Clustering Store Locations and Nash Equilibrium
Often walking through a neighborhood, you might notice that a group of coffee shops are all right next to each other. This strange occurrence actually deals with Game theory and Nash equilibrium. This Ted-Ed Video, made by Jac de Haan, tackles the weird phenomenon of similar stores clustering together in specific parts of cities, towns, and neighborhoods. The video walks through two street vendors competing for customers on a beach. Customers are incentivized to go to the closest street vendor to them to minimize their walk. If both the street vendors equally place themselves along the beach then all the customers benefit from a shorter walk. However, the street vendors will compete with each other to try to get a bigger share of the market. In the end, they reach Nash Equilibrium when they are right next to each other.
The small example of two street vendors competing against one another can be extrapolated to the game theory problem of stores choosing locations in a town. To maximize social welfare, it would make sense for a store to move to a location without other similar stores. The customers would have shorter commutes and therefore would more likely visit the store more frequently, a win-win for themselves and the store. However, the store would be able to make more money by still being closest to the underserved location but moving closer to the other stores in order to try to attract their customers. The stores will constantly be in this cycle of trying to be the closest store to their current customers while also being incentivized to move closer to other stores to gain their customers. Eventually, the stores end up next to each other in a central, high-traffic location. At that point, neither is incentivized to move since they are getting approximately an even portion of the market share, and if they move, they will lose part of their market share by becoming further away from customers.
When the stores are next to each other in a central location, we can model this with a payoff matrix with two stores. At the moment they are sharing the market at 50/50. Whoever moves away loses a share of the market since they are placed in a central (“good”) location. If they both move far, they maximize social welfare, making more money than if they were close (assuming customers are more incentivized to shop at a closer store). However, they will stay close since when they are far, they are always able to chase more profit.
