Discussion Paper No. 704

COLLUSION AND
RESEARCH JOINT VENTURES

Kaz Miyagiwa

December 2007

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Collusion and research joint ventures
Kaz Miyagiwa*
Emory University and Osaka University

Abstract: We examine whether cooperation in R&D leads to product market collusion.
Suppose that firms engage in a stochastic R&D race while maintaining the collusive
equilibrium in a repeated-game framework. Innovation under competitive R&D createsinter-firm asymmetries, which destabilizes the collusive equilibrium. Innovation sharing
through cooperative R&D preserves symmetries, thereby facilitating collusion. Sharing
an efficient technology also increases industry profit, which contributes to the collusion
stability but also raises social welfare. Interestingly, a welfare improvement is less likely
if innovation leads to a large cost reduction. The effect of licensing under competition
R&D is also examined.
JEL Classifications System Numbers: L12, L13
Keywords: Collusion, Research Joint Ventures, Innovation, R&D
Correspondence: Kaz Miyagiwa, Institute of Social and Economic Research, Osaka
University, 6-1 Mihogaoka, Ibaraki, Osaka 567-0047, JAPAN; E-mail:kmiyagiwa@gmail.com.

*

I am grateful to an anonymous referee and especially Yeon-koo Che, Editor of This Journal, for theirvaluable comments and suggestions that led substantial improvements. Thanks also go to Sue Mialon andYuka Ohno for their comments on earlier versions. Errors are my own responsibility.

1. Introduction
This paper evaluates the age-old suspicion that cooperation in R&D leads to
product market collusion. Prior to the 1960s this suspicion was so strong in the U.S. that
antitrust authorities threatened to punish any form of research joint ventures (RJVs) withfull forces of antitrust laws. The sentiment abated during the 1960s and early 1970s,
when key American industries were losing the competitive edge to foreign rivals that had
made considerable technological progress through formation of RJVs.1 Although today
joint R&D activities among firms are encouraged everywhere, the same old suspicion
lingers: does cooperation in R&D facilitate product market collusion?2
To investigate this question analytically, suppose that a group of ex ante
symmetric firms manage implicitly to maintain a collusive equilibrium in an infinitely
repeated-game framework. In such an environment, a firm that discovers a cost-cutting
technology has a strong incentive to lower the price to increase its market share, thereby
destabilizing the collusive arrangement. Further, the prospect that collusion breaks downwith a discovery of new technology destabilizes collusion in pre-discovery periods.
Suppose that firms are allowed to form an RJV to share innovations. Cooperation
in R&D generates two effects that facilitate collusion. First, innovation sharing eliminates
the inter-firm asymmetry, the source of collusion instability mentioned above. Second,innovation sharing gives all firms access to new technology and increases industry profit,
the prospect of which contributes to the stability of collusion.3

1

See Caloghirou, Ioannides and Vonortas (2003).
For example, see the Federal Trade Commission’s Comment and Hearings on Joint Venture Project towitness its continuing ambivalence towards RJVs (http//www.ftc.gov/os/1997/jointven.htm).
3
I am grateful toYeon-koo Che for this insight.
2

2
To separate these two effects, we consider the intermediate case in which firms
license new technology without forming an RJV. Licensing allows industry to capture as
much total surplus as it could as an RJV, but does not eliminate the asymmetry that exists
between licensor and licensee. This asymmetry makes it more difficult for firms tomaintain collusion relative to when they form an RVJ.
Welfare and policy implications of cooperative R&D are also considered.
Although it facilitates collusion, an RJV also increases production efficiency, so social
welfare need not fall. With licensing possibilities, however, an RJV never increasessocial welfare because industry productivity is already high with licensing.
These results are established in a model under the assumptions that innovation is
non-drastic, the innovator has exclusive rights to the innovation for an indefinite period,
and the collusive equilibrium is maintained with threats to Nash reversion. Theseassumptions are relaxed and the implications discussed later in the analysis.
There is a scanty literature on the relationship between cooperation in R&D andproduct market collusion.4 Martin (1995) uses a continuous-time version of a repeatedgame framework with stochastic innovation to show, as in this paper, that cooperative
R&D facilitates collusion. Contrary to our result, he finds that formation of RJVs reduces
social welfare. The difference in welfare assessments lies with his assumption thatcollusion ends with a discovery.5 If innovation is non-drastic, collusion need not end with

4

There is a huge literature on the relative effect of competitive and cooperative R&D, most of which
studies atemporal models, see, e.g., D’Aspremont and Jacquemin (1988), and Kamien, Muller and Zang
(1992). An intertemporal model is developed in Miyagiwa and Ohno (2002).
5
Cabral (2000) considers a similar model under the assumption that firms cannot observe each other’seffort, and shows that firms may set the price below the monopoly price to sustain collusion undercooperative R&D.

3
a discovery of new technology, in which case welfare can be increased by formation of
RJVs as we show below.
While Martin (1995) focuses exclusively on the stability of collusion before
innovation, the stability of collusion after innovation takes center stage in the work of
Lambertini, Poddar and Sasaki (2002, 2003). In the 2002 article, which more relates tothe present paper, the authors consider a three-stage game, in which two firms first decide
whether to form a joint venture, then choose horizontal locations in the Hotelling-style
product space, and finally choose to compete or collude in prices over time. R&D isdeterministic, and corresponds to product location selection. In the second stage, firms
can select a product location freely when acting competitively in R&D but are
constrained to choose a single location when acting as an RJV. When competitive in
R&D, collusive firms have no incentive to locate near the center of the product space,because that would only increase profits from a deviation without increasing theequilibrium profit.6 Therefore, an RJV, which constrains firms to select an identicalproduct location (at the center), makes collusion more difficult to maintain. Their model
however offers no analysis of collusion in pre-discovery periods or the linkages between
behaviors in pre-discovery and post-discovery periods.7

6

Locating at the center, each firm covers half the interval, but the same result obtains if each firm locates at
the midpoint between the center and the end point of the interval. However, in the latter case profit from adeviation is less due to product differentiation.
7
Lambertini, Poddar and Sasaki (2003) develop a non-spatial model of product differentiation, whereformation of an RJV is assumed and focus is on the firms’ (costly) choice of product substitutability for the
maintenance of collusion in post-discovery periods.

