Cooperation may increase the profits of a firm while increasing or decreasing its R&D, the

R&D of the other firm, and/or total R&D.

It cannot be said that higher outgoing spillovers increase or decrease the incentives of a firm to

cooperate. Even if a firm always has lower spillovers than its competitor, there will be spillover regions such

that only the low-spillover firm wants to cooperate, and high spillover regions where only the high-spillover

firm wants to cooperate. This contrasts to asymmetry in costs, where the low cost firm is less willing to

cooperate (Baerenss, 1999).

5. Cooperation and market structure

A related issue is the effect of cooperation on market structure. Does cooperation increase or

decrease asymmetries in costs and market shares between firms? Figure 5a answers this question by

looking at the impact of cooperation on the cost differential between firms, that is, by looking at the sign

of

*c1c-c2

c*-*c1n-c2

n*.

[Figures 5a and 5b here]

As figure 5a shows, in general, cooperation reduces the gap between firms’ costs, implying that

it should not increase the chances of monopolization, except when both spillovers are sufficiently high. Note

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that along the line $1=$2, cooperation has no impact on the cost differential (which is zero in this case), even

within the shaded areas.

To understand this result, we decompose the effect of cooperation on the cost gap in figure 5b.

Note that without cooperation the firm transmitting a higher spillover has a higher cost of production,

because it invests less in R&D. And from proposition 2 we know that cooperation increases R&D more,

or reduces R&D less, by the firm that has the highest spillover. These two effects imply that in general

cooperation reduces the gap between firms’ costs. For instance, when both firms have low spillovers (lower

than 0.5), but $1>$2 (region A of figure 5b), we know that c1n>c2

n, because x1n<x2

n. Cooperation reduces

R&D by both firms, but more so for firm 2, because of its lower spillover. Hence c1 increases less than c2,

and the gap between cost levels is reduced. Moreover, because $1>$2, firm’s 1 cost is less affected

(increased) by the reduction in R&D by firm 2 than firm 2 is affected by the decrease in R&D by firm 1,

further contributing to the decline in the gap between costs. The analysis is even more straightforward when

one firm has a spillover rate that exceeds 0.5, while the spillover of the other firm is below that threshold

(for example, region B of figure 5b). In that case, the high cost firm (i.e. the high spillover firm) increases

its R&D, while the low cost firm (the low spillover firm) reduces its R&D, reducing the gap between costs.

Consider the case where $1>$2>0.5, but such that cooperation reduces the gap between firms’

costs (region C). In this case c1n>c2

n. After cooperation, )x1>)x2 (because $1>$2), which by itself

reduces the cost asymmetry. In addition, there is the effect of spillovers, because firm 2 will benefit from

this larger increase in x1. Therefore in region C of figure 5b, the net effect is to reduce the gap between

firms’ costs. However, if we increase $1 further, the diffusion effect becomes so important as to reduce c2

significantly, increasing the gap between firms’ costs (region D). A similar effect occurs in region E, with

the roles of firms reversed.

Therefore, for a wide range of spillover values cooperation reduces the gap between firms’ costs,

except when the spillovers of both firms are sufficiently high. Paradoxically, it is in this latter case that

cooperation has the most obvious benefits (because of strong underinvestment in the absence of

cooperation).

We know that total profits are higher when cost asymmetry is higher. When cooperation reduces

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cost asymmetries and hence total profits, it reduces the total surplus to be shared (if there is sharing)

between firms. This reduces the scope for side payments, and perhaps collusion as a byproduct of

cooperation, between firms. However, the opposite occurs when spillovers are sufficiently high.

Asymmetries between firms have consequences for their R&D investments. However, the sources

of those asymmetries also matter. Here we compare the impact of asymmetries related to cost, with the

impact of asymmetries related to spillovers. When (only) costs are asymmetric, the high cost firm tends to

invest less in R&D (both with and without cooperation), because it has a smaller output and hence values

cost reduction less. Therefore the ranking of the firms in terms of R&D is not affected by cooperation. The

opposite occurs when the only asymmetry between firms is due to spillovers. Without cooperation, the firm

transmitting high spillovers invests less in R&D. But with cooperation, the firm transmitting high spillovers

invests more (compared to the investment of the other firm) in R&D. The ranking of the firms by R&D is

reversed following cooperation.

