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The possibility of mixed-strategy equilibria with constant-returns-to-scale technology under Bertrand competition

Author

Listed:
  • Todd R. Kaplan

    () (Department of Economics, Ben-Gurion University of the Negev, P.O.B. 653, Beer-Sheva, Israel 84105)

  • David Wettstein

    () (Department of Economics, Ben-Gurion University of the Negev, P.O.B. 653, Beer-Sheva, Israel 84105)

Abstract

We analyze the Nash equilibria of a standard Bertrand model. We show that in addition to the marginal-cost pricing equilibrium there is a possibility for mixed-strategy equilibria yielding positive profit levels. We characterize these equilibria and find that having unbounded revenues is the necessary and sufficient condition for their existence. Hence, we demonstrate that under realistic assumptions the only equilibrium is marginal-cost pricing.

Suggested Citation

  • Todd R. Kaplan & David Wettstein, 2000. "The possibility of mixed-strategy equilibria with constant-returns-to-scale technology under Bertrand competition," Spanish Economic Review, Springer;Spanish Economic Association, vol. 2(1), pages 65-71.
  • Handle: RePEc:spr:specre:v:2:y:2000:i:1:p:65-71
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    Citations

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    Cited by:

    1. Hoernig, Steffen, 2005. "Bertrand Equilibria and Sharing Rules," CEPR Discussion Papers 4972, C.E.P.R. Discussion Papers.
    2. Ludovic Julien, 2011. "A note on Stackelberg competition," Journal of Economics, Springer, vol. 103(2), pages 171-187, June.
    3. Hoernig, Steffen H., 2002. "Mixed Bertrand equilibria under decreasing returns to scale: an embarrassment of riches," Economics Letters, Elsevier, vol. 74(3), pages 359-362, February.
    4. Jann, Ole & Schottmüller, Christoph, 2015. "Correlated equilibria in homogeneous good Bertrand competition," Journal of Mathematical Economics, Elsevier, vol. 57(C), pages 31-37.
    5. Marie-Laure Cabon-Dhersin & Nicolas Drouhin, 2014. "Tacit Collusion in a One-Shot Game of Price Competition with Soft Capacity Constraints," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 23(2), pages 427-442, June.
    6. Marie-Laure Cabon-Dhersin & Nicolas Drouhin, 2012. "Tacit collusion in a one-shot game of price competition with soft capacity constraints," Working Papers hal-00709093, HAL.
    7. Beschorner, Patrick F. E., 2003. "Risk classification and cream skimming on the deregulated German insurance market," W.E.P. - Würzburg Economic Papers 37, University of Würzburg, Chair for Monetary Policy and International Economics.
    8. João Correia-da-Silva & Joana Pinho & Hélder Vasconcelos, 2016. "Sustaining collusion in markets with entry driven by balanced growth," Journal of Economics, Springer, vol. 118(1), pages 1-34, May.
    9. Robert R. Routledge, 2009. "On the existence of Bayesian Bertrand equilibrium," The School of Economics Discussion Paper Series 0917, Economics, The University of Manchester.
    10. repec:hal:journl:halshs-00542486 is not listed on IDEAS
    11. Saporiti Alejandro & Coloma Germán, 2010. "Bertrand Competition in Markets with Fixed Costs," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-30, June.
    12. repec:spr:etbull:v:3:y:2015:i:1:d:10.1007_s40505-014-0049-1 is not listed on IDEAS
    13. Kaplan, Todd R. & Luski, Israel & Wettstein, David, 2003. "Innovative activity and sunk cost," International Journal of Industrial Organization, Elsevier, vol. 21(8), pages 1111-1133, October.
    14. repec:eee:inecon:v:106:y:2017:i:c:p:134-142 is not listed on IDEAS
    15. Todd R. Kaplan & Shmuel Zamir, 2015. "Multiple equilibria in asymmetric first-price auctions," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 65-77, April.
    16. Alejandro Saporiti & German Coloma, 2008. "Bertrand's price competition in markets with fixed costs," RCER Working Papers 541, University of Rochester - Center for Economic Research (RCER).
    17. Steffen Hoernig, 2007. "Bertrand Games and Sharing Rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(3), pages 573-585, June.
    18. Cole, Matthew T. & Davies, Ronald B. & Kaplan, Todd, 2017. "Protection in government procurement auctions," Journal of International Economics, Elsevier, vol. 106(C), pages 134-142.
    19. Routledge, Robert R., 2010. "Bertrand competition with cost uncertainty," Economics Letters, Elsevier, vol. 107(3), pages 356-359, June.

    More about this item

    Keywords

    Bertrand; price competition;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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