4A major difficulty that arises in the analysis of collusion in post-discovery periods
is that there is no natural focal equilibrium due to cost asymmetries.8 There is a small but
growing literature on collusion under cost heterogeneity, which typically assumes thatfirms maximize joint profits, and determines the unique equilibrium price and marketsharing rule by an appeal to the notion of balanced temptation equilibrium of Friedman(1971)9. Bae (1987) initiates this approach in his analysis of Bertrand duopoly, while
Verboven (1997), Rothschild (1999) and Collie (2004) examine Cournot cases. Thisapproach however is not without criticism. Harrington (1991), for example, argues thatthe hypotheses of joint profits maximization and balanced temptation equilibrium areboth ad hoc, and develops an alternative approach based on Nash bargaining.
However, the Harrington (1991) approach may also be subject to a subtler
criticism that it does not model the negotiation process explicitly. If it takes long and hardnegotiations to come to an agreement, such a process is likely to raise suspicion in thewatchful eyes of antitrust authorities, thereby affecting the equilibrium outcome.
Furthermore, when applied to the current situation, both the Nash bargaining and thejoint-profit maximization approach turn out intractable because of ambiguouscomparative-statics results with respect to cost changes. Therefore, in this paper we
propose another approach, which may be called the price leadership hypothesis. Under
this hypothesis, an innovator chooses a price and a market-share rule to maximizes his
individual profit and makes a take-it-or-leave-it offer to the non-innovator. The price

8

This difficulty is absent in Martin (1995) because collusion ends with a discovery in his model, and in
Lambertini, Poddar and Sasaki (2002) because R&D is non-stochastic and R&D decisions are madesimultaneously.

5
leadership hypothesis is robust to the Harrington (1991) criticism and is more tractable
than his or the joint-profit maximization approach.
The remainder of this paper is organized in six sections. In section 2 we give an
overview of the model and discuss the non-cooperative equilibrium. Section 3 establishes
the conditions for the collusive equilibrium under competitive R&D. Section 4 is devoted
to the analysis of firms’ incentives to collude as an RJV. Section 5 examines the case inwhich firms can license new technology without forming an RJV. In Section 6, we extend
the model to cases of drastic innovation, finite-period patent protection, and optimalpunishment schemes. Section 7 concludes.

2. Model2.1 Setup
We consider repeated interactions between two a priori symmetric firms over an
infinite time horizon. Time is discrete and indexed by t ≥ 1. At t = 1 firms possess thecommon technology that enables them to produce homogeneous goods at the constantunit cost of –c . In any period t ≥ 1, each firm decides whether to invest in R&D for the
discovery of a new technology that will reduce the unit cost to –c (< –c ). Investing in R&D
requires a fixed cost k per period.10 R&D investment is risky in the sense that it fails withprobability φ < 1 per period. If both firms invest in R&D, a discovery occurs to either

9This requires that the ratios of the per-period losses due to the breakdown of collusion over the maximum
one-period gains from deviations be the same among firms.
10
The assumption of fixed-intensity R&D, adopted in Bloch and Markowitz (1996), Lambertini, Poddar
and Sasaki (2002, 2003) and others, simplifies the analysis.

6firm with probability 2φ(1 – φ) and to both with probability (1 – φ)2. In the case ofsimultaneous discoveries each firm has an equal chance of obtaining patent protection.11
Call a firm with the patent an innovator, and the other firm a non-innovator. Assume
permanent patent protection for simplicity.
Firms are price-setters. Consumers buy from a firm offering a lower price. In caseof ties, they buy from both firms equally so each firm captures half the market. Demandis stationary and is written D(p), where p is price. D(p) is differentiable, with first andsecond derivatives denoted by D’(p) < 0 and D”(p) ≤ 0. Let pm(c) be the unconstrainedmonopoly price when the unit cost is c, i.e., pm(c) ≡ argmax D(p)(p – c). The conditions
on demand make industry profit strictly concave so pm(c) is unique. It is easy to checkm –that pm(c–) < p (c ).

Lastly, if innovation is drastic, an innovator becomes a monopoly unthreatened by
the non-innovator and hence has no incentive to collude in post-discovery periods. To
study the linkages between pre-discovery and post-discovery behaviors, assume that
innovation is non-drastic, i.e., –c < pm(c–).

2.2 Non-collusive equilibrium
In the non-collusive game, each firm setting prices equal to –c in every period
regardless of histories is a subgame-perfect Nash equilibrium (SPNE). Denote this11

This assumption is often adopted in the literature; see Cardon and Sasaki (1998), for example.

7
strategy profile by λ. Adopting this strategy, firms earn zero profit (excluding theinvestment cost k) before a discovery. After a discovery the innovator limit-prices the
non-innovator and earns the per-period profit of–)(c– – c ) > 0
πL = D(c–while the non-innovator receives zero profits.12
Assuming that both firms invest in R&D, with probability (1 – φ2)/2 each firm has
the chance of obtaining the exclusive right to use the new technology and earning the perperiod profit πL. With probability φ 2 investments flop for both firms, putting them inexactly the same state the next period as they are currently. This recursive structure of themodel leads to the following equation:(1)

Vλ = – k + δ(πL/2)(1 – φ2)/(1 – δ) + δφ2Vλ,where Vλ denotes the present discounted sum of equilibrium profits, and δ (< 1) denotes
the common discount factor. Collecting terms,
Vλ =−k + δ (1 − φ 2 )(π L / 2) / (1 − δ ).
1 − δφ 2

Assume Vλ > 0 so investing in R&D is worthwhile for each firm.

3. Collusion with non-cooperative R&D

12–

Strictly speaking, the innovator sets a price slightly below c to capture the entire market.

8
We now consider a class of trigger strategies with Nash threats that induce
implicit collusion in pre-discovery and post-discovery periods. We begin with noncooperative R&D.
3.1. Collusion in post-discovery periods
In post-discovery periods firms have asymmetric costs. As stated in section 1 we
focus on the equilibrium based on the price leadership hypothesis, under which theinnovator chooses a price and a market-share rule to maximize his profit and makes atake-it-or-leave-it offer to the non-innovator.13 Let (pc, s) denote such an offer, where s (0< s < 1) is the fraction of market served by the innovator.
The price leadership hypothesis amounts to the following. As soon as he has
discovered new technology, the innovator communicates his optimal price and marketshare rule to the non-innovator and executes this decision in the first post-discovery
period. If the non-innovator responds with the same price and the prescribed sales, thenthe collusion is on. Otherwise, the innovator believes that the non-innovator isuninterested in colluding, and starts behaving competitively. Formally, we consider thefollowing strategy profile. Given that there is a discovery in period τ ≥ 1, in period τ + 1
firms set a price equal to pc and split the market according to the market-sharing rule s. Int ≥ τ + 2, they choose (pc, s) if no other outcomes than (pc, s) have been observed since τ+ 1; otherwise they adopt the non-collusive strategy λ forever. Denote this strategy
profile by a (a mnemonic for “after” a discovery).

