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Bertrand Competition under Network Externalities

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  • Masaki Aoyagi

Abstract

Two sellers engage in price competition to attract buyers located on a network. The value of the good of either seller to any buyer depends on the number of neighbors on the network who consume the same good. For a generic specification of consumption externalities, we show that an equilibrium price equals the marginal cost if and only if the buyer network is complete or cyclic. When the externalities are approximately linear in the size of consumption, we identify the classes of networks in which one of the sellers monopolizes the market, or the two sellers segment the market.

Suggested Citation

  • Masaki Aoyagi, 2013. "Bertrand Competition under Network Externalities," ISER Discussion Paper 0884, Institute of Social and Economic Research, The University of Osaka.
    • Handle: RePEc:dpr:wpaper:0884
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    File URL: https://www.iser.osaka-u.ac.jp/static/resources/docs/dp/2013/DP0884.pdf
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    2. Tavasoli, Ali & Fazli, Mehrdad & Ardjmand, Ehsan & Young, William A. & Shakeri, Heman, 2023. "Competitive pricing under local network effects," European Journal of Operational Research, Elsevier, vol. 311(2), pages 545-566.
    3. Vives, Xavier & Vravosinos, Orestis, 2024. "Strategic complementarity in games," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    4. Masaki Aoyagi, 2022. "Many-to-Many Matching on a Skill-Sharing Platform," ISER Discussion Paper 1186, Institute of Social and Economic Research, The University of Osaka.
    5. Chengqing Li & Junjie Zhou, 2025. "Price Regulation with Spillovers," Papers 2508.17301, arXiv.org.
    6. Shixun Wang & Lihong Yang, 2022. "The Network Structure of Innovation Networks," Networks and Spatial Economics, Springer, vol. 22(1), pages 65-96, March.
    7. Tolotti, Marco & Yepez, Jorge, 2020. "Hotelling-Bertrand duopoly competition under firm-specific network effects," Journal of Economic Behavior & Organization, Elsevier, vol. 176(C), pages 105-128.
    8. 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.
    9. Tamás Sebestyén & Balázs Szabó, 2022. "Market interaction structure and equilibrium price heterogeneity in monopolistic competition," Netnomics, Springer, vol. 22(2), pages 259-282, October.
    10. Goyal, S., 2016. "Networks and Markets," Cambridge Working Papers in Economics 1652, Faculty of Economics, University of Cambridge.
    11. Li, Guopeng & Wang, Sijie & Xiong, Yifan & Zhu, Feng, 2025. "Pricing negative externalities in social networks," Journal of Mathematical Economics, Elsevier, vol. 118(C).
    12. 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.
    13. Zenou, Yves & Chen, Ying-Ju & Zhou, Junjie, 2020. "Network Topology and Market Structure," CEPR Discussion Papers 14495, C.E.P.R. Discussion Papers.
    14. Sanjeev Goyal, 2015. "Networks in Economics: A Perspective on the Literature," Cambridge Working Papers in Economics 1548, Faculty of Economics, University of Cambridge.
    15. 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.
    16. 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).
    17. Yunmiao Gui & Huihui Zhai & Feng Dong, 2025. "Value-added services decisions of bilateral platform with user expectation and resources constraint," Electronic Commerce Research, Springer, vol. 25(4), pages 2765-2793, August.
    18. 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.
    19. Masaki Aoyagi, 2020. "Connecting Heterogeneous Agents under Incomplete Information," ISER Discussion Paper 1089, Institute of Social and Economic Research, The University of Osaka.

    More about this item

    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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