Why Target and Walmart locate across the street from each other

Hotelling’s Law

If you've ever been to a mall, you'll often find a surprising situation: stores like Target, Walmart, JCPenney and Kohl's right nearby each other, often within walking distance.

It's a strange phenomenon. Wouldn't competitors choose to locate themselves farther from similar stores, to reduce competition?

Enter Hotelling's Law.

Hotelling's Law and Department Stores

Hotelling's Law is a classic game theory used to model where and why companies choose to locate where they do.

The game is played as follows:

• There are 2 competitors on a beach (or a linear space from -1 to 1 to keep the math simple)
• They sell identical products (i.e. customers don't have a preference between competitors so pricing is not a factor.  Note this also means that "market share" is also dependent on where they choose to locate)
• They can locate anywhere along the beach
• The game is played repeatedly

Each players goal is to capture the maximum market share (or the biggest section of the beach).  

Get Your Hot Dogs!

In the image below, we see two hot dog vendors, each starting at opposite ends of the beach and controlling half of the beach's hot dog market.

However, there is an opportunity to increase market share!  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).

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.

Real-Life Hotelling's Law

There are numerous examples of Hotelling's Law playing out in real life.  

• McDonald's and Burger King
• Whole Foods and Trader Joes
• Gas stations (think of how many gas stations share the same intersection)
• Starbucks, Coffee Bean & Tea Leaf
• Politics - think of the "race to the middle" concept

The list goes on and on (depending on your definition of "comparable" goods).

Target vs. Walmart & JCPenney vs. Kohl's

Department 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:

store_id	store	Latitude	Longitude
w_fa003def	Walmart	36.350885	-94.2398161
w_714aff33	Walmart	36.342235	-94.0714102
k_c25506d1	Kohl's	36.236984	-93.0934503

And as far as the number of stores, our data shows the following:

Store	Number of Records
Walmart	3251
Target	1753
Kohl's	1000
JCPenney	1000

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 Urban

To 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:

These 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!

National - Nearest Target from Walmart		Denver - Nearest Target from Walmart
min	0.13 miles	0.43 miles
mean	18.00 miles	2.09 miles
max	159.34 miles	5.98 miles
std deviation	21.64 miles	1.35 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 Up

Hotelling'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!