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Price vs. Quantity in duopoly with strategic delegation: Role of network externalities

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  • Trishita Bhattacharjee

    (Indira Gandhi Institute of Development Research)

  • Rupayan Pal

    (Indira Gandhi Institute of Development Research)

Abstract

This paper examines the implications of network externalities on equilibrium outcomes in a differentiated products duopoly under strategic managerial delegation through relative performance based incentive contracts. It shows that Miller and Pazgal (2001)'s equivalence result does not go through in the presence of network externalities. Instead, Singh and Vives (1984)'s rankings of equilibrium outcomes under Cournot and Bertrand hold true under relative performance based delegation contracts as well, if there are network externalities. However, when firms can choose whether to compete in price or in quantity, there are two pure strategy Nash equilibria and one mixed strategy Nash equilibrium. Interestingly, in pure strategy Nash equilibria asymmetric competition occurs, where a firm competes in price and its rival firm competes in quantity. Further, the mixed strategy Nash equilibrium probability of a firm to compete in terms of price increases with the strength of network effects and is always greater than the probability to compete in terms of price.

Suggested Citation

  • Trishita Bhattacharjee & Rupayan Pal, 2013. "Price vs. Quantity in duopoly with strategic delegation: Role of network externalities," Indira Gandhi Institute of Development Research, Mumbai Working Papers 2013-010, Indira Gandhi Institute of Development Research, Mumbai, India.
    • Handle: RePEc:ind:igiwpp:2013-010
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    File URL: http://www.igidr.ac.in/pdf/publication/WP-2013-010.pdf
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    References listed on IDEAS

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    Cited by:

    1. A. A. Elsadany & A. M. Awad, 2019. "Dynamics and chaos control of a duopolistic Bertrand competitions under environmental taxes," Annals of Operations Research, Springer, vol. 274(1), pages 211-240, March.
    2. Yasuhiko Nakamura, 2015. "Endogenous Choice of Strategic Variables in an Asymmetric Duopoly with Respect to the Demand Functions that Firms Face," Manchester School, University of Manchester, vol. 83(5), pages 546-567, September.
    3. Luciano Fanti & Domenico Buccella, 2019. "When unionisation is profitable for firms in network industries," Metroeconomica, Wiley Blackwell, vol. 70(4), pages 711-722, November.
    4. Buccella Domenico & Fanti Luciano & Gori Luca, 2024. "Product Quality and Product Compatibility in Network Industries," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 24(1), pages 299-339, January.
    5. Jen-Yao Lee & Chen-Chia Fan & Chien-Shu Tsai, 2023. "Network Externalities and Downstream Collusion under Asymmetric Costs: A Note," Games, MDPI, vol. 14(2), pages 1-11, March.
    6. Luciano Fanti & Domenico Buccella, 2017. "Profit raising entry effects in network industries with Corporate Social Responsibility," Economics and Business Letters, Oviedo University Press, vol. 6(3), pages 59-68.
    7. Yasuhiko Nakamura, 2017. "Choosing Price or Quantity? The Role of Delegation and Network Externalities in a Mixed Duopoly," Australian Economic Papers, Wiley Blackwell, vol. 56(2), pages 174-200, June.
    8. Rupayan Pal, 2014. "Price and quantity competition in network goods duopoly: a reversal result," Economics Bulletin, AccessEcon, vol. 34(2), pages 1019-1027.
    9. Yasuhiko Nakamura, 2021. "Price versus quantity in a duopoly with network externalities under active and passive expectations," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 42(1), pages 120-133, January.
    10. Buccella, Domenico & Fanti, Luciano, 2020. "Do labour union recognition and bargaining deter entry in a network industry? A sequential game model," Utilities Policy, Elsevier, vol. 64(C).
    11. Luciano Fanti & Nicola Meccheri, 2015. "On the Cournot–Bertrand Profit Differential and the Structure of Unionisation in a Managerial Duopoly," Australian Economic Papers, Wiley Blackwell, vol. 54(4), pages 266-287, December.
    12. Chirco, Alessandra & Scrimitore, Marcella, 2013. "Choosing price or quantity? The role of delegation and network externalities," Economics Letters, Elsevier, vol. 121(3), pages 482-486.
    13. Anomita Ghosh & Rupayan Pal, 2014. "Strategic trade policy for network goods oligopolies," Indira Gandhi Institute of Development Research, Mumbai Working Papers 2014-039, Indira Gandhi Institute of Development Research, Mumbai, India.

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    More about this item

    Keywords

    Symmetric competition; Price competition; Network externalities; Quantity competition; Relative performance contract; Strategic delegation;
    All these keywords.

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L22 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Firm Organization and Market Structure
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory

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