R&D in a duopoly under incomplete information

• Author: Srobonti Chattopadhyay,Tarun Kabiraj,Rittwik Chatterjee
• DOI: http://doi.org/10.1111/ijet.12174
• Date: 01 December 2019
• Published date: 01 December 2019

doi: 10.1111/ijet.12174

R&D in a duopoly under incomplete information

Rittwik Chatterjee,∗Srobonti Chattopadhyay†and Tarun Kabiraj‡

The availability of information about rivals may have a significant impact on a firm’s decision

about R&D investment. This paper investigates how the R&D incentiveof a fir m in a Cournot

duopoly maydepend on information st ructures. Weshow that asymmetric information about the

rival’scost reduction may enhance the research incentive of each firm compared to the complete-

information case. However, an additional dimension of asymmetry (e.g. the information about

whether the rival has invested in R&D or not) will reduce the R&D incentive unambiguously

compared to the one-dimensional asymmetry case.

Key wor ds R&D incentive, duopoly,asy mmetric information, type distribution

JEL classification D43, D82, L13, O31

Accepted 24 August2017

1 Introduction

Research and development (R&D) is regarded as essential by both governmentsand pr ivateentities,

though for different reasons. Governments hold R&D to be necessary for the sake of growth and

development so that a country can either stay on the technological frontier or push the frontier

outward. Private entities, on the other hand, take an interest in R&D in order to gain an edge over

rivals and enhance their profits by lowering costs and improvingthe qualit y of an existingproduct or

by introducing a totally different or closely related product.Whether a firm will invest in R&D or not

depends on a wide range of factors, including the availability of the required amount of R&D funds,

the probability of success, the market structure, spill-over effects, the R&D researchform (whether it

is collaborativeor non-cooperative), patent protection, the imitative capability of the rivals, and so on.

R&D incentives based on these factors are extensively discussed in the literature. But the role

of information in determining R&D investment by a firm has drawn little attention so far. The

present paper seeks to discuss how the R&D decision of a firm may depend on various information

structures. Quite obviously, R&D investment depends on factors about which a firm does not have

perfect or complete information. For instance, a competing firm may simply not know whether its

rival is involvedin R&D to reduce production costs or to innovate a new product. This is certainly the

case when the firms are from different countries but possibly compete in a third market.1Evenwhen

∗Centre for Studies in Social Sciences Calcutta, Kolkata, India.

†Vidyasagar College for Women,Kolkata, India.

‡Indian Statistical Institute, Kolkata,India. Email: tarun@isical.ac.in

Authors are greatly indebted to an anonymous referee of this journal for very productive and helpful comments and

suggestions. They also thank Prabal Roy Chowdhury,Sugata Marjit and Krishnendu Ghosh Dastidar for their views and

observations on an earlier draft. However,the usual disclaimer applies.

1These types of scenarios are observed to prevail in the strategic trade literature (see, for instance, Brander

and Spencer 1985).

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International Journal of Economic Theory 15 (2019) 341–359 © IAET 341

R&D under incomplete information Rittwik Chatterjee et al.

the competing firms know whether their rivals have invested in R&D or not, the outcomes of R&D

may be unknown. Consider cost-reducing R&D.It is possible that a firm has incomplete information

about the extent of cost reduction of its rivals. This information asymmetry is well highlighted in the

literature of technology transfer and incumbent–entrant interaction.2

In this paper we focus on the following scenario. Whether a firm is conducting R&D or not,

and if it does then exactly what R&D output it is obtaining, may or may not be observable to its

rivals. The extent of observability of a firm’s R&D decision and its consequenceswill lead to different

information structures. Then the R&D decision of a firm becomes contingent on the availability of

information regarding its rival firms’ R&D decisions and R&D outcome. Hence, the purpose of this

paper is to study how the information structure can affect the R&D decision of a firm. Does more

information provide a greater incentive to investin R&D? We show that the R&D incentive of a firm

can be stronger under incomplete information than under complete information. We construct a

model of Cournot duopoly under incomplete information when the firms interact non-cooperatively

in R&D and product markets. Weassume that R&D investment by a firm lowers its marginal cost of

production, but the extent of cost reduction is not known to the rivals. Since R&D activity involves

a cost, each firm will decide strategically whether to invest in R&D or not. We investigate how this

decision depends on the availability of information. In particular, we study the relation between

R&D incentives and the level of information.

We considerthree distinct scenarios regarding the level of information available to a firm:

rEach firm knows whether its rival conducts R&D or not, and if its rival does conduct R&D, how

much reduction in its marginal cost will occur.

rEach firm knows whether its rival conducts R&D or not, but how much cost reduction occursdue

to R&D for each firm is known only to the firm concerned and not to its rival.

rA firm knows neither whether its rival conducts R&D, nor the actual cost reduction of the rival.

Clearly, the first case is a game with complete information, while the last two cases are games with

incomplete information. When only the extent of cost reduction is private information, but whether

the rival has conducted R&D or not is perfectly observable, let us call this a level I incomplete-

information problem. When the extent of cost reduction of a firm, and whether it has conducted

R&D or not, are both private information, we call this a level II incomplete-information problem.3

Note that in our framework of incomplete information, neither firm knows at the stage of R&D

decision-making whether its rival will be doing R&D,althoug h the firm knowsthat at the beg inning of

production stage it will have that information. However, in either case of level I or level II incomplete

information, a firm cannot observe the actual reduction in its rival’s marginal cost.

We now briefly outline the related literature. R&D incentives in the presence of incomplete

information are a relativelylittle-explored area. There are only a few works related to the R&D decision

under incomplete information. Brocas (2004) analyzes the regulator’srole in providing incentives for

cooperative R&D when the firms possess some privately known skills. Kabiraj and Chattopadhyay

(2015) and Chattopadhyay and Kabiraj (2015) have studied the choice between cooperative and

non-cooperative R&D when firms do not know the realization of rivals’ R&D outcome. Bacchiega

2See, for instance, Milgrom and Roberts (1982), Gallini and Wright(1990), and Beggs (1992).

3Toillustrate, consider the purchase of a license to use a cost-reducing technology. Whenever ything is publicly observable

(i.e. which firm possesses the license and how much cost reduction it achievesis known to ever yone),we have a game of

complete information. When which firm holds the license is known toall, but how much cost reduction will be achieved

by the license-holdingfir m is privateinfor mation, weeffectively have a level I incomplete-information scenario. However,

if which firm holds the license is also unknown, we have a level II incomplete-informationscenario.

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