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The Existence Of Equilibrium In A Differentiated Duopoly With Network Externalities

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  • LUCA LAMBERTINI
  • RAIMONDELLO ORSINI

Abstract

The existence of a pure‐strategy subgame‐perfect equilibrium in qualities and prices is investigated in a duopoly model of vertical differentiation where quality improvements require a quadratic variable cost and network externalities operate. We show that there exists a parameter region where the incentive to predate at the quality stage prevents firms from reaching a pure‐strategy non‐cooperative equilibrium with prices above marginal costs. If network externalities are sufficiently large, a Bertrand equilibrium with zero profits may arise, although the amount of product differentiation is strictly positive.

Suggested Citation

  • Luca Lambertini & Raimondello Orsini, 2005. "The Existence Of Equilibrium In A Differentiated Duopoly With Network Externalities," The Japanese Economic Review, Japanese Economic Association, vol. 56(1), pages 55-66, March.
    • Handle: RePEc:bla:jecrev:v:56:y:2005:i:1:p:55-66
    DOI: 10.1111/j.1468-5876.2005.00300.x
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    1. Tsuyoshi Toshimitsu, 2023. "The Impact of Compatibility on Incentives to Innovate in a Network Goods Market: A Duopoly Case," Discussion Paper Series 253, School of Economics, Kwansei Gakuin University.
    2. Eaton, Derek, 2015. "Innovation and IPRs for Agricultural Crop Varieties as Intermediate Goods," 2015 Conference, August 9-14, 2015, Milan, Italy 211581, International Association of Agricultural Economists.
    3. Yuanzhu Lu & Sougata Poddar, 2015. "Strategic Choice of Network Externality," Working Papers 2015-03, Auckland University of Technology, Department of Economics.
    4. Matsumura, Toshihiro & Matsushima, Noriaki, 2007. "Congestion-reducing investments and economic welfare in a Hotelling model," Economics Letters, Elsevier, vol. 96(2), pages 161-167, August.
    5. Luca Lambertini & Raimondello Orsini, 2013. "On Hotelling's ‘stability in competition’ with network externalities and switching costs," Papers in Regional Science, Wiley Blackwell, vol. 92(4), pages 873-883, November.
    6. Wu, Di & Sun, Ji & Wang, Leonard F.S. & Liu, Huizhong, 2024. "Network externalities in a vertically differentiated luxury goods market," Mathematical Social Sciences, Elsevier, vol. 128(C), pages 100-109.
    7. Francesco Angelini & Corrado Benassi & Massimiliano Castellani, 2021. "Platform competition and willingness to pay in a vertical differentiated two-sided market," Economics Bulletin, AccessEcon, vol. 41(2), pages 772-780.
    8. Eaton, Derek, 2014. "A model of IPRs in the international supply chain of seeds and agricultural production," 2014 International Congress, August 26-29, 2014, Ljubljana, Slovenia 182643, European Association of Agricultural Economists.
    9. Charu Grover & Sangeeta Bansal, 2021. "Effect of green network and emission tax on consumer choice under discrete continuous framework," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 23(4), pages 641-666, October.
    10. Yuanzhu Lu & Sougata Poddar, 2018. "Strategic Choice of Network Externality and Its Impact on Digital Piracy," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 52(1), pages 139-160, February.
    11. L. Lambertini & R. Orsini, 1998. "Monopoly, Quality, and Network Externalities," Working Papers 334, Dipartimento Scienze Economiche, Universita' di Bologna.
    12. Derek Eaton, 2013. "Innovation and IPRs in the Agricultural Seed Sector," CIES Research Paper series 19-2013, Centre for International Environmental Studies, The Graduate Institute.

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