9
We look for the condition that makes a subgame-perfect in post-discovery games.
If firms adopt a, every (post-discovery) subgame belongs to one of the two classes; one inwhich all past outcomes have been (pc, s), and one in which another outcome has been
observed at least in one post-discovery period. In the latter, λ is subgame-perfect, so weneed only to show that a is subgame-perfect in the first class of subgames.
Along this collusive equilibrium path, the innovator earns the per-period profit of
πi = sD(pc)(pc – –c)while the non-innovator earns
πn = (1 - s)D(pc)(pc – –c ).
Since pc maximizes πi, put pc = pm(c–). Then, we can write the above profits asmm–
πi = sm– , and πn = (1 – s)D[p (c–)][p (c–) - c ],where m– denotes the monopoly profit under the new technology:mmm– ≡ D[p (c–)][p (c–) - –c ].

Let vi and vn denote the sums of equilibrium profits for the innovator and the noninnovator, respectively. The recursive structure implies
vi = πi + δvi, and vn = πn + δvn,
and hence:13

As explained in section 1 the main reason for this hypothesis is in its analytical tractability. By design,
this scheme maximizes total profit for the innovator supported by Nash threats but is not optimal in thesense of Abreu (1986, 1988). The optimal collusion scheme is considered in section 6.

10vi = πi/(1 - δ) and vn = πn/(1 - δ).
Now consider a one-period deviation. A non-innovator can set the price slightlymm–
below pm(c–) to capture the entire market for the one-period profit of D[p (c–)][p (c–) - c ]but will lose all future profits when it gets limit-priced. He thus has no incentive tom–deviate if vn ≥ D[pm(c–)][p (c–) - c ], which simplifies to(2)δ ≥ s.

On the other hand, a deviating innovator can earn m– one period and πLin all subsequent
periods. Therefore, the innovator has no incentive to deviate ifvi ≥ m– + δπL/(1 - δ),orδ ≥ (1 – s)m– /(m– – πL)Thus, a is subgame-perfect in post-discovery games if(3)δ ≥ max {(1 – s)m– /(m– – πL), s}.
Now, the innovator chooses s to maximize sm– subject to the non-innovator’s

incentive compatibility condition (2). This puts s = δ. Substituting s = δ in (3) andrearranging yields
(4)

A
δ≥m
– /(2m– – πL) ≡ δ (c–) > 1/2.

11
The strategy profile a is a SPNE if (4) is satisfied. Observe that δA(c–) > 1/2. Given thestandard result that symmetric Bertrand firms can maintain collusion for δ ≥ 0, (4)indicates that a cost asymmetry makes collusion more difficult to maintain.
Define cd by –c = pm(cd). Then –c > cd implies innovation is non-drastic. The next
proposition summarizes what we have found so far.

d
Proposition 1: Assume non-drastic innovation (c– > c ).
A(i) The strategy profile a is a SPNE for δ ≥ m– /(2m– – πL) ≡ δ (c–) > 1/2.

(ii) The collusive equilibrium price and market-sharing rule are
pc = pm(c–) and s = δ > 1/2.

Since s > 1/2, the innovator has a greater market share than the non-innovator, a resultthat is consistent with the findings of Bae (1987) and Harrington (1991). The per-period
equilibrium profits aremm–
πi = δm– and πn = (1 - δ)D[p (c–)][p (c–) - c ].

Observe that the equilibrium profits to each firm are sensitive to the prevailing discountfactor, whereas in Bae (1987) and Harrington (1991) they are independent of it as long as
the discount factor exceeds the threshold level.

12
14
The locus AA in Figure 1 plots δA(c–) against –c . The depiction reflects the fact

that:
m
2
–
– m
∂δA(c
–)/∂c– = D(c )D[p (c–)][c - p (c–)]/(2m– - πL) < 0
A–for pm(c–) > c (i.e., non-drastic innovation). It is easy to check that δ (c–) increases

towards unity as –c falls towards cdwhile in the other direction it approaches 1/2 as –capproaches –c . The intuition is straightforward. The greater a cost reduction, the more of
an incentive to deviate the innovator has. To curb this incentive the threshold discountfactor δA(c–) must rise.
Proposition 1 says that if δ < δA(c–) firms cannot collude at the monopoly pricepm(c–), but it leaves open the question whether they can collude at another price.
However, such partial collusion is impossible as stated in the next lemma. Intuitively,
because the market-sharing rule is sensitive to the discount factor in the present model,
the innovator cannot commit credibly to his offer when the discount factor falls below thecritical level δA(c–). (The proof in Appendix A.)

Lemma 1. If δ < δA(c–), partial collusion is impossible in post-discovery subgames.

14

We limit analysis to δ ≥ 1/2.

13
3.2. Collusion in pre-discovery periods
We now turn to the stability of collusion in pre-discovery periods. Consider the–), the monopoly pricefollowing symmetric strategy: In t = 1, set a price equal to pm(cunder the old technology. In any pre-discovery period t ≥ 2, there are four possible statesof nature.

–) have been observed and there was a discovery in t – 1.
(i) No other prices than pm(c–) have been observed and there has been no discovery to(ii) No other prices than pm(cdate.

–) have been observed at least once in the past and there was a(iii) Prices other than pm(cdiscovery in t – 1.

–) have been observed at least once in the past and there has(iv) Prices other than pm(cbeen no discovery to date.

–). In states (iii) and (iv) adopt
In state (i), adopt a. In state (ii) set the price equal to pm(cλ. Call this strategy profile b (a mnemonic for “before” a discovery).
Since b is subgame-perfect in states (i), (iii) and (iv), we need only to check state(ii). In state (ii) the equilibrium payoff, denoted by Vc, satisfies this recursive equation(5)– /2 − k + δ(1 − φ2)(v + v )/2 + δφ2V ,Vc = minc– denotes the monopoly profit under the old technology; i.e.,
where m– = D[pm(c–)][pm(c–) – –c ).
m

14
The right-hand side of (5) states that in every period before a discovery each firm earns– less the R&D cost, and that each is equally likely to be thehalf the monopoly profit minnovator or the non-innovator the next period, given probability of discovery (1 −φ2).
Collecting terms in (5) yields
Vc =m/2 − k + δ (1 − φ 2 )(vi + vn )/2.
1 - δφ 2

Consider now a one-period deviation. By lowering the price infinitesimally below–), a deviating firm earns (m– – k) in the current period but finds
the monopoly price pm(citself in state (iii) or state (iv) the next period, with a switch to λ. Thus, the following is
the expected profits from a deviation:– − k + δ(1 − φ2)(π /2)/(1 − δ) + δφ2V = m
– +V
m
L
λ
λ
where the equality follows from (1). A deviation is unprofitable if this profit is less thanVc, i.e.,(6)–,
Vc – Vλ ≥ m

where

(7)

Vc – Vλ =– /2δ(1 – φ2)[vi + vn - πL/(1 – δ)]/2 + m
1 – δφ2.

