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Duopoly models with a joint capacity constraint

Author

Listed:
  • Aiyuan Tao

    (Shanghai Lixin University of Accounting and Finance)

  • X. Henry Wang

    (University of Missouri-Columbia)

  • Bill Z. Yang

    (Georgia Southern University)

Abstract

This paper extends two recent models of duopoly with a joint capacity constraint (Nie and Chen in Econ Model 29:1715–1721, 2012; Nie in J Econ 112(3):283–294, 2014) by relaxing their crucial assumption that the game has an equilibrium which is unique and interior. Instead, this paper tackles a more basic issue on when their assumption applies. Our investigation is undertaken by using the best-response curve analysis. Both standard duopoly and mixed duopoly are considered, and both simultaneous moves and sequential moves are investigated. We find that their assumption applies only when the constraint is sufficiently weak, otherwise the equilibrium is either non-unique or corner.

Suggested Citation

  • Aiyuan Tao & X. Henry Wang & Bill Z. Yang, 2018. "Duopoly models with a joint capacity constraint," Journal of Economics, Springer, vol. 125(2), pages 159-172, October.
    • Handle: RePEc:kap:jeczfn:v:125:y:2018:i:2:d:10.1007_s00712-018-0597-1
    DOI: 10.1007/s00712-018-0597-1
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    References listed on IDEAS

    as
    1. Lin Liu & X. Henry Wang & Bill Z. Yang, 2012. "Strategic Choice of Channel Structure in an Oligopoly," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 33(7-8), pages 565-574, October.
    2. Avinash Dixit, 1979. "A Model of Duopoly Suggesting a Theory of Entry Barriers," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 20-32, Spring.
    3. Shapiro, Carl, 1989. "Theories of oligopoly behavior," Handbook of Industrial Organization, in: R. Schmalensee & R. Willig (ed.), Handbook of Industrial Organization, edition 1, volume 1, chapter 6, pages 329-414, Elsevier.
    4. Francisco Facchinei & Christian Kanzow, 2010. "Generalized Nash Equilibrium Problems," Annals of Operations Research, Springer, vol. 175(1), pages 177-211, March.
    5. Nie, Pu-yan & Chen, You-hua, 2012. "Duopoly competitions with capacity constrained input," Economic Modelling, Elsevier, vol. 29(5), pages 1715-1721.
    6. William C. Merrill & Norman Schneider, 1966. "Government Firms in Oligopoly Industries: A Short-Run Analysis," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 80(3), pages 400-412.
    7. Ewerhart, Christian, 2014. "Cournot games with biconcave demand," Games and Economic Behavior, Elsevier, vol. 85(C), pages 37-47.
    8. R. Schmalensee & R. Willig (ed.), 1989. "Handbook of Industrial Organization," Handbook of Industrial Organization, Elsevier, edition 1, volume 2, number 2.
    9. Judy Hsu & X. Wang, 2005. "On Welfare under Cournot and Bertrand Competition in Differentiated Oligopolies," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 27(2), pages 185-191, September.
    10. X. Wang & Bill Yang, 2010. "The sunk-cost effect and optimal two-part pricing," Journal of Economics, Springer, vol. 101(2), pages 133-148, October.
    11. de Fraja, Giovanni & Delbono, Flavio, 1989. "Alternative Strategies of a Public Enterprise in Oligopoly," Oxford Economic Papers, Oxford University Press, vol. 41(2), pages 302-311, April.
    12. R. Schmalensee & R. Willig (ed.), 1989. "Handbook of Industrial Organization," Handbook of Industrial Organization, Elsevier, edition 1, volume 1, number 1.
    13. Pu-yan Nie, 2014. "Effects of capacity constraints on mixed duopoly," Journal of Economics, Springer, vol. 112(3), pages 283-294, July.
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    Cited by:

    1. Orlando, Giuseppe, 2022. "Simulating heterogeneous corporate dynamics via the Rulkov map," Structural Change and Economic Dynamics, Elsevier, vol. 61(C), pages 32-42.
    2. Nie, Pu-yan & Wang, Chan & Wen, Hong-xing, 2021. "Horizontal mergers under uniform resource constraints," Journal of Retailing and Consumer Services, Elsevier, vol. 63(C).
    3. You-hua Chen & Chan Wang & Pu-yan Nie, 2020. "Emission regulation of conventional energy-intensive industries," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 22(4), pages 3723-3737, April.

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    More about this item

    Keywords

    Duopoly; Mixed duopoly; Joint capacity constraint;
    All these keywords.

    JEL classification:

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

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