Necessary and sufficient condition for equilibrium of the Hotelling model
Theoretical Economics
2019-07-16 v1 Information Theory
math.IT
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.
Keywords
Cite
@article{arxiv.1907.06200,
title = {Necessary and sufficient condition for equilibrium of the Hotelling model},
author = {Satoshi Hayashi and Naoki Tsuge},
journal= {arXiv preprint arXiv:1907.06200},
year = {2019}
}