The difference in profits, Vc – Vλ, between the collusive and the competitive paths
increases without bounds as δ goes to unity. Then, (6) holds with strict inequality for ahigh enough δ < 1. On the other hand, when δis sufficiencly close to 1/2, (6) fails, as15
shown in Appendix B. Therefore, there exists a unique δ ∈(1/2, 1) at which (6) holds withB

strict equality. Denote this threshold discount factor by δ (c–).
The locus BB (comprising the thick and dotted segments) in Figure 1 plots δB(c–)
against –c , assuming that firms maintain the collusive equilibrium in post discovery
periods and that φ2 ≥ 1/2. The depiction is based on the following lemma (see Appendix
C for a proof):

Lemma 2: Given that cd < –c< –c(i) ∂δB(c–)/∂c– < 02(ii) 1/2 < δB(c–) < 1/(2φ ).
15(iii) If φ2 ≥ 1/2, there is a point (c–, δ(c–)) at which the loci AA and BB intersect.

2

Thus, the locus BB curves upward as –c falls but stays strictly between 1/2 and 1/(2φ ). If
φ2 < 1/2, however, the upper bound exceeds unity, implying that the locus BB may stay
above the locus AA for all –c > cd.

15This establishes the existence. There may be more than one such point. However, the results we show
below do not depend on the uniqueness.

16
Finally, the analysis of this subsection is predicated on there being collusion in
post-discovery periods, i.e., δ ≥ δA(c–). Thus, we have

B
Proposition 2: If δ ≥ max {δA(c–), δ (c–)} > 1/2, the strategy profile b is subgame-perfectand entails collusion in pre-discovery and post-discovery periods.

The prospect that a cost asymmetry can destabilize collusion in post-discovery
periods makes collusion more difficult to maintain in pre-discovery periods, during whichcosts are symmetric. In Figure 1, collusion is sustainable before and after a discovery ifB
the (δ, –c ) pair is in region 1 defined by the set {(δ, –c )| δ ≥ max {δA(c–), δ (c–)}}. Outside

region 1, the strategy profile b cannot support full collusion. In region 2 defined by theB
set {(δ , –c )| δ A(c–) ≤ δ < δ (c–)}, for example, firms can maintain collusion after a–) cannot
discovery but cannot before a discovery, because the monopoly price pm(csatisfy the no-deviation condition (6). The question is: can firms collude partially, that is,–) until there is a discovery? As in theat a price different from the monopoly price pm(cpost-discovery game, the next lemma shows they cannot (the proof in Appendix D).

B
Lemma 3. If δA(c–) ≤ δ < δ (c–) there is no partial collusion in pre-discovery periods.

17Thus, in region 2, although they cannot collude in pre-discovery periods, firms can fully
collude in post-discovery periods by playing a competitive one-shot game until there is a
discovery and then switch to playing a. This is a SPNE, yielding zero profits (minus
investment cost k) until a discovery and m– /2 per period afterwards.
Outside of regions 1 and 2, firms cannot collude partially after a discovery. Given
that they play a limit-price game after a discovery, however, firms may still be able tocollude up to a discovery by playing (the pre-discovery components of) b until a
discovery and then switching to λ. Since firms adopting this strategy play the limitpricing game after a discovery, the first term in the numerator of (7) vanishes, and thecondition to support collusion in pre-discovery period is given by– /2)/(1 − δφ2) > m–,(minstead of by (6). This inequality holds if δ ≥ 1/(2φ2). This condition is satisfied if the(δ, –c ) pair is in region 3 of Figure 1 defined by {(δ, –c )| 1/(2 φ2) ≤ δ < δ A(c–)}, which is
non-empty if φ is greater than 2 /2. Outside all these regions firms cannot collude at all.

4. Research joint ventures
We interpret the RJV broadly to encompass any technology-sharing arrangement
including a royalty-free cross-licensing agreement, under which each firm runs its own
research lab, incurs own R&D costs and gains free access to any innovations made by18partners. We thus assume that each firm retains its R&D facility and shares technology
with each other, as is commonly assumed in the RVJ literature.16
4.1 Collusion in post-discovery periods
Suppose there is a discovery in period τ ≥ 1 and the firms adopt the following
post-discovery strategy, denoted by α. In τ + 1, set a price equal to the monopoly pricempm(c–) under the new technology. In all t + τ, (t ≥ 2), choose p (c–) if no other prices thanpm(c–) have been observed since τ + 1; otherwise set a price to –c . Thus, α is a standard
collusive strategy profile for symmetric price-setting duopoly and is a SPNE for δ ≥ 1/2.
Compared with Proposition 1, this result shows that formation of an RJV facilitates
collusion in post-discovery periods by preventing a cost asymmetry from arising. The
question is how low the threshold discount factor falls in pre-discovery periods. We turnto this question next.
4.2 Collusion in pre-discovery periods
Consider the following collusive strategy denote by β: In t = 1, set a price equal to–) under the old technology. In any pre-discovery period t ≥ 2,
the monopoly price pm(cthere are four possible states of nature.

–) have been observed, and there was a discovery in t – 1.
(i) No other prices than pm(c–) have been observed and there has been no discovery to(ii) No other prices than pm(c
date.

16

See Kamien, Muller and Zang (1992) and Miyagiwa and Ohno (2002), for example.

19–) have been observed at least in one period in the past and(iii) Prices other than pm(cthere was a discovery in t – 1.17–) have been observed at least once in the past and there has(iv) Prices other than pm(cbeen no discovery to date.

