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

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

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and then stumble
across three on the same corner?

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Why do grocery stores,
auto repair shops and restaurants

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always seem to exist in groups

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instead of being spread evenly
throughout a community?

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While there are several factors

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that might go into deciding
where to place your business,

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

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called Hotelling's Model
of Spatial Competition.

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Imagine that you sell
ice cream at the beach.

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

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

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In the middle.

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

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at each end of the beach,

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but your cart serves
as many people as possible.

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One day you show up at work

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just as your cousin Teddy
is arriving at the beach

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with his own ice cream cart.

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In fact, he's selling

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exactly the same type
of ice cream as you are.

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You agree that you will split
the beach in half.

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

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

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right in the middle of your territory.

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Teddy sets up a quarter mile
north of the center,

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in the middle of Teddy territory.

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

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

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walk to the closest cart.

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No one walks
more than a quarter of a mile,

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and both vendors sell
to half of the beachgoers.

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Game theorists consider
this a socially optimal solution.

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It minimizes the maximum number
of steps any visitor must take

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in order to reach an ice cream cart.

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The next day, when you arrive at work,

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

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You return to your location
a quarter mile south of center

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

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

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

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

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and set up right in the center
of Teddy territory,

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

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

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When Teddy arrives,
he sets up just south of you

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stealing all of the southerly customers,

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

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

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

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

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Throughout the course of the day,

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both of you continue
to periodically move south

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towards the bulk of the ice cream buyers,

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

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

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At this point, you
and your competitive cousin

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have reached what game theorists
call a Nash Equilibrium -

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the point where neither of you
can improve your position

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by deviating from your current strategy.

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Your original strategy,

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

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

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

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

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

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without making your current
customers worse off.

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However, you no longer have
a socially optimal solution,

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since customers at either end of the beach

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

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Think about all the fast food chains,

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clothing boutiques,
or mobile phone kiosks at the mall.

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Customers may be better served

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by distributing services
throughout a community,

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but this leaves businesses vulnerable
to aggressive competition.

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

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and businesses are free to compete
with marketing strategies,

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by differentiating their product line,
and with price cuts,

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but at the heart of their strategy,

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companies like to keep their competition
as close as possible.