Baerenss (1999) finds that with asymmetries in production costs, cooperation tends to preserve

the near-monopolistic position of the low-cost firm. Here, however, for a wide range of spillovers, including

when asymmetries in spillovers (and hence in costs) are very strong, cooperation tends to reduce the cost

differential between firms, hence making the market structure more symmetric.

Röller et al. (1997) find that RJVs reduce the asymmetry between firms’ production costs.

However, in their model there are no spillovers (there is only voluntary information sharing under

cooperation). The analysis here shows that their result depends on the special modeling of spillovers they

adopt. Moreover, one of the reasons asymmetric RJVs are less likely to arise in their model is that

cooperation tends to reduce cost asymmetries, which penalizes the low-cost firm. This effect does not arise

here. In the model studied here, there is no clear link between the impact of cooperation on cost asymmetry

on the one hand, and the incentives for cooperation on the other. Comparing figures 4 and 5a, we see that

cooperation can be beneficial to both firms both when it increases and when it decreases cost variance.

6. Effective cost reduction, consumer surplus and welfare

In a world with symmetric spillovers, R&D and effective cost reduction move in the same direction

14

following cooperation (for given spillovers). However, this need not be the case with asymmetric spillovers.

When the R&D of the two firms move in opposite directions, the change in total R&D does not provide

enough information to determine the impact on effective cost reduction. Effective cost reduction is defined

as

Q = x1(1+$1)+x2(1+$2).

Figure 6a shows the effect of cooperation on Q. When $1 and/or $2 are sufficiently high, Q

increases with cooperation. However, when both spillover rates are low, cooperation decreases Q. To

understand this result, it is necessary to examine the effect of cooperation on the R&D of each firm. A

change in R&D by a firm transmitting high spillovers has more impact on Q than a change in R&D by a firm

transmitting low spillovers. From the point of view of effective cost reduction with asymmetric spillovers,

it should be noted that cooperation has the “virtue” of increasing R&D by the firm transmitting high

spillovers (higher than 0.5) and reducing R&D by the firm transmitting low spillovers. There is, hence, a

built in bias toward an increase in effective cost reduction.

[Figures 6a and 6b here]

Figure 6b decomposes the spillover space into 8 regions, based on the impact of cooperation on

individual R&D, total R&D, spillovers, and the impact on Q. In region A, R&D of both firms decline,

implying a decline in total R&D and in Q. In region B, the R&D of both firms increase, increasing total

R&D and Q. In region C, x1 declines and $1 is low, while x2 increases and $2 is high; the effect of x2

dominates, increasing total R&D; and the high level of $2 induces the increase in Q. The converse occurs

in region D. The analysis in region E is similar to that in region C, except that total R&D declines; but the

impact on Q is still positive. Similarly, the analysis in region F is similar to that in region D, except for the

impact on total R&D. Consider now region G, where the behavior of x1, x2, and x is similar to region E,

except that now the effect of the decline in x1 dominates, inducing a reduction in Q. In a similar fashion,

region H is similar to region F, except that the effect of the decline in x2 dominates, inducing a reduction

in Q.

The above analysis shows that when cooperation moves the R&D of both firms in the same

direction, the impact of cooperation on Q is obvious. This is the case usually studied in the literature, where

15

spillovers are symmetric. However, more analysis is required to determine the net impact on Q when R&D

investments move in opposite directions. In general, effective cost reduction moves in the same direction

as the R&D of the firm transmitting high spillovers, i.e. it increases with cooperation. The notable exceptions

are regions G and H, where cooperation reduces Q in spite of the fact that the firm transmitting high

spillovers increases its R&D. What happens here is that the “high” spillover is just above 0.5, implying a

moderate increase in R&D by one firm, while the “low” spillover is rather low, implying a substantial

reduction in R&D by the other firm., with the negative effect dominating. Note the gradual change in the

impact of cooperation as we move clockwise from region A to region B: from a situation where individual

and total R&D, as well as Q decline (A), we move to a region where x2 increases (G), then to a region

where x2 and Q increase (E), then to a region where x2, x, and Q increase (C), and finally to a region

where both firms increase their R&D, increasing Q (B).

Consider next the impact of cooperation on consumer surplus. It turns out that the values of

spillovers for which cooperation increases consumer surplus are the same values for which cooperation

increases effective cost reduction (this is illustrated on figure 6a). Hence effective cost reduction could be

used as a criterion to evaluate the effect of cooperation on consumer surplus.