–). In state (iii) set a price equal to
In state (i) adopt α. In state (ii) set a price equal to pm(c–c in every period. In state (iv), withdraw from the RJV and switch to playing λ forever.
The strategy profile β is subgame-perfect in states (i), (iii) and (iv), so we only
need to check state (ii). In that state, VJ, the equilibrium profit per firm, satisfies thefollowing recursive equation:– /2 – k + δ(1 − φ2)(m/2)/(1 - δ) + δφ2V ,VJ = m–J– less the R&D cost before
which indicates that each firms earn half the monopoly profit ma discovery and also splits the post-discovery profit. Collecting terms, we obtainVJ =m / 2 − k + δ (1 − φ 2 )(m / 2) / (1 − δ ).
1 − δφ 2– but
A one-period deviation before a discovery raises a deviating firm’s profit to m
puts firms in states (iii) or (iv) the next period, depending on whether there is a discovery
during the period in question. In state (iii), which occurs with probability (1 −φ2), firms
share the innovation but a switch to playing the one-shot symmetric Bertrand game

17Here, a subtle question arises: who owns the innovation when a deviation occurs. We assume that
innovation is shared since it has occurred before breakup of the RJV.

20
forever wipes out all future profits. In state (iv), which arises with probability φ2, firms
switch to the non-collusive strategy λ, which has the prevent value of Vλ. Thus, adeviation yields the profit of– – k + δφ2V .
m
λA firm therefore has no incentive to deviate if– – k + δφ2V .
VJ ≥ mλAfter arranging terms, this condition can be rewritten2–δ(1 - φ2)(m– /2)/(1 - δ) + δφ (VJ – Vλ) ≥ m/2

(8)
where

VJ – Vλ =–δ(1 - φ2)(m– /2 - πL/2)/(1 - δ) + m/2
1 - δφ2.

Differentiation shows that the left-hand side of (8) is increasing in δ for the same
reason explicated in the case of non-cooperative R&D. Further, we prove, in Appendix E,that (8) holds with strict inequality at δ = 1/2 . Thus, (8) holds with strict inequality for allδ ≥ 1/2. Hence,

Proposition 3. The strategy β is subgame perfect for δ ≥ 1/2

Thus, formation of an RJV lowers the threshold discount factors both in pre-discovery
and in post-discovery periods to 1/2 for all –c > cd. A comparison with the non-

21
cooperative case, in which the threshold discount factor exceeds 1/2, indicates thatcooperative R&D leads to collusion everywhere outside region 1. It is in this sense thatformation of an RJV facilitates collusion.

Proposition 4. Formation of an RJV facilitates collusion for all –c > cd if
B
1/2 ≤ δ < max {δA(c–), δ (c–)}.

4.3 Welfare implications
Collusion reduces social welfare as firms set the monopoly price. However, it
should not be inferred that cooperation in R&D should be banned or penalized, forsharing of new can increase social welfare by making not just the innovator but both
firms more efficient. The net welfare impact of cooperation in R&D thus depends on boththese factors.
In region 1 of Figure 1, firms collude before and after a discovery without
cooperation in R&D. Therefore, formation of an RJV does not exacerbate the market
distortions, and the technology-sharing effect raises welfare. In region 2, without
cooperation in R&D firms manage to maintain collusion only after a discovery. Then, by
the efficiency argument, welfare must rise with formation of an RJV in post-discovery
periods. However, welfare falls in pre-discovery periods as firms collude as an RJV. The
net welfare impact is in general ambiguous.
In region 3, without cooperation in R&D firms can collude only before a
discovery. Thus, formation of an RJV generates no welfare change before a discovery. In

22post-discovery periods, firms collude only as an RJV. While monopoly pricing reduces
welfare, technology sharing increases welfare. In this particular case, however, industry
without an RJV is just as efficient as with an RJV, because due to limit-pricing only theinnovator is active. Therefore, formation of an RJV results only in monopoly pricing,
reducing welfare.18 To show this formally, let p(x) = D-1(p) be the inverse demand
function. Then social welfare without formation of the RJV is given byD(c)∫ p(x)dx − D(c)c + D(c)(c − c)

WC =

0

where the first two terms on the right is consumer surplus and the third is industry profit.
Similarly, social welfare with the RJV is writtenD[ p m (c)]

∫

J

W =

p(x)dx − D[ p m (c)]p m (c) + D[ p m (c)][ p m (c) − c] .

0Taking the difference,
D(c)

J

C

W –W = −∫p(x)dx + {D(c) − D[ p m (c)]}c .

D[ p m (c)]Since p(x) between the limits of integration is greater than –c , we haveD(c)∫D[ p m (c)]D(c)p(x)dx >∫cdx = {D(c) − D[ p m (c)]}c .

D[ p m (c)]Therefore, WJ – WC < 0; although having no welfare effect in the pre-discovery phase,formation of an RJV reduces post-discovery welfare. Similarly, welfare falls
unambiguously outside the three regions.

18

As observed by Yeon-Koo Che, this is strictly due to price competition. If the non-innovator also

23
To sum, an RJV increases welfare only by making the whole industry more
efficient instead of just the innovator through innovation sharing. Although a large cost
reduction can therefore result in a greater welfare improvement, with a large cost
reduction we are likely to be in regions 3 and 4 initially, where formation of an RJVlowers welfare as we saw above. Thus we have a counterintuitive result: sharing a costcutting technology under R&D cooperation drives welfare improvements, but with alarge cost reduction welfare is likely to fall with formation of an RJV. In contrast, with asmall cost reduction, firms are likely to be collusive anyway, so formation of an RJV has
only the beneficial technology-sharing effect. This observation has the obvious policy
implication for antitrust authorities: firms should be more closely monitored for
anticompetitive behavior when an RJV aims at a major technological breakthrough.

5. Licensing without RJVs19
In this section, we allow firms to license innovation without forming an RJV. As
mentioned in section 1, formation of an RJV in preceding sections facilitates collusion
through two effects. One is the asymmetry story. Innovation sharing eliminates inter-firm
asymmetry, a source of instability. The other is the efficiency story; the prospect of agreater industry profit in post-discovery periods makes collusion easier to maintain in
pre-discovery periods.
Licensing allows both firms to use innovation, thereby making industry as
efficient as with an RJV. However, with licensing there remains an inter-firm asymmetry

produced, an RJV improves production efficiency so the welfare might increase.
19
I thank Yeon-koo Che for his suggestion to explore this issue.

