Generalising Bertrand competition: a special case of the Hotelling model

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• 作者：Manzur Rashid
• 关键词：Bertrand model ; Discontinuous payoffs ; Duopoly ; Hotelling model ; Price dispersion
• 刊名：Economic Theory Bulletin
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：4
• 期：2
• 页码：187-198
• 全文大小：441 KB
• 刊物主题：Economic Theory; Economics general; Game Theory, Economics, Social and Behav. Sciences;
• 出版者：Springer International Publishing
• ISSN：2196-1093
• 卷排序：4

文摘

In the classic Bertrand duopoly, a firm need only undercut its competitor by an arbitrarily small amount in order to sell to all the consumers. This paper generalises the Bertrand model so that a firm must be more than \(\varepsilon \) cheaper than its competitor in order to take the market. I characterise the unique symmetric mixed-strategy equilibrium. Firms earn strictly positive expected profits in equilibrium which are increasing in \(\varepsilon \). The model is also a special case of the price-setting stage of the Hotelling model with a non-uniform distribution of consumers. The model can also be formulated as one of sequential search without replacement from a discrete distribution of prices.