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Bertrand competition under network externalities

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  • Aoyagi, Masaki

Abstract

Two firms engage in price competition to attract buyers located on a network. The value of the good of either firm to any buyer depends on the number of neighbors on the network who adopt the same good. When the size of externalities increases linearly with the number of adoptions, we identify the set of pricing strategies that are consistent with an equilibrium in which one of the firms monopolizes the market. The set includes marginal cost (MC) pricing as well as bipartition pricing, which offers discounts to some buyers and charges markups to others. We show that MC pricing fails to be an equilibrium under non-linear externalities in a general network, but identify conditions for an equilibrium with bipartition pricing to be robust against perturbations in the externalities from linearity. The analysis is applied to platform competition in a two-sided market under local and approximately linear externalities.

Suggested Citation

  • Aoyagi, Masaki, 2018. "Bertrand competition under network externalities," Journal of Economic Theory, Elsevier, vol. 178(C), pages 517-550.
    • Handle: RePEc:eee:jetheo:v:178:y:2018:i:c:p:517-550
    DOI: 10.1016/j.jet.2018.10.006
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    2. Ying‐Ju Chen & Yves Zenou & Junjie Zhou, 2018. "Competitive pricing strategies in social networks," RAND Journal of Economics, RAND Corporation, vol. 49(3), pages 672-705, September.
    3. Masaki Aoyagi, 2022. "Many-to-Many Matching on a Skill-Sharing Platform," ISER Discussion Paper 1186, Institute of Social and Economic Research, Osaka University.
    4. Shixun Wang & Lihong Yang, 2022. "The Network Structure of Innovation Networks," Networks and Spatial Economics, Springer, vol. 22(1), pages 65-96, March.
    5. Ningyuan Chen & Ying-Ju Chen, 2021. "Duopoly Competition with Network Effects in Discrete Choice Models," Operations Research, INFORMS, vol. 69(2), pages 545-559, March.
    6. Tamás Sebestyén & Balázs Szabó, 2022. "Market interaction structure and equilibrium price heterogeneity in monopolistic competition," Netnomics, Springer, vol. 22(2), pages 259-282, October.
    7. Goyal, S., 2016. "Networks and Markets," Cambridge Working Papers in Economics 1652, Faculty of Economics, University of Cambridge.
    8. Zenou, Yves & Chen, Ying-Ju & Zhou, Junjie, 2020. "Network Topology and Market Structure," CEPR Discussion Papers 14495, C.E.P.R. Discussion Papers.
    9. Sanjeev Goyal, 2015. "Networks in Economics: A Perspective on the Literature," Cambridge Working Papers in Economics 1548, Faculty of Economics, University of Cambridge.
    10. Vintila Alexandra & Roman Mihai Daniel, 2021. "Bertrand competition under asymmetric conditions," Proceedings of the International Conference on Business Excellence, Sciendo, vol. 15(1), pages 235-244, December.
    11. Chen, Ying-Ju & Zenou, Yves & Zhou, Junjie, 2022. "The impact of network topology and market structure on pricing," Journal of Economic Theory, Elsevier, vol. 204(C).
    12. Ryo Itoh & Zonghui Li, 2021. "Effects of dual networks on tax strategies: geography and transaction," The Japanese Economic Review, Springer, vol. 72(1), pages 97-128, January.
    13. Masaki Aoyagi, 2020. "Connecting Heterogeneous Agents under Incomplete Information," ISER Discussion Paper 1089, Institute of Social and Economic Research, Osaka University.

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    More about this item

    Keywords

    Divide and conquer; Price discrimination; Two-sided markets; Local externalities;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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