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Necessary and sufficient condition for equilibrium of the Hotelling model

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  • Satoshi Hayashi
  • Naoki Tsuge

Abstract

We study a model of vendors competing to sell a homogeneous product to customers spread evenly along a linear city. This model is based on Hotelling's celebrated paper in 1929. Our aim in this paper is to present a necessary and sufficient condition for the equilibrium. This yields a representation for the equilibrium. To achieve this, we first formulate the model mathematically. Next, we prove that the condition holds if and only if vendors are equilibrium.

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  • Satoshi Hayashi & Naoki Tsuge, 2019. "Necessary and sufficient condition for equilibrium of the Hotelling model," Papers 1907.06200, arXiv.org.
  • Handle: RePEc:arx:papers:1907.06200
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    File URL: http://arxiv.org/pdf/1907.06200
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    1. B. Curtis Eaton & Richard G. Lipsey, 1975. "The Principle of Minimum Differentiation Reconsidered: Some New Developments in the Theory of Spatial Competition," Review of Economic Studies, Oxford University Press, vol. 42(1), pages 27-49.
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