WEBVTT 00:00:15.108 --> 00:00:19.085 Why are gas stations always built right next to other gas stations? 00:00:19.109 --> 00:00:21.815 Why can I drive for a mile without finding a coffee shop 00:00:21.839 --> 00:00:24.143 and then stumble across three on the same corner? 00:00:24.167 --> 00:00:27.051 Why do grocery stores, auto repair shops and restaurants 00:00:27.075 --> 00:00:28.718 always seem to exist in groups 00:00:28.742 --> 00:00:31.901 instead of being spread evenly throughout a community? 00:00:31.925 --> 00:00:33.456 While there are several factors 00:00:33.480 --> 00:00:36.164 that might go into deciding where to place your business, 00:00:36.188 --> 00:00:39.796 clusters of similar companies can be explained by a very simple story 00:00:39.820 --> 00:00:42.292 called Hotelling's Model of Spatial Competition. 00:00:43.121 --> 00:00:45.217 Imagine that you sell ice cream at the beach. 00:00:45.241 --> 00:00:48.051 Your beach is one mile long and you have no competition. 00:00:48.075 --> 00:00:51.269 Where would you place your cart in order to sell the most product? 00:00:51.293 --> 00:00:52.368 In the middle. 00:00:52.392 --> 00:00:55.418 The one-half-mile walk may be too far for some people 00:00:55.442 --> 00:00:56.741 at each end of the beach, 00:00:56.765 --> 00:00:59.770 but your cart serves as many people as possible. 00:00:59.794 --> 00:01:01.118 One day you show up at work 00:01:01.142 --> 00:01:03.522 just as your cousin Teddy is arriving at the beach 00:01:03.546 --> 00:01:04.900 with his own ice cream cart. 00:01:04.925 --> 00:01:06.317 In fact, he's selling 00:01:06.341 --> 00:01:08.516 exactly the same type of ice cream as you are. 00:01:08.540 --> 00:01:10.793 You agree that you will split the beach in half. 00:01:10.817 --> 00:01:13.634 In order to ensure that customers don't have to walk too far 00:01:13.658 --> 00:01:16.572 you set up your cart a quarter mile south of the beach center, 00:01:16.596 --> 00:01:18.412 right in the middle of your territory. 00:01:18.436 --> 00:01:20.751 Teddy sets up a quarter mile north of the center, 00:01:20.775 --> 00:01:22.768 in the middle of Teddy territory. 00:01:22.792 --> 00:01:25.935 With this agreement, everyone south of you buys ice cream from you. 00:01:25.959 --> 00:01:29.489 Everyone north of Teddy buys from him, and the 50% of beachgoers in between 00:01:29.513 --> 00:01:31.172 walk to the closest cart. 00:01:31.196 --> 00:01:33.751 No one walks more than a quarter of a mile, 00:01:33.775 --> 00:01:36.653 and both vendors sell to half of the beachgoers. 00:01:36.677 --> 00:01:40.836 Game theorists consider this a socially optimal solution. 00:01:40.860 --> 00:01:44.352 It minimizes the maximum number of steps any visitor must take 00:01:44.376 --> 00:01:46.352 in order to reach an ice cream cart. 00:01:46.376 --> 00:01:48.235 The next day, when you arrive at work, 00:01:48.259 --> 00:01:51.034 Teddy has set up his cart in the middle of the beach. 00:01:51.058 --> 00:01:54.301 You return to your location a quarter mile south of center 00:01:54.325 --> 00:01:57.069 and get the 25% of customers to the south of you. 00:01:57.093 --> 00:02:00.635 Teddy still gets all of the customers north in Teddy territory, 00:02:00.659 --> 00:02:04.702 but now you split the 25% of people in between the two carts. 00:02:04.726 --> 00:02:07.584 Day three of the ice cream wars, you get to the beach early, 00:02:07.608 --> 00:02:10.167 and set up right in the center of Teddy territory, 00:02:10.191 --> 00:02:13.632 assuming you'll serve the 75% of beachgoers to your south, 00:02:13.656 --> 00:02:17.026 leaving your cousin to sell to the 25% of customers to the north. 00:02:17.050 --> 00:02:20.520 When Teddy arrives, he sets up just south of you 00:02:20.544 --> 00:02:22.451 stealing all of the southerly customers, 00:02:22.475 --> 00:02:25.259 and leaving you with a small group of people to the north. 00:02:25.283 --> 00:02:29.336 Not to be outdone, you move 10 paces south of Teddy to regain your customers. 00:02:29.360 --> 00:02:32.836 When you take a mid-day break, Teddy shuffles 10 paces south of you, 00:02:32.860 --> 00:02:36.535 and again, steals back all the customers to the far end of the beach. 00:02:36.559 --> 00:02:38.134 Throughout the course of the day, 00:02:38.158 --> 00:02:40.417 both of you continue to periodically move south 00:02:40.441 --> 00:02:42.836 towards the bulk of the ice cream buyers, 00:02:42.860 --> 00:02:45.860 until both of you eventually end up at the center of the beach, 00:02:45.884 --> 00:02:49.719 back to back, each serving 50% of the ice-cream-hungry beachgoers. 00:02:49.743 --> 00:02:51.935 At this point, you and your competitive cousin 00:02:51.959 --> 00:02:54.951 have reached what game theorists call a Nash Equilibrium - 00:02:54.975 --> 00:02:57.774 the point where neither of you can improve your position 00:02:57.798 --> 00:02:59.937 by deviating from your current strategy. 00:02:59.961 --> 00:03:01.398 Your original strategy, 00:03:01.422 --> 00:03:04.446 where you were each a quarter mile from the middle of the beach, 00:03:04.470 --> 00:03:07.086 didn't last, because it wasn't a Nash Equilibrium. 00:03:07.110 --> 00:03:10.936 Either of you could move your cart towards the other to sell more ice cream. 00:03:10.960 --> 00:03:13.246 With both of you now in the center of the beach, 00:03:13.270 --> 00:03:16.902 you can't reposition your cart closer to your furthest customers 00:03:16.926 --> 00:03:19.212 without making your current customers worse off. 00:03:19.236 --> 00:03:22.568 However, you no longer have a socially optimal solution, 00:03:22.592 --> 00:03:24.592 since customers at either end of the beach 00:03:24.616 --> 00:03:27.602 have to walk further than necessary to get a sweet treat. 00:03:27.626 --> 00:03:29.570 Think about all the fast food chains, 00:03:29.594 --> 00:03:32.271 clothing boutiques, or mobile phone kiosks at the mall. 00:03:32.295 --> 00:03:33.879 Customers may be better served 00:03:33.903 --> 00:03:36.164 by distributing services throughout a community, 00:03:36.188 --> 00:03:39.520 but this leaves businesses vulnerable to aggressive competition. 00:03:39.544 --> 00:03:42.786 In the real world, customers come from more than one direction, 00:03:42.810 --> 00:03:45.715 and businesses are free to compete with marketing strategies, 00:03:45.739 --> 00:03:48.501 by differentiating their product line, and with price cuts, 00:03:48.525 --> 00:03:50.252 but at the heart of their strategy, 00:03:50.276 --> 00:03:53.621 companies like to keep their competition as close as possible.