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Hotelling competition and the gamma distribution

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  • Tarbush, Bassel

Abstract

I show that in any symmetric Nash equilibrium of Hotelling's pure location game, as the number of firms becomes large, the limiting distribution of market shares converges to a Gamma(2,2) distribution. Remarkably, this is true regardless of the distribution of consumers. The proof for the invariance of the limiting market share distribution builds on results from the theory of statistical spacings.

Suggested Citation

  • Tarbush, Bassel, 2018. "Hotelling competition and the gamma distribution," Games and Economic Behavior, Elsevier, vol. 111(C), pages 222-240.
    • Handle: RePEc:eee:gamebe:v:111:y:2018:i:c:p:222-240
    DOI: 10.1016/j.geb.2018.06.009
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    Cited by:

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    More about this item

    Keywords

    Spatial games; Hotelling's pure location game; Market structure; Statistical spacings; Gamma distribution;
    All these keywords.

    JEL classification:

    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D30 - Microeconomics - - Distribution - - - General

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