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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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    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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