 Original Research
 Open Access
Product competition and R&D investment under spillovers within full or partial collusion games
 Kai Zhao†^{1}Email author
Received: 22 March 2014
Accepted: 8 April 2015
Published: 29 April 2015
Abstract
The paper investigates firms’ behavior and outcomes (levels of costreducing R&D, output, profit and welfare in equilibrium) in a differentiated duopoly with process innovation. One of the important features in this paper is that spillovers operate in the R&D stage and are tied to the degree of product substitutability as well as the extent of technological proximity/alienation of the research paths leading to cost reduction. Using this feature, the paper tries to explore and compare four separate organization setups (Full Competition, Semicollusion in Production, Semicollusion in R&D and Full Collusion). It is found that under technological proximity, competitions at the upstream stage depress R&D investment, and firms colluding in R&D regardless of their production strategy always yield more profit and generate higher social welfare than firms colluding in output; under technological alienation, R&D cooperation may reduce firms’ interest to invest in R&D, and it is possible that firms in the Full Collusion regime produce most and generate the highest level of social welfare.
Keywords
 R&D
 Spillover
 Semicollusion
 Product differentiation
 Horizontal merger
JEL Classification
 D43
 L13
 O31
1 Introduction
Nowadays, economies in Latin America are becoming more and more knowledge based. Innovation becomes essential to spur economic growth and to raise living standards. At the firm level, either competition or collusion could reward innovation by providing strong incentives for firms to be more efficient than their rivals. This paper aims to study the extent to which innovation incentives in a duopoly change according to the extent of product substitutability and the “technological distance” of firms. We draw particular attention to firms’ (full/partial) collusive behavior and attempt to address the following questions: What type of collusion (partial, full, none) should firms choose, and which one is more conducive to technological advancement and a firm’s growth? How do firms choose different types of collusion, and how do these affect market outcomes? Can the collusive strategy improve the consumer surplus and the social welfare, and which one serves best?
Innovation through R&D investment leads to more efficient use of resources, creating sustainable competitive advantages. The most important aspect of R&D investment is the externality (spillovers) which has been studied through the divergence between the social and private returns of production process. The public goods feature of knowledge generates spillovers which allow others to use the owner’s innovation free of charge. Due to the spillover effect, the rate of return from an innovation is lesser and as a result, the incentives for carrying out R&D are reduced. The individual firm fears that competitors use its internal research results and thus probably increase their profits without having to bear the expenses. Therefore, the researching firm will only have limited incentive to invest in R&D. However, from the collective viewpoint, spillovers strengthen the dissemination of new knowledge available for the whole society, and improve the social welfare (Amir 2000).
Within a game where firms are first engaged in costly research efforts to adopt a lowercost technology and then compete in a Cournot fashion with homogeneous products, (D’Aspremont and Jacquemin 1988) (henceforth “AJ”) show that firms invest more under R&D cooperation than under R&D competition for sufficiently high spillover effects (full competition versus full cooperation). Kamien et al. (1992) (henceforth “KMZ”) extend the AJ model to a more general framework with product differentiation and allow firms to participate in a research joint venture (RJV). They show that firms should be encouraged to form a RJV only if they coordinate their R&D decisions while maintaining competition for sales. Concerning the welfare effects of cooperative R&D with spillovers, cooperation raises social welfare when the spillover is high (Suzumura 1992).
