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Generalising Bertrand competition: a special case of the Hotelling model

Rashid, M; (2015) Generalising Bertrand competition: a special case of the Hotelling model. Economic Theory Bulletin 10.1007/s40505-015-0077-5. (In press). Green open access

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Abstract

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.

Type: Article
Title: Generalising Bertrand competition: a special case of the Hotelling model
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s40505-015-0077-5
Publisher version: http://dx.doi.org/10.1007/s40505-015-0077-5
Language: English
Additional information: This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > UCL School of Management
URI: https://discovery.ucl.ac.uk/id/eprint/1472704
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