Price and quantity competition in an asymmetric duopoly with licensing

• Author: Shuai Niu
• DOI: http://doi.org/10.1111/jpet.12332
• Date: 01 December 2018
• Published date: 01 December 2018

Received: 27 December 2017

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Accepted: 9 August 2018

DOI: 10.1111/jpet.12332

ORIGINAL ARTICLE

Price and quantity competition in an asymmetric

duopoly with licensing

Shuai Niu

School of Economics, Shandong University,

Jinan, China

Correspondence

Shuai Niu, School of Economics, Shandong

University, Jinan, Shandong 250100, China.

Email: niushuai1@163.com

Funding information

The Social Science Planning Fund Program of

Shandong Province, China, Grant/Award

Number: 16DJJJ05; The Academic Prosperity

Program of School of Economics, Shandong

University

By introducing licensing, this study reconsiders the relative

dominance of price‐and quantity‐setting strategies in an

asymmetric duopoly. It shows that if the initial cost

difference is small or the goods are close substitutes, then

both firms will prefer the quantity strategy. Conversely, for

the other cases, heterogeneous‐strategy equilibrium will

appear, under which the low‐cost firm will choose a price

strategy and the high‐cost firm will choose a quantity

strategy. With an endogenous mode of market competition,

licensing has always proven to be welfare‐improving.

KEYWORDS

licensing, price, quantity

JEL CLASSIFICATION

L13, L24, L40

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INTRODUCTION

In the previous literature, the theoretical analysis of licensing is confined to the setting in which, after technology

transfer, firms adopt the same or homogeneous strategies to compete in the final product market, that is, they act

as either price‐or quantity‐setters. For example, Kamien and Tauman (1986) explored how much profit an external

owner of a cost‐reducing invention can realize by licensing it to a Cournot oligopoly through fixed fees or per‐unit

royalties.

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Under the same model setting, the optimal combination of fixed fees and per‐unit royalties, that is, two‐

part tariff licensing, was considered in the study by Sen and Tauman (2007). Concerning the internal‐patentee case,

Katz and Shapiro (1985) and Marjit (1990) discussed fixed‐fee licensing in a Cournot duopoly with homogeneous

goods. Mukhopadhyay, Kabiraj, and Mukherjee (1999) extended this discussion by introducing product

differentiation in their study. Wang (1998), (2002) compared fixed‐fee licensing and per‐unit royalty licensing in

a Cournot duopoly. As an extension, Poddar and Sinha (2010) discussed the two‐part tariff licensing. Fixed‐fee

licensing and two‐part tariff licensing in a Cournot oligopoly were considered in Faulí‐Oller, González, and Sandonís

J Public Econ Theory. 2018;20:896–913.wileyonlinelibrary.com/journal/jpet896

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© 2018 Wiley Periodicals, Inc.

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Katz and Shapiro (1986) analyzed licensing by means of an auction. Kamien (1992) provided a nice review of the related literature.

(2013) and Marjit, Kabiraj, and Mukherjee (2000), respectively. Licensing in a Bertrand duopoly was analyzed in

Erkal (2005) and Wang and Yang (1999).

However, in reality, firms often adopt different or heterogeneous competition strategies, that is, some firms choose

a price‐setting strategy and the others a quantity‐setting strategy. For example, in the market for small cars, firms such

as Honda and Subaru set the quantity and let the price adjust to achieve market clearing, whereas firms such as Saturn

and Scion set the price and produce according to consumerorders (refer to V. J. Tremblay, Tremblay, and Isariyawongse

(2013)). Furthermore, Flath (2012) empirically tested the competition mode of 70, four‐digit standard industrial

classification Japanese manufacturing industries using annual data from 1961 to 1990. Flath found that the likelihood

function favors the Cournot, Bertrand, and hybrid (under which some firms choose a quantity strategy, while the others

choose a price strategy) specifications in 5, 35, and 30 industries, respectively.

The above facts reveal a gap between theory and reality. The first contribution of this study is to fill the

aforementioned gap, that is, it theoretically discusses licensing in a duopoly when firms may adopt different

strategies to compete in the final product market. The conclusions reached are stated as Proposition 1.

As can be inferred from Proposition 1, under licensing, variations in the market competition mode lead to a

change in the equilibrium profit. By being aware of the profit differential between different competition modes,

firms can strategically choose the competition strategy before licensing to achieve their most favorable competition

mode. An analysis of this issue—the endogenous formation of the market competition mode with licensing—

constitutes the second contribution of this study. Proposition 2 summarizes the conclusions reached.

Another feature of the previous licensing literature is that the market competition mode is set to be

exogenously determined. In other words, the market competition mode is the same with as well as without

licensing. Additionally, the welfare implications of licensing are concluded under this setting. However,

according to Faulí‐Oller and Sandonís (2002) and Mukherjee (2010), the introduction of licensing has changed

the profit differential between different competition modes. It follows that the equilibrium competition mode

with licensing and that without licensing might be different. This prompts a reconsideration of the welfare

effects of licensing, which is the third contribution of this study (refer to Proposition 3 and Proposition 4 for

the conclusions reached).

The remainder of this paper is organized as follows. Related literature is reviewed in the succeeding section.

Section 3 lists the basic model setup and introduces a three‐stage game. By solving the game backward, Section 4

explains the determination of the licensing policy and compares the relative dominance of price‐and quantity‐

setting strategies. The welfare implications of licensing are discussed in Section 5. Section 6 tests the robustness of

the conclusions of this study by introducing a third firm, making the initial cost difference endogenous, and

assuming that firms choose between price‐and quantity‐setting strategies post, rather than before, licensing.

Section 7 summarizes the main findings of this study. The proofs of lemmas, propositions, and results in this study

can be found in the Online Appendix.

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RELATED LITERATURE

The licensing literature discussed in the Introduction has extensively examined the case in which patents give their

owners perfect protection (also referred to as the iron‐clad patent). Recently, economists have begun to pay

attention to the licensing properties of a process innovation covered by a patent of uncertain validity. Pioneering

works in this area include (Amir, Encaoua, & Lefouili, 2014; Encaoua & Lefouili, 2009; Farrell & Shapiro, 2008).

By analyzing the endogenous formation of the market competition mode, this study also embeds literature on

the relative dominance of price‐and quantity‐setting strategies. In a duopoly, Singh and Vives (1984) proved that if

goods are substitutes and firms choose a competition strategy simultaneously and irrevocably before the final

NIU

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