Compared to aforementioned works, this paper emphasizes the “close relationship” between product differentiation and R&D spillovers. The key feature is to consider that the extent of product differentiation determines the ability of a firm to appropriate its rival’s R&D effort. In addition, this ability is influenced by the sensibility of spillovers relative to product differentiation, in other words, technological distance. Several explanations can be provided to justify this “close relationship”. First, when products are close substitutes, R&D efforts are less firm specific and a firm can more easily benefit from the discovery of a more efficient production technique resulting from rival’s R&D effort. Second, the exchange of technological information between engineers of competing firms is recognized as an important source of R&D spillovers (Severinov 2001). Spillovers are believed to be higher between technological neighbors. According to this view, the ability to make productive use of another firm’s knowledge depends on the degree of technological distance between firms. Every technology has a somewhat unique set of applications and language. Researchers in similar technological fields will interact in professional organizations, publish in commonly read journals, and, increasingly, browse a common set of web pages. It is natural to consider that the dissemination of technological knowledge across competing firms is strong when firms’ technologies are similar. Furthermore, the abovementioned “close relationship” is divided into two categories: concave relationship (technological proximity) where firms adopt similar technologies (i.e., the similar smart phones produced by Apple, Blackberry, Nokia ...), convex relationship (technological alienation) where firms adopt different technologies (i.e., electricity can be produced by different technologies). To be more concrete, we take the electricity production, for example, electric power companies are differentiated by voltages, a commercial consumer may need a voltage level of 11 kV or 440 V while a residential consumer needs power at level of 240 V, this difference of voltages refers to product differentiation. The electricity can be produced by different technologies (i.e., solar panels, wind turbines, nuclear energy), this refers to the extent of technological distance. The R&D flow between companies employing the same output (voltage) and the same technique is obviously greater.
In location models, the distance between firms determines the degree of product differentiation. By considering that R&D spillover depends negatively on firms’ product location, it is shown that R&D effort is positively associated with the differentiation of products^{1} (Piga and PoyagoTheotoky 2005). However, they do not address the important issue of cooperative behavior between firms in their models.
In this paper, we consider a twostage game where firms with heterogeneous products competing in a Cournot fashion engage in upstream R&D and downstream production. At each stage, the competing firms can either coordinate their decisions or adopt noncooperative strategy. This assumption allows us to compare the Subgame Perfect Nash Equilibrium (henceforth “SPNE”) emerging in the four separate scenarios : full competition, semicollusion in Production^{2}, Semicollusion in R&D^{3} and Full Collusion^{4}. Compared to Kamien et al. (1992) which claim that the R&D investment by firms engaged in Semicollusion in R&D is unambiguously greater than that in the Full Competition regime irrespective of spillovers, we demonstrate in fact which regime generates more R&D effort in equilibrium depends upon both the degree of product differentiation and the extent of technological distance. If we restrict our attention to the concave relationship, Full Collusion participants spend most on R&D, and Semicollusion participants spend more than firms in the Full Competition regime. This ranking of R&D efforts is unalterable and independent of the product differentiation, and the competition at the upstream stage depresses R&D investment. Firms colluding in R&D regardless of their production strategy always yield more profit and generate higher social welfare than firms colluding in output independently of R&D strategy. When products are close substitutes, the synergy effects prevail over the anticompetitive effects due to the high spillovers, Full Collusion becomes a welfareenhancing regime. Focusing on the convex relationship, R&D cooperation may reduce firms’ interest to invest in R&D, and it is possible that firms in the Full Collusion regime produce most and generate the highest level of social welfare. Furthermore, horizontal mergers might be interpreted as a Full Collusion where the participants coordinate their decisions with respect to all of strategic variables. Thus, we launch the discussion about antitrust policy, and shed light on the leniency of the total welfare standard and the restrictiveness of the consumer welfare standard.
The rest of this paper is organized as follows. Section 2 presents the model and solves the SPNE in the four alternative regimes. We compare R&D effort, profit, consumer surplus and social welfare according to firms’ behavior (competitive or collusive) in Sect. 3. Section 4 concludes this paper.
2 The model
2.1 Hypothesis
Four alternative scenarios. Source own table
Four alternative scenarios  First stage (R&D)  Seconde stage (production) 

