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

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Why is it that I can 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 instead of being spread evenly throughout a community?

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While there are several factors 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, but your cart serves as many people as possible.

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One day you show up at work just as your cousin Teddy is arriving at the beach

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with his own ice cream cart. In fact, he's selling 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 insure that customer's 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. 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, 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, 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 have reached what game theorists call a Nash Equilibrium -

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the point where neither of you can improve your position by deviating from your current strategy.

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Your original strategy, 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 toward 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, clothing boutiques, or mobile phone kiosks at the mall.

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Customers may be better served 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, companies like to keep their competition

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as close as possible.