Necessary and sufficient condition for equilibrium of the Hotelling model

Satoshi Hayashi; Naoki Tsuge

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arXiv · 1907.06200

Necessary and sufficient condition for equilibrium of the Hotelling model

Satoshi Hayashi·Naoki Tsuge

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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. 2019-07-14. Necessary and sufficient condition for equilibrium of the Hotelling model. https://arxiv.org/abs/1907.06200

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