Full competition (regime F)  Firms compete in R&D; each firm decides its own R&D level given R&D efforts of the other firm  Firms compete; each firm decides its own output to maximize the individual profit 
Semicollusion in Production (Production Cartel) (regime P)  Firms compete in R&D; each firm decides its own R&D level given R&D efforts of the other firm  Firms coordinate their production activities to maximize the joint profit 
Semicollusion in R&D (R&D Cartel) (regime R)  Firms coordinate their R&D activities to maximize the joint profit; cooperative behavior in R&D does not change the level of spillovers  Firms compete; each firm decides its own output to maximize the individual profit 
Full collusion (Horizontal Merger) (regime M)  Firms coordinate their R&D activities to maximize the joint profit; cooperative behavior in R&D does not change the level of spillovers  Firms coordinate their production activities to maximize the joint profit 
2.2 Subgame equilibrium in the four regimes
2.2.1 Full competition

\(\frac{\partial q_i^F\left( x_i^F,x_j^F\right) }{\partial x_j^F } < 0\), if \(h> 1+ \frac{\log (\frac{1}{2})}{\log \gamma }\)

\(\frac{\partial q_i^F\left( x_i^F,x_j^F\right) }{\partial x_j^F } > 0\), otherwise
2.2.2 Semicollusion in production
2.2.3 Semicollusion in R&D
2.2.4 Full collusion (horizontal merger)
Despite the ostensibly widespread use of Full Collusion to exploit the complementarities in firm’s R&D process, the formal literature on R&D has almost focus exclusively on research joint venture, whereby firms share out technological knowledge (\(\beta =1\)) while continuing to compete against each other in product market (see Kamien et al. 1992).^{8} Here, we regard this scenario as the framework of multidimensional coordination in which firms cooperate in both R&D and production stages. Since, the products are imperfectly substitutable, Full Collusion^{9} means that the firms maximize their joint profit in each stage.
3 Comparison of different regimes
3.1 R&D effort
Result 1
 (i)
When firms have same behavior in the upstream stage, the downstream cooperation can incite firms to exert more R&D investment.
 (ii)
When firms adopt different technologies and produce differentiated goods (cf. Fig. 2, green area), the firms colluding in production will invest most in R&D.
 (iii)
Under technological proximity, firms with twostage cooperation have most incentive to invest in R&D without ambiguity.
Proof

\(x^P > x^F > x^M > x^R\) (zone I)

\(x^P > x^M > x^F > x^R\) (zone II)

\(x^P > x^M > x^R > x^F\) (zone III)

\(x^M > x^P > x^R > x^F\) (zone IV)

