An application of Hotelling’s Law (1929) in a two-dimensional space.
By Hugo Lhuillier (2016)
Hotelling (1929) studied competition between firms in an oligopolistic context, adding to the initial work of Edgeworth the importance of geographical location. In his original model, firms could compete with each other by changing both their price and their location. A detailed description of the original model can be found here.
This application of Hotelling’s model simplifies it by only considering changes in location, assuming identical prices across firms and constant prices over time. If changes in locations are likely to be stickier than variations in prices, one could instead interpret this model as one of competition in advertising campaigns. In this way, firms do not change the location of their store in every period but vary the position where their ads are located, such as to maximise the number of people that will see them.
Following Ottino, Stonedahl, and Wilensky (2009), this application extends the original paper by allowing stores to move along a plane (two-dimension movement). One difference between the NetLogo representation and ours is the way distance between consumers and firms is defined. In their model, one unit of distance corresponds to the four cardinal directions around a given coordinate. Here, we also include the positions at the north-west, north-east, south-east and south-west.
The model implements the JAS-mine Model-Collector-Observer architecture, with two @Entity class: firms and consumers/households. The parameters characterizing the grid and the number of firms are annotated in the model with @GUIparameter. The
The timing of events is as follow: in each period,
As in the original model, a stable equilibrium exists for a duopoly (two firms), in which case it is located at the middle of the plane. For numbers of stores greater than two, the existence of an equilibrium depends on the specific number of firms. An even number of firms tends to display more regular and stable patterns than an odd number of firms.
Specifically for four firms, a (stable) equilibrium emerges with each firm having a quarter of the market. Similarly for eight firms, all firms ends up with an eight of the market. Furthermore, firms behave as in the four-firms case, with two firms per quarter of the grid, and these two firms located on the same spot.
The source code repository for this model is available on GitHub at https://github.com/jasmineRepo/HotellingsLaw. Executable versions of the demo models including Hotelling's Law can be found at https://sourceforge.net/projects/jas-mine/files/Demo%20Models/.
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