WEBVTT 00:00:15.108 --> 00:00:19.109 Why are gas stations always built right next to other gas stations? 00:00:19.109 --> 00:00:21.809 Why is it that I can drive for a mile without finding a coffee shop 00:00:21.809 --> 00:00:24.143 and then stumble across three on the same corner? 00:00:24.143 --> 00:00:27.075 Why do grocery stores, auto repair shops and restaurants 00:00:27.075 --> 00:00:31.925 always seem to exist in groups instead of being spread evenly throughout a community? 00:00:31.925 --> 00:00:35.843 While there are several factors that might go into deciding where to place your business, 00:00:35.843 --> 00:00:39.475 clusters of similar companies can be explained by a very simple story 00:00:39.475 --> 00:00:43.711 called Hotelling's Model of Spatial Competition. 00:00:43.711 --> 00:00:45.092 Imagine that you sell ice cream at the beach. 00:00:45.092 --> 00:00:48.075 Your beach is one mile long and you have no competition. 00:00:48.075 --> 00:00:51.293 Where would you place your cart in order to sell the most product? 00:00:51.293 --> 00:00:52.392 In the middle. 00:00:52.392 --> 00:00:55.442 The one-half-mile walk may be too far for some people 00:00:55.442 --> 00:00:58.776 at each end of the beach, but your cart serves as many people as possible. 00:00:58.776 --> 00:01:02.692 One day you show up at work just as your cousin Teddy is arriving at the beach 00:01:02.692 --> 00:01:07.342 with his own ice cream cart. In fact, he's selling exactly the same type of ice cream as you are. 00:01:07.342 --> 00:01:10.810 You agree that you will split the beach in half. 00:01:10.810 --> 00:01:13.126 In order to insure that customer's don't have to walk too far 00:01:13.126 --> 00:01:16.376 you set up your cart a quarter mile south of the beach center, 00:01:16.376 --> 00:01:18.294 right in the middle of your territory. 00:01:18.294 --> 00:01:20.775 Teddy sets up a quarter mile north of the center, 00:01:20.775 --> 00:01:22.792 in the middle of Teddy territory. 00:01:22.792 --> 00:01:25.293 With this agreement, everyone south of you buys ice cream from you. 00:01:25.293 --> 00:01:29.241 Everyone north of Teddy buys from him, and the 50% of beachgoers in between 00:01:29.241 --> 00:01:33.775 walk to the closest cart. No one walks more than a quarter of a mile, 00:01:33.775 --> 00:01:36.677 and both vendors sell to half of the beachgoers. 00:01:36.677 --> 00:01:40.860 Game theorists consider this a socially optimal solution. 00:01:40.860 --> 00:01:44.376 It minimizes the maximum number of steps any visitor must take 00:01:44.376 --> 00:01:46.376 in order to reach an ice cream cart. 00:01:46.376 --> 00:01:48.259 The next day, when you arrive at work, 00:01:48.259 --> 00:01:51.058 Teddy has set up his cart in the middle of the beach. 00:01:51.058 --> 00:01:54.325 You return to your location a quarter mile south of center 00:01:54.325 --> 00:01:57.093 and get the 25% of customers to the south of you. 00:01:57.093 --> 00:02:00.659 Teddy still gets all of the customers north in Teddy territory, 00:02:00.659 --> 00:02:04.726 but now you split the 25% of people in between the two carts. 00:02:04.726 --> 00:02:07.559 Day three of the ice cream wars, you get to the beach early, 00:02:07.559 --> 00:02:10.191 and set up right in the center of Teddy territory, 00:02:10.191 --> 00:02:14.276 assuming you'll serve the 75% of beachgoers to your south, 00:02:14.276 --> 00:02:17.576 leaving your cousin to sell to the 25% of customers to the north. 00:02:17.576 --> 00:02:20.544 When Teddy arrives, he sets up just south of you 00:02:20.544 --> 00:02:24.859 stealing all of the southerly customers, and leaving you with a small group of people to the north. 00:02:24.859 --> 00:02:29.360 Not to be outdone, you move 10 paces south of Teddy to regain your customers. 00:02:29.360 --> 00:02:32.860 When you take a mid-day break, Teddy shuffles 10 paces south of you, 00:02:32.860 --> 00:02:36.559 and again, steals back all the customers to the far end of the beach. 00:02:36.559 --> 00:02:40.025 Throughout the course of the day, both of you continue to periodically move south 00:02:40.025 --> 00:02:42.860 towards the bulk of the ice cream buyers, 00:02:42.860 --> 00:02:45.475 until both of you eventually end up at the center of the beach, 00:02:45.475 --> 00:02:49.743 back to back, each serving 50% of the ice-cream-hungry beachgoers. 00:02:49.743 --> 00:02:54.975 At this point, you and your competitive cousin have reached what game theorists call a Nash Equilibrium - 00:02:54.975 --> 00:02:59.961 the point where neither of you can improve your position by deviating from your current strategy. 00:02:59.961 --> 00:03:03.859 Your original strategy, where you were each a quarter mile from the middle of the beach, 00:03:03.859 --> 00:03:07.110 didn't last, because it wasn't a Nash Equilibrium. 00:03:07.110 --> 00:03:10.960 Either of you could move your cart toward the other to sell more ice cream. 00:03:10.960 --> 00:03:12.825 With both of you now in the center of the beach, 00:03:12.825 --> 00:03:16.926 you can't reposition your cart closer to your furthest customers 00:03:16.926 --> 00:03:19.193 without making your current customers worse off. 00:03:19.193 --> 00:03:22.592 However, you no longer have a socially optimal solution, 00:03:22.592 --> 00:03:24.425 since customers at either end of the beach 00:03:24.425 --> 00:03:27.626 have to walk further than necessary to get a sweet treat. 00:03:27.626 --> 00:03:32.295 Think about all the fast food chains, clothing boutiques, or mobile phone kiosks at the mall. 00:03:32.295 --> 00:03:36.009 Customers may be better served by distributing services throughout a community, 00:03:36.009 --> 00:03:39.544 but this leaves businesses vulnerable to aggressive competition. 00:03:39.544 --> 00:03:42.810 In the real world, customers come from more than one direction, 00:03:42.810 --> 00:03:45.693 and businesses are free to compete with marketing strategies, 00:03:45.693 --> 00:03:47.508 by differentiating their product line, and with price cuts, 00:03:47.508 --> 00:03:51.942 but at the heart of their strategy, companies like to keep their competition 00:03:51.942 --> 00:03:55.942 as close as possible.