\(x^M > x^R > x^P > x^F\) (zone V)
First of all, we find when firms have same behavior (cooperation or competition) in the upstream R&D stage, firms allowed to cooperate in the product market always exert more R&D efforts in equilibrium, compared to firms competing in the downstream stage (\(x^M > x^R\) and \(x^P > x^F\) \(\forall \ \gamma , h\)). As we know, R&D efforts reduce the marginal cost and indirectly lead to a decrease of the product price. When firms can collude in the downstream stage, they restrict their outputs for a given R&D effort and as a consequence, the negative impact of R&D efforts on the product price is alleviated. Conversely, an intense product competition dissipates the benefits of R&D effort and, therefore, shrinks the incentive to invest in R&D. The output cooperation has a positive impact on R&D investment and then induces firms to undertake more R&D than they would under competition in the downstream stage.
The output cooperation reinforces the R&D effort for a given behavior at upstream stage. However, when the behavior at downstream stage is given, the R&D cooperation does not unambiguously increase research efforts. If we compare the regime \(F\) with the regime \(R\) (corresponding, respectively, to the lowest level in terms of R&D effort), it is found that R&D cooperation could be detrimental to R&D effort in zone I and zone II. This finding is in sharp contrast with the existing literature, for instance, Kamien et al. (1992) show that \(x^R\) is unambiguously greater than \(x^F\) without taking into account the close relationship emphasized in this paper.
The striking outcome we find here is that R&D investment under regime \(P\) can be the largest (cf. Fig. 2, green area). It is different from the conventional wisdom that merged (twostage cooperation) firms have more incentive to invest in R&D, because they appropriate all of the R&D efforts. The spillover effect (in zones I,II and III) constitutes a positive, but very small externality. When firms cooperate in the upstream stage (regimes M, R), on the one hand this small externality is internalized, on the other hand the R&D cooperation cannot promote the spending on common research of firms due to technological alienation (convexity). However, Semicollusion in Production can intensify the R&D competition by production cooperation, and incites firms to invest more in R&D. Therefore, the regime P leads to the highest level of R&D effort in green area. Moreover, if we restrict our attention to the case where the relationship between product differentiation and R&D spillover is concave (red area), the ranking of R&D efforts (\(x^M > x^R > x^P > x^F\)) does not alter, and it is independent of the product differentiation. It means that the Full Collusion participants spend more on R&D than Semicollusion ones, under concave relationship (technological proximity).
In Fig. 3, we plot the curves in \(\gamma \in [0,\frac{1}{4}]\) and \(h \in [1, \frac{3}{2}]\) space to zoom and emphasize the area \(x^{\mathrm{FB}}>\max \{x^F, x^R, x^P, x^M\}\). The smooth curve \(x^{\mathrm{FB}}=0\) divides the pattern into two parts and the left one represents \(x^{\mathrm{FB}}>0\). The intersection area between the smooth curve and the zigzag curve (\(x^{\mathrm{FB}}=x^P\)) defines combinations of \(\gamma\) and \(h\) where \(x^P > x^{\mathrm{FB}}\). D’Aspremont and Jacquemin (1988) and Henriques (1990) show that the social optimum R&D effort was unambiguously greater than the level of R&D investment in equilibrium under the fully cooperative or noncooperative or mixed^{10} game. Compared to them, we find the similar result when firms produce sufficiently heterogeneous goods. Furthermore, it is worthwhile to note \(x^P\) can be higher than \(x^{\mathrm{FB}}\) in an infinitesimal area where a higher level of R&D effort corresponds to a wasteful duplication.
3.2 Output and consumer surplus
Result 2
 (i)
The level of output and consumer welfare in fully cooperative scenario can be higher (cf. Fig. 4, green area) than that in partially cooperative or fully noncooperative situations.
 (ii)
When firms adopt similar technologies (concavity), R&D cooperation (regimes M and R) encourages firms to produce more, and leads to fierce output competition.
 (iii)
Firms under Full Competition can produce most and achieve the highest level of consumer welfare (red area), if and only if they use very different technologies and produce highly differentiated goods.
Proof

\(q^F > q^R > q^P > q^M\) (zone I)

\(q^R > q^F > q^P > q^M\) (zone II)

\(q^R > q^F > q^M > q^P\) (zone III)

\(q^R > q^M > q^F > q^P\) (zone IV)

\(q^R > q^M > q^P > q^F\) (zone V)

\(q^M > q^R > q^F > q^P\) (zone VI)

