The Math Behind Why Competing Stores Always Open Next to Each Other

February 2, 2016 | Elizabeth Knowles

Starbucks coffee shop sign
Photo credit: Marco Paköeningrat/Flickr (CC BY-SA 2.0)

It all has to do with game theory.

If you live in a big enough city, I’m sure that you’ve got at least one corner in your neighborhood with three coffee shops, banks or pharmacies. Despite the apparent lack of logic in the planning, competing stores frequently seem to pop up next to each other.

Why would competing stores decide to increase their competition like that? That’s a question for game theorists. Game theory is the area of mathematics that studies how people interact when they have to make decisions that affect each other. It looks at how people choose to cooperate or look out for themselves, and at how optimal solutions vary depending on whether they want what’s best for a single person or a set of people as a whole.

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As explained in this Ted-Ed video by Jac de Haan and by Luke Rowsell, the competing store situation comes down to something called Hotelling’s model of spatial competition.

Basically, if two stores wanted to open up in a given territory, it would make most sense for them to set up ¼ and ¾ of the way through the area. Thus, both stores would get customers from half the population, and nobody would have to walk farther than ¼ of the territory from where they are. That’s what’s called the socially optimal solution.

However, each store could do better — by gaining a larger proportion of the customer base — by setting up closer to the center line. Customers on the side of the store that moved might have to walk farther, but the store would be stealing some from their competitor’s pool.

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If one store were to move, the other could do better by moving as well — that is until both stores were located right in the middle. They would both be back to serving half the community, but many customers would have to walk farther.

This is called the Nash Equilibrium — “The point where neither of you can improve your position by deviating from your current strategy.”


Of course, real life doesn’t work quite this theoretically, as there are property costs, marketing strategies and other factors to consider. But next time you go for a walk, keep an eye out for clusters of competing stores. Maybe their planning isn’t so poor after all!

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