Hotelling Competition and the Gamma Distribution
Posted: 30 Aug 2017 Last revised: 28 Sep 2019
Date Written: September 18, 2018
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
JEL Classification: D21, D30
Suggested Citation: Suggested Citation
Tarbush, Bassel, Hotelling Competition and the Gamma Distribution (September 18, 2018). Games and Economic Behavior, Vol. 111, 2018, Available at SSRN: https://ssrn.com/abstract=3022629 or http://dx.doi.org/10.2139/ssrn.3022629
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