\(q^M > q^R > q^P > q^F\) (zone VII)
There is no stable hierarchy because the impact of R&D effort is complicated and exerts two conflicting effects on the output of rival firm. On the one hand, R&D effort is managed to induce the firm to expand output at expense of its rival by cutting down its own production cost. It is considered as the substitutability effect (an increase in its own output leads to a decrease in rival’s output) which is greater, the more substitutable the products are. On the other hand, the R&D effort can reduce the rival firm’s cost, thereby increase its rival firm’s output. It is regarded as the spillover effect (boosting rival’s output) which is greater the larger the spillover is. Since the spillover depends positively on the degree of product differentiation, when products are quasi homogeneous, both substitutability effect and spillover effect enlarge. Whether the output (consumer surplus) increases depends on the interplay of these two conflicting effects. If the spillover effect prevails over the substitutability effect, firms are motivated to expand output; otherwise, they prefer to shrink output.
According to Fig. 4, it is clear that firms colluding in R&D produce more than firms competing on R&D (\(q^R, q^M > q^P, q^F\)) when the relationship between substitutability and spillover is concave (\(h<1\)). This result holds always true regardless of product differentiation. Under the circumstance that the leakage of knowhow is relatively strong (concave relationship), firms cooperating on R&D are willing to spend more on R&D efforts (Result 1), the marginal costs of both firms are reduced so much that the spillover effect prevails over the substitutability effect, and firms are motivated to expand output. The curve \(V_F=0\) is a watershed of the relationship between \(q^R\) and \(q^F\) which is consistent with the corollary shown in Kamien et al. (1992)^{12}.
The relationship \(q^R > q^P\) holds true for all \(\gamma\) and \(h\). The intuition behind this stems from the variation of competition intensity^{13}. Under regime \(R\), upstream collusion leads to much more fierce rivalry in noncooperative output stage. Furthermore, since firms collude in output under regime \(P\), the market becomes looser, and the firms have more incentives to increase the price by reducing output.
We find also that the firms colluding in output produce less than the firms competing in production market when the goods are sufficiently differentiated (zones I, II, III). First, the downstream output cooperation induces firms to increase the price and decrease the output; second, as the low value for \(\gamma\) generates the small spillovers, the R&D efforts exerted by firm \(i\) cannot sufficiently reduce its rival ’s marginal cost, this spillover effect is not strong enough to compensate the decrease in output due to production cooperation, therefore, firms have to shrink output.
3.3 Profit
According to Brod and Shivakumar (1999)^{14} (henceforth, "BS"), the profit under Full Competition could be greater than under Semicollusion in Production in some cases. When there is the “close relationship” between product differentiation and R&D spillovers, we have the following result:
Result 3
 (i)
The firms in Full Collusion are most profitable while the firms in Full Competition are least profitable.
 (ii)
When firms adopt similar technologies (concavity), they prefer taking part in R&D Cartel to joining in Production Cartel (cf. Fig. 5, red area).
 (iii)
When firms adopt different technologies (convexity), the firms in Production Cartel could generate more profit than that in R&D Cartel (cf. green area \(\pi ^P > \pi ^R\) and white area \(\pi ^P < \pi ^R\)).
Proof
When the spillover is relative to the product differentiation, the profit of the firms in the regime \(P\) always prevails over the one in the regime \(F\). This result is in contrast with Brod and Shivakumar (1999) which shows that the profit under regime \(F\) could be higher than under regime \(P\). Furthermore, in line with semicollusion literature (Matsui 1989; Fershtman and Gandal 1994), we establish the possibility that R&D Cartel is less profitable than Production Cartel.
We find that the profit of firms with fully cooperative behavior prevails over onedimension cooperation profit which is higher than the profit earned by the firm in Full Competition. It is only that the relationship between two types of semidelegation can be altered. The alluring question is which type of semicollusion (Production Cartel or R&D Cartel) will be more beneficial for firms.
Under concave relationship (technological proximity), firms colluding in R&D generate always more profit than firms colluding in output. The intuition of this result is the following: compared to the regime \(P\), the distinctive advantage of the regime \(R\) is that firms invest more in R&D under concave relationship (See Result 1), thereby, firms are more competitive due to costsaving by R&D investment; furthermore, according to Result 2, firms in the regime \(R\) produce more than firms in the regime \(P\). Despite the fact that R&D investment is expensive, the profit of the firms in the regime \(R\) is still higher than that in the regime \(P\) when \(h < 1\).
The inverse outcome \(\pi ^P > \pi ^R\) can take place for some plausible \(\gamma\) under convexity condition (technological alienation). In particular, when \(h\) is approximately greater than the critical value which is equal to \(1.12\), \(\pi ^P>\pi ^R\) holds always true.
3.4 Social welfare
Result 4
 (i)
Full Collusion can generate the highest level in social welfare, in particular when firms produce the similar goods (cf. Fig. 6, green area).
 (ii)
When firms produce the differentiated goods (red area), Semicollusion in R&D enhances most the social welfare.
Proof

\(W^F > W^R > W^P > W^M\) (zone I)

\(W^R > W^F > W^P > W^M\) (zone II)

\(W^R > W^F > W^M > W^P\) (zone III)

