Necessary and sufficient condition for equilibrium of the Hotelling model

07/14/2019

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by   Satoshi Hayashi, et al.

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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.