24
in profit between the innovator (licensor) and the non-innovator (licensee). We show that
this asymmetry makes collusion more difficult to maintain with licensing than with an
RJV in pre-discovery periods but not in post-discovery periods.
The analysis of this section follows that of section 3. However, to save space wereplicate only the relevant part from that section. With licensing, a rich taxonomy ofcases may also arise, depending on the legal environments; for example, the durations oflicensing and conditions for discontinuation or annulment of licenses. For simplicity, we
suppose that a licensing agreement is good only for one period but extendable
indefinitely as long as both parties agree to keep it.
Let a licensing contract be represented by a triplet {p, s, F}, where p is a price, s isa market share to the innovator and F is a licensing fee or transfer from the non-innovatorto the innovator. Suppose that the innovator makes a take-it-or-leave-it offer to the noninnovator, and firms share innovation if the non-innovator accepts the offer. On thecollusive equilibrium path with an licensing agreement, the non-innovator enjoys the
profit (1 – s)D(p)(p - –c ) – F and the non-innovator sD(p)(p - –c ) + F per period.
We characterize the optimal contract in three steps. First, if the non-innovator
refuses licensing, firms can still collude as in subsection 3.1, yielding to the nonm–
innovator the equilibrium profit (1 - δ)D[pm(c–)][p (c–) - c ] per period. The optimal

licensing fee extracts any gain to the non-innovator; i.e., F is given bym–
F = (1 – s)D(p)(p - –c ) - (1 - δ)D[pm(c–)][p (c–) - c ].

Using this, the profit to the innovator is written25m–
D(p)(p - –c ) - (1 - δ)D[pm(c–)][p (c–) - c ].
m

Since the second term is independent of p, the innovator sets p = p (c–) to maximize theabove profit. With this pricing, the optimal licensing fee is written
(9)

m
m
–
F* = (1 – s)m– - (1 - δ)D[p (c–)][p (c–) - c ].

Next, with the optimal price pm(c–), a one-period deviation allows the noninnovator to capture the entire market less the licensing fee for just one period, after
which it gets limit-priced and loses all the future profits. Therefore, a deviation would
yield
m
m
m
–
D[pm(c–)][p (c–)- –c ] – F* = sm
– + (1 - δ)D[p (c–)][p (c–) - c ].

On the other hand, since the optimal licensing fee F* extracts any increase in profit,m–keeping his equilibrium profit per period at (1 - δ)D[pm(c–)][p (c–) - c ] as in subsection

3.1. Thus, the non-innovator has no incentive to deviate if
m
m
m
–
–
D[pm(c–)][p (c–) - c ] ≥ sm
– + (1 - δ)D[p (c–)][p (c–) - c ].

This simplifies tom–δD[pm(c–)][p (c–) - c ] ≥ sm–.

The optimal market share must satisfy this constraint, and hence we havem– .
s* = δD[pm(c–)][p (c–) - c ]/m–

26
Since the right-hand side expression of the above equation is less than δ, a comparison
with the counterpart in proposition 1 indicates that licensing results in a smaller market
share for the innovator. In equilibrium, however, due to the licensing fee the innovator
earns a greater net profit equaling:
m
m
–
s*m
– + F* = m– - (1 - δ)D[p (c–)][p (c–) - c ].

Finally, the licensing agreement must be incentive-compatible for the innovator.
A one-period deviation would yield m– + F* in the current period. As the innovatorswitches to limit-pricing in the next period, with the license annulled, the stream of
discounted profits from the next period on sums to δπL/(1 - δ). Thus, a deviation yieldsmm–m– + F* + δπL/(1 - δ) = 2m
– - D[p (c–)][p (c–) - c ] + δπL/(1 - δ)

where (9) is used to get the right-hand side. The innovator has no incentive to deviate if
this sum is less than the equilibrium profits; i.e.,
m
m
–
(s*m
– + F*)/(1 - δ) ≥ 2m
– - D[p (c–)][p (c–) - c ] + δπL/(1 - δ).

Substituting for s* and F* and canceling terms simplifies this toAδ≥m– /(2m– - πL) ≡ δ (c–),

the condition identical to (4) in section 3.1. Thus, the condition for collusion in postdiscovery periods is unaffected by licensing. It follows that a greater industry profit due
to cooperation in R&D has no role in the incentive to collude in post-discovery periods.
However, a greater equilibrium industry profit after a discovery raises the
expected profit before a discovery from (vi + vn)/2 to m
– /2 in the expression Vc. That is,27with licensing the collusive equilibrium profit before a discovery is equal to VJ instead of
Vc. On the other hand, the profit from a deviation before a discovery is unaffected bylicensing and equals Vλ. Then, following the procedure of section 4, we can show thatA
collusion can be maintained in pre-discovery periods for δ ≥ max{δA(c–), 1/2} = δ (c–). In

terms of figure 1, licensing enables firms collude before and after a discovery in regions 1
and 2, while without licensing they could not collude before a discovery in region 2, asshown in section 3.1. The analysis for regions 3 and 4 is unaffected by licensing.
Now reconsider formation of an RJV. Since licensing enables firms to collude
before and after discovery in regions 1 and 2, formation of an RJV facilitates collusion
only in regions 3 and 4. Further, since firms share innovation with licensing and capture agreater industry profit after a discovery, an RJV does not generate additional efficiency
gains, and hence does not increase welfare. In regions 3 and 4, an RJV facilitates
collusion and reduces welfare. Without licensing an RJV increased welfare in region 1
due to the efficiency gain and the net effect was ambiguous in region 2. With licensing,
however, an RJV causes no welfare changes in these regions.
In section 1 we indicated that an RJV can facilitate collusion by elimination ofinter-firm asymmetries and generation of a greater industry profit. The analysis of thissection can disentangle these two effects. First, both an RJV and licensing yields theidentical expected collusive equilibrium profits before a discovery equal to VJ. Yet, due
to the post-discovery asymmetry with licensing, firms cannot collude in regions 3 and 4
without forming an RJV. Thus, elimination of the post-discovery asymmetry is
responsible for successful collusion in regions 3 and 4 with an RJV. Second, in region 2

28
firms could not collude before a discovery without licensing but can collude withlicensing or an RJV, both of which yields a greater surplus. Thus, collusion in region 2 isfacilitated by the prospect of a greater profit with an RJV.

