I’m not in the restaurant business, I’m in the real estate business–Ray Kroc, founder of McDonald’s

America is the land of choice. If you want a fast food burger, you don’t have to settle for McDonald’s or Burger King. You get to choose: for where there is a McDonald’s, there is often a Burger King nearby, many times right across the street.

For example, here’s a map of McDonald’s and Burger King locations near Miami Beach in Florida:

(click on image for larger size)

Map from Fastfoodmaps.com

There are practical reasons why stores locate near each other. In a previous article, Why do gas stations locate near each other?, I suggested two stores competing would cluster in a central location as a result of competitive forces.

But what happens when there are more than 2 stores? More specifically, what happens when two business are each building multiple stores and competing on market share? What is the best strategy, and what kind of distribution of locations will result?

Below I will use a game theory model to consider the strategy. The model suggests it is best for both businesses to choose the most valuable locations, leading again to stores locating near each other.

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"All will be well if you use your mind for your decisions, and mind only your decisions." Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon. .

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The location game

McDonald’s stresses the importance of location on its website:

McDonald’s looks for the best locations within the marketplace to provide our customers with convenience. We build quality restaurants in neighborhoods as well as airports, malls, tollways, and colleges at a value to our customers.

It’s safe to say Burger King, as a competitor, would research location as well. So in the model, we will assume that both businesses are equally knowledgeable about market location information.

Below is the game. The source of this game is “Hagar’s Battle” which is presented in the excellent book Game Theory Evolving in Chapter 4.

McDonald’s and Burger King are each planning to develop 5 stores in a metropolitan area. Each finds there are 10 possible locations, with values given as 10, 9, 8, …, 1 points (these can be interpreted values as potential profit size in millions of dollars).

The game works as follows. Each simultaneously chooses where to build each of the 5 stores. The payoffs will depend on where the stores are located.

If a location ends up having both stores, then they split the value of the location. If a location ends up with just one store, then the business that built that store gets the entire value.

For example:

–If McDonald’s and Burger King both build at location 10, then the profits are split as 5 to each

–If McDonald’s alone builds at location 9, then it gets the entire value of 9 points

Assuming that McDonald’s and Burger King are looking to maximize total market share, what’s the strategy in this game? Do they choose to compete in the most valuable locations, or would it make sense to branch out and capitalize on a smaller market?

More general: Two stores compete for n locations with values a n > a n-1 > … > a 1 . Each chooses to build a store on m < n locations. If the two choose the same location, the value is split. If one uniquely picks a location, then it gets the entire value. What’s the strategy if each wants to maximize market share?

The strategy for the game

There are many variables in the game, but surprisingly it is very easy to solve. In fact, there is a weakly dominant strategy for each business!

Specifically, it is a weakly dominant strategy for each business to pick the 5 highest value locations. Or more generally, to keep picking the highest value locations.

Let’s consider an example to see why. Assume that McDonald’s picks the 5 highest locations of 6 to 10, and Burger King avoids the highest value location, settling for locations 5 to 9.

McDonald’s: 6, 7, 8, 9, 10

Burger King: 5, 6, 7, 8, 9

McDonald’s and Burger King will split the value for locations 6 to 9–so neither gets an advantage and each earns 15. Burger King will win the value of 5, but then McDonald’s wins the highest value location of 10. In net, McDonald’s will be 5 value points higher than Burger King. Precisely, McDonald’s will get 25 points, or 56 percent of the market to Burger King’s 20 points and 44 percent of the market.

Payoff to scenario:

McDonald’s: 6, 7, 8, 9, 10 –> total 25 (market share 56 percent)

Burger King: 5, 6, 7, 8, 9 –> total 20 (market share 44 percent)

Could this possibly be an equilibrium? No way! Burger King will realize it is better to choose location 10. In that case, both will evenly split the market, each getting 20 points and having equal market share of 50 percent.

Payoff to BK for switching to 10:

McDonald’s: 6, 7, 8, 9, 10 –> total 20 (market share 50 percent)

Burger King: 6, 7, 8, 9, 10 –> total 20 (market share 50 percent)

You can logically reason that once both companies are in the most valuable locations that neither will want to deviate. Anyone who gives up prime real estate will necessarily yield more points than it will gain and end up with lower market share.

Now you will note something interesting here. Burger King is getting the same profit total under both scenarios, but it prefers the second scenario because its market share is higher. In this game–and one could argue in real life perhaps–the two restaurants are competing for size. This is against the standard economics assumption that companies should focus on profit. One could argue that the focus on size is justified as a longer term strategy to build the reputation and set a foundation for longer-term profits.

Solving the game more formally

We want to prove it’s best to pick the highest value locations. Let’s suppose that some company does not do that. Instead, it passes over location j and picks lower value location i.

We will prove it is always beneficial to switch to the higher location. The payoff to switching from location i to location j is given by the following four possibilities:

Other company is located: i but not j: gain j – i/2 > 0 j but not i: split more valued market j j and i: split more valued market j neither j nor i: gain j – i

The point is this: if you switch from a lower valued market to a higher valued one, you will always be gaining in market share by either gaining in absolute profit or by splitting a more valued market that the other company had won previously.

The result is that each company finds it is best to pick the highest valued locations.

The conclusion

The location game suggests why fast food restaurants could cluster together. They are competing for the best locations and they find it most valuable to fight it out to keep even in the game of market share.

Over time the game will change, and they might open more branches. But where one fast food chain pops up, it’s likely the other chain will follow.

Discussion questions

1. Rarely are McDonald’s and Burger King stores built simultaneously. Someone builds first, and the other copies. Under what conditions would it be better to be the first store in a location? Or to be second?

2. In an airport and in small towns, you are unlikely to find both restaurants. Why might that be?

3. How does the game change if the companies are focused on profit instead of market share?