Stores next to one another
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A: Why are gas stations always built right next to other gas stations?
B: While there are several factors that may go into deciding where to place your business, clusters of similar companies by a very simple story called hotellingâs model of spatial competition
A: What does that story tell?
B: Imagine that youâre selling ice cream at the beach. Your beach is one mile long and you have no competition. Where would you place your cart in order to sell the most product? In the middle, the one-half-mile walk may be too far for some people at each end of the beach, but your cart serves as many people as possible. One day, you show up at work just as your cousin Teddy is arriving at the beach with his own ice cream cart. In fact, heâs selling exactly the type of ice cream as you are. You agree that youâll split the beach in half. In order to ensure that customers donât have to walk too far, you set up your cart a quarter mile south of the beach center, right in the middle of your territory. Teddy sets up a quarter mile north of the center, in the middle of Terry territory. With this agrement, everyone south of you buys ice cream from you. Everyone north of Teddy buys from him and the 50% of beachgoes in between walk to the closest cart. No one walks more than a quarter of a mile and both vendors sell to half of beachgoes. Game theorists consider this a socially optimal solution. It minimizes the maximum number of steps any visitor must take in order to reach an ice cream cart.
The next day, when you arrive at work, Teddyâs has set up his cart in the middle of the beach. You return to your location at quarter mile south of center and get the 25% of customers to the south of you. Teddy still gets all the customers north in Teddyâs territory, but now you split the 25% of people in between the two carts.
Day three of the ice cream wars, you get to the beach early and set up right in the center of Teddy territory, assuming you serve the 75% of beachgoes to your south, leaving your cousin to sell to the 25% of customers of the north. When Teddy arrives, he sets up just south of you, stealing all of the souhterly customers and leaving you with a small group of people to the north. Not to be outdone, you move 10 paces south of Teddy to regain your customers.
When you take a mid-day break, Teddy shuffles 10 paces south of you and, again, steals back all the customers to the far end of the beach. Throughout the course of the day, both of you continue to periodically move south towards to the buld of the ice cream buyers, until both of you eventually end up at the center of the beach, back to back, each serving 50% of the ice-cream-hungry beachgoes.
At this point, you and your comptitive cousin have reach game theorists called a Nash equilibrium. The point where neither of you can improve your position by deviating from your current strategy
Your original strategy, where you were each a quarter mile from the middle of the beach, didnât last becasue it wasnât a Nash equilibrium. Either of you could move your cart towards the other to sell more ice cream. With both of you now in the center of the beach, you canât reposition your cart closer to your further customers without making your current customers worse off
However, you no longer have a socially optimal solution since customers at either end of the beach have to walk further than necessary to get a sweat treat