6. Extensions
In section we relax the following assumptions of the model. They are (i) nondrastic innovation, (ii) permanent patent protection, and (iii) Nash threats (punishment by
reversions to repeated play of a one-shot game).
First, suppose innovation is drastic as in Martin (1995). With drastic innovation
an innovator becomes a monopoly so there is no collusion in post-discovery periods.
Thus, the analysis is similar to the one associated with region 3; namely, formation of an
RJV facilitates collusion in post-discovery periods and lowers social welfare, which isexactly what Martin (1995) has argued.
Second, suppose that patent life is finite. If patent life is, say, T periods, the valueof new technology to the innovator falls from πL/(1 - δ) under permanent patentT

protection to πL(1 - δ )/(1 − δ).20 In the collusive equilibrium finite patent life thus
decreases the value of a deviation, thereby making collusion easier to maintain both
before and after a discovery.
Third, it is well known in the implicit collusion literature that collusion can besustained for a lower range of discount factors if firms can commit to a severer
punishment scheme than Nash reversions. In a recent paper Thal (2006) considers such a29scheme for Bertrand duopoly with asymmetric costs, and finds that a credible punishment
strategy with an Abreu (1986, 1988) stick-and-carrot structure reduces the payoff to thefirm with lowest cost to zero. Although not concerned with the uniqueness of equilibrium
selection, when applied to our model, her analysis implies that there is an optimalpunishment scheme that can reduce the threshold discount factor after a discovery to 1/2
without formation of an RJV. However, it is not clear whether the threshold discountfactor also falls to 1/2 in pre-discovery periods. Nonetheless, in Appendix F we show thatthat is the case under the assumption of linear demand. In that case, firms can collude
before and after a discovery at any discount factor greater or equal to 1/2 without forming
an RJV, meaning that cooperation in R&D always improves social welfare throughefficiency gains.

7. Concluding remarks
We examine whether cooperation in R&D leads to product market collusion. Ourmodel has two firms managing implicitly to maintain the collusive equilibrium while
engaged in a stochastic R&D race. Under competitive R&D, innovation gives rise to aninter-firm cost asymmetry and can destabilizes collusion when the discount factor is low
or the cost reduction under new technology is large. The prospect that collusion ends with
innovation further destabilizes collusion in pre-discovery periods. Innovation sharing
under cooperative R&D preserves a cost symmetry and also raises industry surplus, bothof which facilitate collusion in product markets. These two effects can be studied

20

In period T + 1 the technology becomes public and competition wipes out profits for the innovator.

30
separately by considering the intermediate case, in which firms license without forming
an RJV.
Although facilitating collusion, cooperation in R&D does not necessarily decreasesocial welfare in the absence of licensing, as sharing of new technology improves
efficiency in production. Although new technology is the driving force for a welfare
improvement, cooperation in R&D is more likely to decrease welfare if the cost falls toomuch under new technology.
Our qualitative results are robust to alternative assumptions concerning the typeof innovation (drastic or non-drastic), patent length, and punishment mechanisms. Ourmodel can be extended further. For example, more complex licensing schemes such as
multi-period binding licensing contracts can be explored within out model. Anotherinteresting extension would be to the case of quantity-setting firms. Since quantity
competition is less competitive it is generally more difficult to maintain collusion thanwith price competition. While we leave these extensions for future research, we believethat our basic insight and results will remain valid and relevant.

31
Appendices
Appendix A: Proof of Lemma 1. Let δ < δA(c–) be given. Suppose there is a pair (p*, s*),where p* ≠ pm(c–), such that p* maximizes the innovator’s profit s*m– * = s*D(p*)(p* - –c )and satisfies the no-deviation constraints for both the innovator and the non-innovator.
Case 1. p* < pm(c–)
Partial collusion is stable ifδ ≥ max {(1 – s*)m
– *)/(m– * – πL), s*}
If δ ≥ (1 – s*)m
– *)/(m– * – πL) > s*, s* can be increased up to δ, increasing the profit to theinnovator without violating the no-deviation constraint. So, at the optimum the innovator
sets s* = δ. Therefore, we haveδ ≥ (1 – δ)m– */(m– * – πL)orδ≥m
– */(2m– * – πL).
But the right-hand side is decreasing in m* for 0 ≤ m– *≤ m– , and henceAδ≥m– */(2m– * – πL) > m– /(2m– – πL) = δ (c–),

which contradicts the assumption δ < δA(c–).
m –Case: pm(c–) < p* < p (c )There is no deviation if

32δ ≥ max {(m– - s*m– *)/(m– – πL), s*}.
Again, s* can be increased up to δ without violating this constraint so δ = s*. We canwrite the above asδ ≥ (m– - δm– *)/(m– – πL).
that is,δ≥m– /(m– – πL + m– *).
But since m–* < m
–
A
δ≥m
– /(m
– – πL + m– *) > m– /(2m– – πL) = δ (c–),

a contradiction.

–).
Case 3: p* ≥ pm(cThe innovator does not deviate if– - (1 – s*)m
– *]/m–,δ ≥ [mand the non-innovator does not ifδ ≥ (m– – s*m– *)/(m– – πL).
Partial collusion is sustained if both conditions hold. The first must hold with equality,
for otherwise the innovator can increase profit by raising s*. Therefore, s* satisfies– = (1 – s*)m– *.
(1 - δ)mUsing this the second condition can be written– –δ(m– – πL) ≥ (m– – s*m– *) = m– + (1 - δ)m – m*

33
Collecting terms,– ––δ ≥ [m– + m – m*]/[(m– – πL + m] > m– /(2m– – πL) = δ (c–),
Aa contradiction. ❏Appendix B: We show that (6) fails at δ = 1/2. Assume the contrary, and evaluate (6) at δ
= 1/2 to obtain this equivalent condition:
m
m
–
–
m
– + D[p (c–)][p (c–) – c ] – πL – 2m ≥ 0.

(B1)

However, we can express the left-hand side of (B1) as
m
m –
m –
–
– –
–
D[pm(c–)][2p (c–) – c – –c ] – D(c )(c – –c ) – 2D[p (c )][p (c ) – c )–)[pm(c ) – –c ] – 2D[pm(c–)][pm(c–) – –c )< 2D(c–< 0,–) for D[pm(c )] while thewhere the first inequality is obtained from substitution of D(c––) is the profit-maximizing price at cost –c . Thissecond follows the fact that pm(ccontradiction is what we wanted. ❏B
B
Appendix C: We prove Lemma 2. Proof of Result (i) dδB(c–)/dc– < 0. Write δ (c–) = δ tosave space. δB is implicitly defined by (6) or satisfies this implicit function– = 0.
g(δB, –c ) ≡ VJ – V λ – m

34
where VJ – Vλ is given by (7). Write g(δB, –c ) = g. Straightforward differentiation of (7)shows that ∂g/∂δB > 0. On the other hand,sgn {∂g/∂c–} = sgn {∂(VJ – Vλ)/∂c–} = sgn {∂(πi + πn – πL)/∂c–}
The last derivative is–– δBD[pm(c–)] + D(c ) > 0–
since pm(c–) > c . Therefore, by the implicit-function theorem we conclude thatBdδB(c–)/dc– = – (∂g/∂c–)/(∂g/∂δ ) < 0.

