If the Red hot dog vendor moves to the 0 marker, it captures the market from -1 to 0 AND from 0 to 0.
5, while the Blue vendor retains 0.
5 to 1 (see below).
By the Red Vendors moving to 0, it captures an additional 0.
5 the beach.
Somewhat surprisingly, the optimal solution is for each hot dog vendor to locate exactly in the middle, as they have access to the largest market, without giving their competitor the option to relocate and take market share from them.
This outcome is the Nash Equilibrium of the location game, and is the solution Hotelling’s Law — competitors locate near to each other to maximize market share.
If you’re interested in more of the game theory/math behind this result, I’d highly recommend Presh Talwalkar’s site: Mind Your Decisions.
Optimal solution is for both competitors to co-locateReal-Life Hotelling’s LawThere are numerous examples of Hotelling’s Law playing out in real life.
McDonald’s and Burger KingWhole Foods and Trader JoesGas stations (think of how many gas stations share the same intersection)Starbucks, Coffee Bean & Tea LeafPolitics — think of the “race to the middle” conceptThe list goes on and on (depending on your definition of “comparable” goods).
Walmart & JCPenney vs.
Kohl’sDepartment stores are another interesting example of this — the sell nearly identical products at with very low margins.
To see how these stores choose to locate themselves, I’ve collected geolocation data for all Target, Walmart, JCPenney, and Kohl’s locations in the USA.
Below is a sample of the data:And as far as the number of stores, our data shows the following:Let’s begin by simply plotting all of our geolocations onto a single map (code is at the end of the post)Pretty sweet!.We see clusters of stores in urban areas likely corresponding to population density, which is what we’d expect based purely on market demand.
Most interestingly: Walmart has far more retail space in rural parts of the country compared to the other retailers.
Getting UrbanTo attempt to control for population densities, let’s take an urban location with a relatively dense population to see if we see clustering at the city-level.
Below we see the Denver metro area:Looking at Target and Walmart, we can see some stores that are very closely clustered together:Clusters of Walmart and Target retail locationsThese maps definitely indicate Hotelling’s Law could be in play.
After computing the distances between stores, the average distance between the nearest Targets and Walmarts in the Denver area is only 2.
09 miles!Another interesting takeaway: Targets are near Walmarts, but not vice-versa.
The nearest Walmart from a Target location is on average 13.
7 miles away, where the nearest Target from a Walmart location is on average 18 miles away.
Here’s another interesting view of Miami’s Target and Walmart locations:Wrapping UpHotelling’s Law certainly applies when modeling how retailers choose to locate.
Obviously, it is a model, so it doesn’t take into account relocation costs (moving a Target store down the street one block would be quite expensive), pricing differences, brand loyalties, and many other variables.
However, it does do a good job of illustrating the unintuitive result that competitors are often located very close to one another.
For future analyses, including census data, drive times between stores, and population density would likely make for more robust results.
We’ll save that for next time!Code!.. More details