Why do competitors open their stores next to one another? - Jac de Haan

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Why are all the gas stations, cafes and restaurants in one crowded spot? As two competitive cousins vie for ice-cream-selling domination on one small beach, discover how game theory and the Nash Equilibrium inform these retail hotspots.

Lesson by Jac de Haan, animation by Luke Rowsell.

Why are gas stations always built
right next to other gas stations?

Why can I drive for a mile
without finding a coffee shop

and then stumble
across three on the same corner?

Why do grocery stores,
auto repair shops and restaurants

always seem to exist in groups

instead of being spread evenly
throughout a community?

While there are several factors

that might go into deciding
where to place your business,

clusters of similar companies can
be explained by a very simple story

called Hotelling's Model
of Spatial Competition.

Imagine that you sell
ice cream at the beach.

Your beach is one mile long
and you have no competition.

Where would you place your cart
in order to sell the most product?

In the middle.

The one-half-mile walk may
be too far for some people

at each end of the beach,

but your cart serves
as many people as possible.

One day you show up at work

just as your cousin Teddy
is arriving at the beach

with his own ice cream cart.

In fact, he's selling

exactly the same type
of ice cream as you are.

You agree that you will split
the beach in half.

In order to ensure that customers
don't have to walk too far

you set up your cart a quarter mile
south of the beach center,

right in the middle of your territory.

Teddy sets up a quarter mile
north of the center,

in the middle of Teddy territory.

With this agreement, everyone south
of you buys ice cream from you.

Everyone north of Teddy buys from him,
and the 50% of beachgoers in between

walk to the closest cart.

No one walks
more than a quarter of a mile,

and both vendors sell
to half of the beachgoers.

Game theorists consider
this a socially optimal solution.

It minimizes the maximum number
of steps any visitor must take

in order to reach an ice cream cart.

The next day, when you arrive at work,

Teddy has set up his cart
in the middle of the beach.

You return to your location
a quarter mile south of center

and get the 25% of customers
to the south of you.

Teddy still gets all of the customers
north in Teddy territory,

but now you split the 25% of people
in between the two carts.

Day three of the ice cream wars,
you get to the beach early,

and set up right in the center
of Teddy territory,

assuming you'll serve
the 75% of beachgoers to your south,

leaving your cousin to sell
to the 25% of customers to the north.

When Teddy arrives,
he sets up just south of you

stealing all of the southerly customers,

and leaving you with a small group
of people to the north.

Not to be outdone, you move 10 paces
south of Teddy to regain your customers.

When you take a mid-day break,
Teddy shuffles 10 paces south of you,

and again, steals back all the customers
to the far end of the beach.

Throughout the course of the day,

both of you continue
to periodically move south

towards the bulk of the ice cream buyers,

until both of you eventually end up
at the center of the beach,

back to back, each serving 50%
of the ice-cream-hungry beachgoers.

At this point, you
and your competitive cousin

have reached what game theorists
call a Nash Equilibrium -

the point where neither of you
can improve your position

by deviating from your current strategy.

Your original strategy,

where you were each a quarter mile
from the middle of the beach,

didn't last, because it wasn't
a Nash Equilibrium.

Either of you could move your cart
towards the other to sell more ice cream.

With both of you now
in the center of the beach,

you can't reposition your cart
closer to your furthest customers

without making your current
customers worse off.

However, you no longer have
a socially optimal solution,

since customers at either end of the beach

have to walk further than necessary
to get a sweet treat.

Think about all the fast food chains,

clothing boutiques,
or mobile phone kiosks at the mall.

Customers may be better served

by distributing services
throughout a community,

but this leaves businesses vulnerable
to aggressive competition.

In the real world, customers come
from more than one direction,

and businesses are free to compete
with marketing strategies,

by differentiating their product line,
and with price cuts,

but at the heart of their strategy,

companies like to keep their competition
as close as possible.