– /2)(1 − δφ2). Therefore, if
Proof of Result (ii): As –c approaches cd, Vc – Vλ approaches (mδ > 1/(2φ2), (6) holds with strict inequality at the limit –c = cd, that is,– /2)/(1 − δφ2) > m–.
(m
2
This implies that δB(c–) is bounded from above by 1/(2φ ).

Proof of Result (iii). Suppose that φ2 ≥ 1/2. Then 1/(2φ2) ≤ 1. Hence, 1 > δB(c–) > 1/2 bydresult (ii) of lemma 2. On the other hand, δA(c–) approaches unity as –c approaches c , andapproaches 1/2 as –c nears –c . Thus, the two loci cross each other. ❏BAppendix D. We prove Lemma 3: Let δ be given such that δA(c–) ≤ δ < δ (c–). Suppose–) and the total profit m– * = D(p*)(p* - –c ) < m– satisfying
there is a price p* ≠ pm(c

35

– */2
δ(1 – φ2)[vi + vn - πL/(1 – δ)]/2 + m
1 – δφ2–*≥m

But firms cannot collude fully so

–>
m

– /2
δ(1 – φ2)[vi + vn - πL/(1 – δ)]/2 + m
1 – δφ2.

Adding and simplifying– -m– *]/[2(1 - δφ2)] ≥ m
– -m
–*
[m
which holds only if
δ >1/ (2φ2).
By Lemma 2,
1/(2φ2) > δB(c–).
These two imply δ > δB(c–), a contradiction. ❏Appendix E: We show that (8) holds with strict inequality at δ = 1/2. First we show:
(E1)

L –
m
– –π –m

m
m –
m –
– –
–
= D[pm(c–)][p (c–) – –c ] – D(c )(c – –c ) – D[p (c )][p (c ) – c )m– –– m– –> D[pm(c–)][p (c–) – –c ] – D(c )(c – –c ) – D(c )[p (c ) –c )m
– m–
= D[pm(c–)][p (c–) – –c ] – D(c )[p (c ) – –c ) > 0.

Second, evaluate VJ – Vλ at δ = 1/2 to obtain

36

VJ – Vλ =–(1 - φ2)(m– – πL) + m
2 - φ2.

– from it.
Subtract m(E2)– = (1 - φ2)(m – πL – m– )/(2 - φ2) > 0
VJ – Vλ – m–by (E1). Finally, evaluate the left-hand side of (8) at δ = 1/2 to obtain(E3)

2(1 – φ2)m– /2 + φ (VJ – Vλ)/22–> (1 – φ2)m
– /2 + φ m/2

– /2,
>m
where the first inequality uses (E2). But (E3) shows that (8) holds with strict inequality atδ = 1/2. ❏Appendix F: Since he receives zero profits following a deviation, the innovator has no– /(1 – δ) ≥ m– , or s ≥ 1 – δ. Likewise, the non-innovator does notincentive to deviate if sm
deviate if s ≤ δ. Thus, 1 – δ ≤ s ≤ δ. At δ = 1/2, this means s = 1/2. Now, modify the prediscovery components of b as follows. In state (iv) firms set price equal to –c until a
discovery, after which they switch to the stick-and-carrot strategy described by Thal
(2006). Then, a one-period deviation before a discovery yields zero profits (excluding k)past the period in which a deviation occurs, regardless of histories. It follows that a

37deviant firm chooses not to invest in R&D investment. With this modification, (6)becomes–.
Vc ≥ mSubstituting δ = 1/2 and canceling terms, we can write this condition as
m
m
–
–
m
– + D[p (c–)][p (c–) – c ] – 2m ≥ 0.

This condition may or may not hold in general but it does hold under the assumption of
linear demand as can easily be confirmed by directly evaluation of the profits. If it does,
then firms can maintain collusion before and after innovation at any δ ≥ 1/2 as undercooperative R&D. ❏38
References
Abreu, D., 1986, Extremal equilibria of oligopolistic supergames, Journal of Economic
Theory 39, 191-225.
Abreu, D., 1988, Towards a theory of discounted repeated game, Econometrica 56, 383396
Bae, Y., 1987, A price-setting supergame between heterogeneous firms, European
Economic Review 31, 1159-1171
Bloch, F., and Markowitz, P, 1996, Optimal disclosure delay in multistage R&D
competition, International Journal of Industrial Organization 14, 159-179
Cabral, L. M. B., 2000, R&D cooperation and product market competition, International
Journal of Industrial Organization 18, 1033-1047
Caloghirou, Y., S. Ioannides, and N.S. Vonortas, 2003, Research joint ventures, Journalof Economic Surveys 17, 541-570
Cardon, J. H. and Sasaki, D., 1998, Preemptive search and R&D clustering, RAND
Journal of Economics 29, 324-338
Collie, D.R., 2004, Sustaining collusion with asymmetric costs, unpublished paper.
D’Aspremont, C, and Jacquemin, A., 1988, Cooperative and noncooperative R&D in
duopoly with spillovers, American Economic Review 78, 1133-1137.
Friedman, J.W., 1971, A non-cooperative equilibrium for supergames, Review of
Economic Studies 38, 1 – 12.
Harrington, Jr., J. E., 1991, The determination of price and output quotas in aheterogeneous cartel, International Economic Review 32, 767-792

39
Kamien, M. I., E. Muller, and I. Zang, 1992, Research joint ventures, and R&D cartels,
American Economic Review 82, 1293-1306.
Lambertini, L., S. Poddar and D. Sasaki, 2002, Research joint ventures, productdifferentiation, and price collusion, International Journal of Industrial
Organization 20, 829-854
Lambertini, L., S. Poddar and D. Sasaki, 2003, RJVs in product innovation and cartel
stability, Review of Economic Design 7, 465-477.
Martin, S., 1995, R&D joint ventures and tacit product market collusion, European
Journal of Political Economy 11, 733-741
Miyagiwa, K., and Y. Ohno, 2002, Uncertainty, spillovers, and cooperative R&D,
International Journal of Industrial Organization, 855-876
Rothschild, R., 1999, Cartel stability when costs are heterogeneous, International Journalof Industrial Organization 17, 717-734
Thal, J., Optimal collusion under cost asymmetry, unpublished paper
Verboven, F., 1997, Collusive behavior with heterogeneous firms, Journal of Economic
Behavior and Organization 33, 121-136

Region 3
1

A
Region 1

1
2φ 2

B

Region 2
B

1
2

δ

c
–

–
c

cd

Figure 1A