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Judo Economics in Markets with Multiple Firms

Author

Listed:
  • Daniel Cracau

    () (Faculty of Economics and Management, Otto-von-Guericke University Magdeburg)

  • Benjamin Franz

    () (University of Oxford, Mathematical Institute)

Abstract

We study a sequential Bertrand game with one dominant market incumbent and multiple small entrants selling homogeneous products. Whilst the equilibrium for the case of a single entrant is well-known from Gelman and Salop (1983), we derive properties of the N-firm equilibrium and present an algorithm that can be used to calculate this equilibrium. Using this algorithm we derive the exact equilibrium for the cases of two and three small entrants. For more than three entrants only approximate results are possible. We use numerical results to gain further understanding of the equilibrium for an increasing number of firms and in particular for the case where N diverges to infinity. Similarly to the two-firm Judo equilibrium, we see that a capacity limitation for the small rms is necessary to achieve positive profits.

Suggested Citation

  • Daniel Cracau & Benjamin Franz, 2013. "Judo Economics in Markets with Multiple Firms," FEMM Working Papers 130013, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
  • Handle: RePEc:mag:wpaper:130013
    as

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    File URL: http://www.fww.ovgu.de/fww_media/femm/femm_2013/2013_13.pdf
    File Function: First version, 2011
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    References listed on IDEAS

    as
    1. Sorgard, Lars, 1997. "Judo economics reconsidered: Capacity limitation, entry and collusion," International Journal of Industrial Organization, Elsevier, vol. 15(3), pages 349-368, May.
    2. B. Curtis Eaton & Roger Ware, 1987. "A Theory of Market Structure with Sequential Entry," RAND Journal of Economics, The RAND Corporation, vol. 18(1), pages 1-16, Spring.
    3. Cracau, Daniel, 2013. "Judo economics in markets with asymmetric firms," Economics Letters, Elsevier, vol. 119(1), pages 35-37.
    4. Ludovic Julien & Olivier Musy & Aurélien Saïdi, 2012. "On hierarchical competition in oligopoly," Journal of Economics, Springer, vol. 107(3), pages 217-237, November.
    5. Anderson, Simon P. & Engers, Maxim, 1992. "Stackelberg versus Cournot oligopoly equilibrium," International Journal of Industrial Organization, Elsevier, vol. 10(1), pages 127-135, March.
    6. Daniel Cracau & Abdolkarim Sadrieh, 2016. "Coexistence of Small and Dominant Firms in Bertrand Competition: Judo Economics in the Lab," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 172(4), pages 665-693, December.
    7. Robson, Arthur J, 1990. "Stackelberg and Marshall," American Economic Review, American Economic Association, vol. 80(1), pages 69-82, March.
    8. Judith R. Gelman & Steven C. Salop, 1983. "Judo Economics: Capacity Limitation and Coupon Competition," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 315-325, Autumn.
    9. Dan Kovenock & Raymond Deneckere & Tom Faith & Beth Allen, 2000. "Capacity precommitment as a barrier to entry: A Bertrand-Edgeworth approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(3), pages 501-530.
    10. Dave Furth & Dan Kovenock, 1993. "Price leadership in a duopoly with capacity constraints and product differentiation," Journal of Economics, Springer, vol. 57(1), pages 1-35, February.
    11. Federico Etro, 2008. "Stackelberg Competition with Endogenous Entry," Economic Journal, Royal Economic Society, vol. 118(532), pages 1670-1697, October.
    12. Boyer, Marcel & Moreaux, Michel, 1986. "Perfect competition as the limit of a hierarchical market game," Economics Letters, Elsevier, vol. 22(2-3), pages 115-118.
    13. Vives, Xavier, 1988. "Sequential entry, industry structure and welfare," European Economic Review, Elsevier, vol. 32(8), pages 1671-1687, October.
    14. repec:rje:randje:v:37:y:2006:1:p:146-154 is not listed on IDEAS
    15. Federico Etro, 2006. "Aggressive leaders," RAND Journal of Economics, RAND Corporation, vol. 37(1), pages 146-154, March.
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    More about this item

    Keywords

    Sequential Bertrand Competition; Judo Economics; N-firm oligopoly;

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms

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