Consider now the impact of cooperation on total welfare, defined as the sum of producer and

consumer surplus. In the model with symmetric spillovers, welfare and effective cost reduction move in

tandem, as long as there is underinvestment in R&D, which is generally the case. This automatic link

between welfare and Q is broken with asymmetric spillovers. Figure 7 shows the impact of cooperation

on welfare. As expected, cooperation increases welfare when one or both spillovers are sufficiently high,

so that one or both firms increase their R&D, and, when only one firm does so, at least one spillover rate

is sufficiently high for that increase to be substantial, and to have a significant effect on diffusion.

[Figure 7 here]

Comparing figures 6a and 7, we see that the boundary separating the positive from the negative

effects of cooperation on welfare lies below the boundary determining its impact on effective cost reduction

and consumer surplus, indicating that there are regions where cooperation reduces R&D and effective cost

reduction (and hence consumer surplus), but increases welfare. This increase in welfare is due to the

16

increase in total profits. These regions are illustrated on figure 8a.

[Figures 8a and 8b here]

In these regions cooperation is controversial: it reduces total R&D, effective cost reduction,

consumer surplus, to the benefit of one or both firms. Figure 8b illustrates this in detail. In region A,

cooperation reduces Q and CS, but increases the profits of both firms and total welfare. In region B,

cooperation reduces Q, CS and B1, but increases B2 and total welfare. The lower shaded region of figure

8a could be decomposed in a similar fashion. Even if total welfare increases in these regions, especially

region B, such a drastic redistribution of benefits is unlikely to appeal to regulators. Moreover, in region

B, the tradeoff is not only between consumers and firms, but also between firms.

When will cooperation be profitable to both firms, and also socially beneficial, at least as indicated

by the total welfare criterion? Figure 9a answers this question, by presenting the intersection of figures 4

and 7. This occurs when spillovers are close to being symmetric and high, and when spillovers are very

asymmetric but their average is close to 0.5. Interestingly, regions where spillovers are asymmetric and their

average is close to 0.5 but they are both quite close to 0.5 are not socially beneficial; this explains the

curvatures in figure 9a. For example, close to the left curvature, the profits of both firms increase, but the

reduction in x1 is substantial, and the increase in x2 is not important enough to outweigh it, so that effective

cost reduction and consumer surplus suffer enough to decrease total welfare.

[Figures 9a and 9b here]

A related question is: when will firms choose to cooperate even when this is harmful to society? The

spillover regions satisfying these conditions are illustrated on figure 9b. This occurs when spillovers are

symmetric and low, and when they are intermediate and asymmetric, with their average value close to 0.5.

How, then, does accounting for asymmetric spillovers change our views about what should be the

treatment of RJVs? First, what matters for the impact of cooperation on R&D is the average spillover rate

of all firms. Hence cooperation between two firms, one transmitting a high spillover, and the other

transmitting a low spillover, can be beneficial. Second, there is a wide range of spillover values for which

cooperation, as modeled here, is not beneficial to both firms. If cooperation is observed in those instances,

either there are other dimensions to cooperation, beyond the scope of the current paper (like information

5.Product differentiation softens competit ion between firms, increases their market power and increases

investments in R&D (see Atallah, 2004). Therefore one would expect that in the presence of product differentiation, there

is a wider range of spillovers over which bo th firms benefit from cooperation, and also over which cooperation increases

total R&D.

17

sharing, cost sharing, improvements in research efficiency, or risk sharing, for instance); or, firms are

engaged in other cooperative -or collusive- practices which make R&D cooperation profitable to all of

them. Finally, cooperation may benefit firms but reduce welfare when spillovers are low and symmetric,

and when they are asymmetric but very close to 0.5 with their average close to 0.5.

7. Conclusions

This paper argued that it is important to account for the asymmetry of technological spillovers

between firms. This asymmetry has implications for the impact of cooperation on R&D and on market

structure, for the profitability of cooperation, and for the social benefits and costs of cooperation. The

symmetric spillover case considered almost exclusively in the literature gives a very partial snapshot of the

effects of spillovers and cooperation. By assuming away ex-post asymmetries, the symmetric model

neglects many of the complications arising from R&D cooperation, which usually takes place between

asymmetric partners, with spillovers being but one of many sources of asymmetries.