\(W^R > W^M > W^F > W^P\) (zone IV)

\(W^R > W^M > W^P > W^F\) (zone V)

\(W^M > W^R > W^F > W^P\) (zone VI)

\(W^M > W^R > W^P > W^F\) (zone VII)
We highlight that the collusive behavior in both stages could enhance the welfare (zones VI, VII). If we consider the social welfare equilibrium level in the Full Competition regime as the criterion value, not only the Full Collusion regime but also Semicollusion can improve the welfare. For example, the regime \(R\) is the welfare dominant regime when products are sufficiently differentiated. We find also under concavity condition, firms colluding in R&D regardless of their production strategy always enhance more social welfare than firms colluding in output independently of R&D strategy. Semicollusion in Production can lead to a decrease in social welfare under convexity condition (zones I, II, III, IV).
Although the hierarchies in terms of welfare are the same as the ones concerning consumer surplus (output) which are depicted in Sect. 3.2 (Result 2), it is clear that there are some points of dissimilarity, such as the location of the different zones and the size of zones. In virtue of this dissimilarity, the discussion on antitrust policy is unsealed. In what follows, we focus on the difference between consumer welfare standard and total welfare standard.
3.5 Merger control: consumer welfare standard Vs total welfare standard
On the basis of Result 4, we conclude that society can benefit from not only the cooperative behavior in one dimension (Semicollusion in R&D or in Production) but also from the horizontal merger (Full Collusion). Therefore, all regimes can yield the highest level of welfare for plausible parameter combinations.
Nowadays, most countries have laws or regulations that require competition authorities to scrutinize horizontal mergers. These authorities normally do not examine whether a particular merger is likely to affect welfare because it substantially lessens competition (USA) or significantly impedes effective competition (European Union). The US or EU applies a consumer welfare criteria to mergers. Canada, Australia and New Zealand, however, consider a merger’s effects on aggregate surplus and had a very explicit aggregate surplus standard (Motta 2004).
Consequently, we make use of both total welfare standard and consumer welfare standard within our framework, to analyze the difference between two abovementioned criteria, to examine whether the merger prohibited under aggregate welfare standard can be authorized under consumer welfare standard or inversely.
In Fig. 7, on the right side of curve Consumer Welfare Standard, the horizontal merger is accepted by consumer welfare standard. Total welfare standard authorizes the merger when the beach of parameter combination locates to the right of the curve named Total Welfare Standard. It is straightforward that there is the gap (dashed area) between two mentioned curves which sheds light on the looseness of the total welfare standard and the preciseness of the consumer surplus standard. Due to the prohibition by competition authorities, in the left side, the firms have to lean to the less attracting regimes which yield less profit compared to merger one. Therefore, the firms prefer the Semicollusion in R&D (semicollusion^{16}) in the prohibited merger zone (\(\pi ^R > \pi ^F\)).
4 Concluding remarks
In the traditional onedimensional framework, collusion increases producer profits, but damages consumer welfare without ambiguity (Textbook^{17} view). However, this argument ignores the effects of other nonproduction activities, such as R&D. Recently, as shown in Revisionist^{18} view, within twodimensional game, semicollusion may be profitable and efficient (Brod and Shivakumar 1999) under some circumstances, while it can be unprofitable and inefficient. Previous works have shown whether producers and consumers would be better off under product market cooperation depends particularly on product differentiation and R&D spillovers.
