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Existence of Equilibrium in A Differentiated Duopoly With Network Externalities

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  • L. Lambertini
  • R. 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 appears in consumer utility. Full market coverage is assumed. We show that the incentive to predate prevents firms to reach a pure strategy noncooperative 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. If the weight of network externalities exceeds that of hedonic satisfaction in consumer preferences, then predation is always a dominant strategy.

Suggested Citation

  • L. Lambertini & R. Orsini, 1998. "Existence of Equilibrium in A Differentiated Duopoly With Network Externalities," Working Papers 333, Dipartimento Scienze Economiche, Universita' di Bologna.
    • Handle: RePEc:bol:bodewp:333
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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Yuanzhu Lu & Sougata Poddar, 2015. "Strategic Choice of Network Externality," Working Papers 2015-03, Auckland University of Technology, Department of Economics.
    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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