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Bertrand Equilibria and Sharing Rules

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  • Hoernig, Steffen

Abstract

We analyze how sharing rules affect Nash equilibria in Bertrand games, where the sharing of profits at ties is a decisive assumption. Necessary conditions for either positive or zero equilibrium profits are derived. Zero profit equilibria are shown to exist under weak conditions if the sharing rule is sign-preserving. For Bertrand markets we define the class of expectation sharing rules, where profits at ties are derived from some distribution of quantities. In this class the winner-take-all sharing rule is the only one that is always sign-preserving, while for each pair of demand and cost functions there may be many others.

Suggested Citation

  • Hoernig, Steffen, 2005. "Bertrand Equilibria and Sharing Rules," FEUNL Working Paper Series wp468, Universidade Nova de Lisboa, Faculdade de Economia.
  • Handle: RePEc:unl:unlfep:wp468
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    References listed on IDEAS

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    1. Dastidar, Krishnendu Ghosh, 1995. "On the Existence of Pure Strategy Bertrand Equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 19-32, January.
    2. Simon, Leo K & Zame, William R, 1990. "Discontinuous Games and Endogenous Sharing Rules," Econometrica, Econometric Society, vol. 58(4), pages 861-872, July.
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    4. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    5. John Morgan & Michael R. Baye, 2002. "Winner-take-all price competition," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(2), pages 271-282.
    6. Baye, Michael R. & Morgan, John, 1999. "A folk theorem for one-shot Bertrand games," Economics Letters, Elsevier, vol. 65(1), pages 59-65, October.
    7. 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.
    8. Osborne, Martin J. & Pitchik, Carolyn, 1986. "Price competition in a capacity-constrained duopoly," Journal of Economic Theory, Elsevier, vol. 38(2), pages 238-260, April.
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    1. 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.

    More about this item

    Keywords

    Bertrand games; Sharing rule; Tie-breaking rule; Sign-preserving sharing rules; Expectation sharing rules;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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