From a policy point of view, the model emphasizes the fact agreement on cooperation is difficult

for a wide range of asymmetric spillovers. In such instances, the government may have a role to play in

terms of providing incentives for cooperation, or coordinating cooperation between firms. As for the

desirability of cooperation, the issue of whether cooperation is socially beneficial or not hinges upon the

evaluation of the externalities related to the technologies of all the firms involved, and not only on whether

the common spillover rate in an industry -which does not exist- is low or high.

Asymmetric spillovers may interact with other dimensions of cooperation, such as cooperation on

product R&D,5 cooperation between firms producing complementary products, the incentives for

information sharing, and the formation of research joint ventures. These issues constitute fertile areas for

future research.

18

References

Amir, R., and Wooders, J., 1999, ‘Effects of one-way spillovers on market shares, industry price, welfare,and R&D cooperation’, Journal of Economics & Management Strategy, 8(2):223-49.

Amir, R., and Wooders, R., 2000, ‘One-Way Spillovers, Endogenous Innovator/Imitator Roles, andResearch Joint Ventures’, Games and Economic Behavior, 31:1-25.

Baerenss, A., 1999, R&D Joint Ventures: The Case of Asymmetric Firms, Working Paper 99-17,Center for Economic Analysis, Department of Economics, University of Colorado at Boulder.

Cohen, W. M., and Levinthal, D. A., 1989, ‘Innovation and Learning: The Two Faces of R&D’, TheEconomic Journal, 99:569-96.

D’Aspremont, C., and Jacquemin, A., 1988, ‘Cooperative and Noncooperative R&D in Duopoly withSpillovers’, American Economic Review, 78:1133-37.

De Bondt, R., and Henriques, I., 1995, ‘Strategic Investment with Asymmetric Spillovers’, CanadianJournal of Economics, 28(3):656-74.

Jarmin, R. S., 1993, Asymmetric Learning Spillovers, Working paper 93-7, Center for EconomicStudies CES, U.S. Census Bureau, April.

Kamien, M. I., and Zang, I., ‘Meet Me Halfway: Research Joint Ventures and Absorptive Capacity’,International Journal of Industrial Organization, 18:7:995-1012.

Röller, L. H., Tombak, M. M., and Siebert, R., 1997, Why Firms Form Research Joint Ventures:Theory and Evidence, Discussion paper 97-6, Social Science Research Center WZB, Berlin.

19

Appendix

Proof of Proposition 1.

(7)

We know that A>", hence the sign of (7) does not depend on either A or ". While ( affects the magnitude

of the difference, it does not affect the sign of (7). However, this is difficult to establish analytically, and

hence we have to rely on simulations only for that parameter. We first choose any value of (, say (=60

(the value used in the text). The remaining expression depends only on $1 and $2, but is still too complex

to be analyzed analytically. The simplest way is to plot the difference:

[Figure 8 here]

As figure 8 shows, the difference is positive when $i>0.5 and negative for $i<0.5, and it does not depend

on $j.

Reproducing this figure for any other value of ( (satisfying the second-order conditions) yields the same

result: the separating line is at $i=0.5. Hence the value of ( has no consequence for the result. �

Proof of Proposition 2.

From (6) we know that )x1)$2=)x2)$1. Assume that $1>0.5 and $2>0.5, which means that )$1>0 and

)$2>0. In that case, xc>xn, because the R&D of both firms increase by proposition 1.

Similarly, When $1<0.5 and $2<0.5, which means that )$1<0 and )$2<0, we have that xc<xn, because

the R&D of both firms decrease.

Consider the case when )$2>0 and )$1<0 and assume that $1+$2>1. These two conditions require that

*)$2*>*)$1*. By (6) this implies that *)x2*>*)x1* Y x2c-x2

n>x1n-x1

c Y xc>xn.

The same argument establishes the result when the signs of )$1 and )$2 are reversed.

20

This establishes the if part of the proposition. The only if part is established using the same logic, starting

from the sign of xc-xn, and using proposition 1 and (6) to establish the signs and magnitudes of $1 and $2.�

A B C D E F G H

x1 - + - + - + - +

x2 - + + - + - + -

x - + + + - - - -

$1 low high low high low high low high

$2 low high high low high low high low

Q - + + + + + - -