A Data-Driven Examination of Hotelling's Linear City Model.

In his seminal work stability in competition, Hotelling developed a model for identifying the spatial equilibrium for two competing firms such that they maximize their market-share. He considered a linear area of fixed length and he showed that in this setting the two competing firms should be located side-by-side in the middle of the line. Hotelling's study has been then adopted and used to analyze and explain other phenomena in a variety of fields. However, the linear city model is purely theoretical, without any empirical validation. The goal of this study is to explore Hotelling's Law in its original space - i.e., that of firm competition - and identify possible adjustments needed to describe its application/validity in a non-linear city. In particular, we collect data from location-based social networks that include information for the number of customers in a venue and we compare them with the expectations from Hotelling's original law. Overall, we identify that at a large geographic scale there is correlation between the market-share and the inter-venue distance, which is consistent with the Hotelling's Law. However, as we zoom into smaller scales there are deviations from the expectations from Hotelling's law, possibly due to higher sensitivity to the necessary assumptions. Our findings enhance the literature on optimal location placement for a venue and can provide additional insights for owners in regards to the linear city model.