Hotelling competition and the gamma distribution

• 成果类型: Article
• 署名作者: Tarbush, Bassel
• 署名单位: University of Oxford
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2018.06.009
• 发表日期: 2018
• 页码: 222-240
• 关键词: Spatial games; Hotelling's pure location game; market structure; Statistical spacings; gamma distribution

摘要

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. (C) 2018 Elsevier Inc. All rights reserved.