Hotelling competition and the gamma distribution

Bassel Tarbush

Games and Economic Behavior, 2018, vol. 111, issue C, 222-240

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.

Keywords: Spatial games; Hotelling's pure location game; Market structure; Statistical spacings; Gamma distribution (search for similar items in EconPapers)
JEL-codes: D21 D30 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:111:y:2018:i:c:p:222-240

DOI: 10.1016/j.geb.2018.06.009

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