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Price competition with population uncertainty

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  • Ritzberger, Klaus

Abstract

The Bertrand paradox holds that price competition among at least two firms eliminates all profits in equilibrium, when firms have identical constant marginal costs. This assumes that the number of competitors is common knowledge among firms. If firms are uncertain about the number of their competitors, there is no pure strategy equilibrium. But in mixed strategies an equilibrium exists. In this equilibrium it takes a large market to wipe out profits. Thus, with population uncertainty, two are not enough for competition.

Suggested Citation

  • Ritzberger, Klaus, 2009. "Price competition with population uncertainty," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 145-157, September.
  • Handle: RePEc:eee:matsoc:v:58:y:2009:i:2:p:145-157
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    References listed on IDEAS

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    1. Janssen, Maarten & Rasmusen, Eric, 2002. "Bertrand Competition under Uncertainty," Journal of Industrial Economics, Wiley Blackwell, vol. 50(1), pages 11-21, March.
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    5. Roger B. Myerson, 1998. "Population uncertainty and Poisson games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 375-392.
    6. Myerson, Roger B., 2000. "Large Poisson Games," Journal of Economic Theory, Elsevier, vol. 94(1), pages 7-45, September.
    7. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Oxford University Press, vol. 53(1), pages 1-26.
    8. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," Review of Economic Studies, Oxford University Press, vol. 53(1), pages 27-41.
    9. 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.
    10. Thepot, Jacques, 1995. "Bertrand oligopoly with decreasing returns to scale," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 689-718.
    11. Spulber, Daniel F, 1995. "Bertrand Competition When Rivals' Costs Are Unknown," Journal of Industrial Economics, Wiley Blackwell, vol. 43(1), pages 1-11, March.
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    Cited by:

    1. repec:spr:dyngam:v:7:y:2017:i:3:d:10.1007_s13235-016-0197-z is not listed on IDEAS
    2. Meroni, Claudia & Pimienta, Carlos, 2017. "The structure of Nash equilibria in Poisson games," Journal of Economic Theory, Elsevier, vol. 169(C), pages 128-144.
    3. De Sinopoli, Francesco & Meroni, Claudia & Pimienta, Carlos, 2014. "Strategic stability in Poisson games," Journal of Economic Theory, Elsevier, vol. 153(C), pages 46-63.
    4. Pierre Bernhard & Marc Deschamps, 2017. "On Dynamic Games with Randomly Arriving Players," Dynamic Games and Applications, Springer, vol. 7(3), pages 360-385, September.
    5. Kultti Klaus, 2011. "Sellers Like Clusters," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-28, December.

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