This paper emphasizes the “close relationship” between product differentiation and spillovers, and studies the significative relevance in the scenarios where firms can either coordinate their decisions or adopt noncooperative strategy (Full Competition, Full Collusion and Semicollusion regimes) at each stage. Kamien et al. (1992) claim that the investment by firms engaged in the regime \(R\) is unambiguously greater than that in the regime \(F\) irrespective of spillovers. We demonstrate in fact which regime generates more R&D effort in equilibrium depends upon both the degree of product differentiation and the technological distance. If we restrict our attention to the concave relationship, the ranking of R&D efforts is unalterable and independent of the product differentiation, competitions at the upstream stage depress R&D investment. Firms colluding in R&D regardless of their production strategy always yield more profit and generate higher social welfare than firms colluding in output independently of R&D strategy. When products are close substitutes, Full Collusion is a welfareenhancing regime.
In addition, a discussion about antitrust policy is carried out. By focusing upon the distinctness of different antitrust criteria, this framework sheds light on the looseness of the total welfare standard and the preciseness of the consumer welfare standard. This outcome will be verified, in future work, by considering the interaction between Competition Authorities and firms, in a context of asymmetric information^{19}.
There are some possible extensions of this framework: first, we will check the robustness of the result obtained in this paper, when there would be more than two firms in the market; second, we will investigate whether our model can get the similar results within a dynamic^{20} duopoly game, by supposing the R&D investments for costreducing innovation over continuous time; third, the parameter of spillover depends only on the degree of product differentiation in this model, however, the government can control the parameter of spillover using the intellectual property right policy, and it is an important extension of this model to enrich the policy implication; fourth, the degree of product differentiation is exogenously given in our model, however, firms have strategic incentives to control to maximize their profit, and it is better to consider the case that the degree of product differentiation is determined endogenously.
The greater the distance between firms, the more differentiated the firms’ products, the less the R&D spillover.
If \(\gamma =0\), firms’ products are not substitutable and each firm acts as a monopolist. Note that, when products are perfect substitutes, the spillover obviously equals to 1 and the game cannot be solved. See D’Aspremont and Jacquemin (1988).
From the perspective of technological distance, it is straightforward that the more technologies are similar, the greater are spillovers, for a given level of product differentiation.
Kamien et al. (1992) provide a thorough analysis of RJV, contrasting the case of RJV Competition where firms pool R&D results, but behave noncooperatively at both stages, and RJV Cartelization (the pooling of R&D results with cooperative determination of R&D investment, but competition in subsequent product market stage). Suzumura (1992) and Suzumura and Yanagawa (1993) contain a closely related analysis. D’Aspremont and Jacquemin (1988) do allow for merger under which firms pool R&D results and cooperate in both stage of the game. It is worth noting that there are the analysis of the converse case to RJV, where all firms compete in R&D stage, but then collude in outputs, see Fershtman and Gandal (1994) and Brod and Shivakumar (1999).
Firms cooperate in R&D, but remain noncooperative in output. This game corresponds to the Semicollusion in R&D within our framework.
D’Aspremont and Jacquemin (1988) and Henriques (1990) demonstrate the level of output in noncooperative twostage case is always higher than that in fully cooperative situation. In addition, they claim that the mixed game can generate more output than noncooperative twostage game for large spillovers. These models based on the assumption of homogenous goods.
They demonstrate the price (output) in R&D cartelization is less (more) than the price in R&D competition if and only if \(\gamma \le 2 \beta\).
