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Bertrand Equilibria and Sharing Rules

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  • Hoernig, Steffen

Abstract

We analyse 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-takes-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," CEPR Discussion Papers 4972, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:4972
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    Cited by:

    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.

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    More about this item

    Keywords

    Bertrand games; Sharing rule; Tie-breaking rule; Sign-preserving sharing rules; Expectation sharing rules;
    All these keywords.

    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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