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Judo Economics in Markets with Multiple Firms

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  • 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.

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Bibliographic Info

Paper provided by Otto-von-Guericke University Magdeburg, Faculty of Economics and Management in its series FEMM Working Papers with number 130013.

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Length: 27 pages
Date of creation: Jul 2013
Date of revision:
Handle: RePEc:mag:wpaper:130013

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

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References

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  1. Boyer, Marcel & Moreaux, Michel, 1986. "Perfect competition as the limit of a hierarchical market game," Economics Letters, Elsevier, Elsevier, vol. 22(2-3), pages 115-118.
  2. Daniel Cracau, 2013. "Judo Economics in Markets with Asymmetric Firms," FEMM Working Papers, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management 130002, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
  3. Federico Etro, 2006. "Aggressive leaders," RAND Journal of Economics, RAND Corporation, RAND Corporation, vol. 37(1), pages 146-154, 03.
  4. Robson, Arthur J, 1990. "Stackelberg and Marshall," American Economic Review, American Economic Association, American Economic Association, vol. 80(1), pages 69-82, March.
  5. Judith R. Gelman & Steven C. Salop, 1983. "Judo Economics: Capacity Limitation and Coupon Competition," Bell Journal of Economics, The RAND Corporation, The RAND Corporation, vol. 14(2), pages 315-325, Autumn.
  6. Beth Allen & Raymond Deneckere & Tom Faith & Dan Kovenock, 1994. "Capacity Precommitment as a Barrier to Entry:A Bertrand-Edgeworth Approach," Industrial Organization, EconWPA 9411002, EconWPA, revised 14 Nov 1994.
  7. Sorgard, Lars, 1997. "Judo economics reconsidered: Capacity limitation, entry and collusion," International Journal of Industrial Organization, Elsevier, Elsevier, vol. 15(3), pages 349-368, May.
  8. Furth, D. & Kovenock, D., 1990. "Price Leadership In A Duopoly With Capacity Constraints And Product Differentiation," Purdue University Economics Working Papers, Purdue University, Department of Economics 992, Purdue University, Department of Economics.
  9. repec:rje:randje:v:37:y:2006:1:p:146-154 is not listed on IDEAS
  10. B. Curtis Eaton & Roger Ware, 1987. "A Theory of Market Structure with Sequential Entry," RAND Journal of Economics, The RAND Corporation, The RAND Corporation, vol. 18(1), pages 1-16, Spring.
  11. Vives, Xavier, 1988. "Sequential entry, industry structure and welfare," European Economic Review, Elsevier, Elsevier, vol. 32(8), pages 1671-1687, October.
  12. Ludovic Julien & Olivier Musy & Aurélien Saïdi, 2012. "On hierarchical competition in oligopoly," Journal of Economics, Springer, Springer, vol. 107(3), pages 217-237, November.
  13. Federico Etro, 2008. "Stackelberg Competition with Endogenous Entry," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 118(532), pages 1670-1697, October.
  14. Anderson, Simon P. & Engers, Maxim, 1992. "Stackelberg versus Cournot oligopoly equilibrium," International Journal of Industrial Organization, Elsevier, Elsevier, vol. 10(1), pages 127-135, March.
  15. Abdolkarim Sadrieh & Daniel Cracau, 2013. "Coexistence of small and dominant firms in Bertrand competition: Judo economics in the lab," FEMM Working Papers, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management 130001, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
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