In an onestage game, cartels increase industry profits and exacerbate the consumer surplus. In a model where firms collude in production, but compete in R&D, the cartel members may be worse off and consumers better off due to overinvestment by firms eager to improve their position in the cartel. Brod and Shivakumar (1999) analyze a twostage model and examine the effect of semicollusion when the nonproduction activity is R&D. Firms choose their R&D effort in a first stage and output in a second stage. They shed light on the fact that in the presence of spillovers, firms and consumers could be both better off, peradventure both worse off, by a semicollusive production cartel. We are attired by this fascinating outcome. Thereupon, we try to approach the indepth analysis and understand the driving forces of this result. We find, however, that the findings of Brod and Shivakumar (1999) are disputable. The incorrect SPNE values of perfirm R&D effort, output and profit due to improper handling result in the inaccuracy of their main propositions. When the goods are sufficiently substitutable, the proposition 1 does not hold. In other words, there is no absolute predominance of production cartel in terms of R&D effort. Since the optimum equilibrium of cartel at the production stage could be negative for certain combination parameters (the degree of product differentiation and the level of spillovers), we find the region D depicted as “Consumers prefer Production Cartel; firms prefer Competition” could not always satisfy the conditions mentioned in proposition 2. In "Appendix 2", we focus upon their calculative errors, and show what the correct solution can be.
Note that in reality, the Production Cartel is prohibited. Thus, we exclude it in antitrust control analysis.
The textbook view: while the firms benefit from product market collusion, consumer welfare is higher under noncooperation in the product market. See more in Jacquemin and Slade (1989).
Declarations
Acknowledgments
I am grateful to Nicolas Le Pape, Thierry Penard and Bernard Franck for thoughtful comments and suggestions. I also thank Said Souam and JeanPascal Gayant. We have received helpful comments on earlier drafts of this article from participants at the ESEM, AFSE and seminar participants at GAINS. This work is supported by the Research Funds of Huaqiao University (HQHRZD201403). I am grateful for the very painstaking efforts made by the editor and the referee in providing me with very valuable suggestions and comments. All remaining errors are mine.
Conflict of interest
The author declares that he has no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
References
 Amir R (2000) Modelling imperfectly appropriable R&D via spillover. Int J Ind Organ 18(7):1013–1032View ArticleGoogle Scholar
 Audretsch D, Feldman M (1996) Knowledge spillovers and the geography of innovation and production. Am Econ Rev 86(3):630–640Google Scholar
 Baptista R, Swann P (1998) Do firms in clusters innovate more? Res Policy 27:525–540View ArticleGoogle Scholar
 Besanko D, Spulber DF (1989) Antitrust enforcement under asymmetric information. Econ J 99:408–425View ArticleGoogle Scholar
 Brod A, Shivakumar R (1999) Advantageous semicollusion. J Ind Econ 47(2):221–230View ArticleGoogle Scholar
 Cellini R, Lambertini L (2009) Dynamic R&D with spillovers: competition vs cooperation. J Econ Dyn Control 33(3):568–582View ArticleGoogle Scholar
 D’Aspremont C, Jacquemin A (1988) Cooperative and noncooperative R&D in duopoly with spillovers. Am Econ Rev 78:1133–1137Google Scholar
 Fershtman C, Gandal N (1994) Disadvantageous semicollusion. Int J Ind Organ 12:141–154View ArticleGoogle Scholar
 Henriques I (1990) Cooperative and noncooperative R&D in duopoly with spillovers: comment. Am Econ Rev 80:638–640Google Scholar
 Jacquemin A, Slade M (1989) Cartels collusion and horizontal merger. Handbook of industrial organization (New York, NorthHolland)Google Scholar
 Kamien M, Muller E, Zang I (1992) Research joint ventures and R&D cartels. Am Econ Rev 82:1293–1306Google Scholar
 Matsui A (1989) Consumerbenefited cartels under strategic capacity investment competition. Int J Ind Organ 7:451–470View ArticleGoogle Scholar
 Mitchell S (1993) The welfare effects of rentsaving and rentseeking. Canad J Econ 26:660–669View ArticleGoogle Scholar
 Motta M (2004) Competition policy: theory and practice. Cambrige University Press, pp 579Google Scholar
 Pénard T, Souam S (2002) Collusion et politique de la concurrence en information asymétrique. Ann d’éonomie et de Stat 66:209–233Google Scholar
 Piga C, PoyagoTheotoky J (2005) Endogenous R&D spillovers and locational choice. Regional Sci Urban Econ 35:127–139View ArticleGoogle Scholar
 Severinov S (2001) On information sharing and incentives in R&D. RAND J Econ 32:542–564View ArticleGoogle Scholar
 Suzumura K (1992) Cooperative and noncooperative R&D in an oligopoly with spillovers. Am Econ Rev 82:1307–1320Google Scholar
 Suzumura K, Yanagawa N (1993) Cooperative and noncooperative R&D in an oligopoly with spillovers: strategic substites vesrsus strategic complements. Hitotsubashi J Econ 34:1–11Google Scholar