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Judo Economics in Markets with Multiple Firms

  • Daniel Cracau

    ()

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

  • Benjamin Franz

    ()

    (University of Oxford, Mathematical Institute)

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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File URL: http://www.fww.ovgu.de/fww_media/femm/femm_2013/2013_13.pdf
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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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Web page: http://www.ww.uni-magdeburg.de

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  1. 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.
  2. Daniel Cracau, 2013. "Judo Economics in Markets with Asymmetric Firms," FEMM Working Papers 130002, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
  3. Allen, B. & Deneckere, R. & Faith, T. & Kovenock, D., 1994. "Capacity Precommitment as a Barrier to Entry: A Bertrand-Edgeworth Approach," Purdue University Economics Working Papers 1062, Purdue University, Department of Economics.
  4. Robson, Arthur J, 1990. "Stackelberg and Marshall," American Economic Review, American Economic Association, vol. 80(1), pages 69-82, March.
  5. Federico Etro, 2006. "Aggressive leaders," RAND Journal of Economics, RAND Corporation, vol. 37(1), pages 146-154, 03.
  6. Federico Etro, 2007. "Stackelberg competition with endogenous entry," Working Papers 121, University of Milano-Bicocca, Department of Economics, revised 2007.
  7. Sorgard, L., 1995. "Judo Economics Reconsidered: Capacity Limitation, Entry and Collusion," Papers 18/95, Norwegian School of Economics and Business Administration-.
  8. Vives, Xavier, 1988. "Sequential entry, industry structure and welfare," European Economic Review, Elsevier, vol. 32(8), pages 1671-1687, October.
  9. repec:rje:randje:v:37:y:2006:1:p:146-154 is not listed on IDEAS
  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. 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.
  12. Abdolkarim Sadrieh & Daniel Cracau, 2013. "Coexistence of small and dominant firms in Bertrand competition: Judo economics in the lab," FEMM Working Papers 130001, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
  13. Ludovic Julien & Olivier Musy & Aurélien Saïdi, 2012. "On hierarchical competition in oligopoly," Journal of Economics, Springer, vol. 107(3), pages 217-237, November.
  14. Anderson, Simon P. & Engers, Maxim, 1992. "Stackelberg versus Cournot oligopoly equilibrium," International Journal of Industrial Organization, Elsevier, vol. 10(1), pages 127-135, March.
  15. 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.
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