Why is it that I can drive for a mile without finding a coffee shop and then stumble across three on the same corner?

為什麼我開了一英里，都沒見到咖啡店，卻在同一個街角一次撞見三家呢？

Why do grocery stores, auto repair shops and restaurants always seem to exist in groups instead of being spread evenly throughout a community?

為什麼雜貨店、汽車行、還有餐廳似乎總是成群地出現，而不是在整個社區中平均分佈呢？

While there are several factors that might go into deciding where to place your business, clusters of similar companies can be explained by a very simple story, called Hotelling's Model of Spatial Competition.

儘管決定要在哪裡開店，需要考慮許多因素，但類似的店家會成群出現，可以用一個很簡單的故事來解釋，那就是「空間競爭的霍特林模型」。

Imagine that you sell ice cream at the beach.

想像你打算在沙灘上賣冰棒。

Your beach is one mile long and you have no competition.

沙灘有一英里長，而且你沒有其他競爭者。

Where would you place your cart in order to sell the most product?

為了賣出最多的冰棒， 你會把推車放在哪？

In the middle.

正中間。

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.

半哩對於某些在沙灘盡頭的人或許太遠了，但是你的推車已經盡可能地服務最多的人了。

One day you show up at work just as your cousin Teddy is arriving at the beach with his own ice cream cart.

有天你去工作的時候， 恰巧遇到你親戚 Teddy 也推著冰棒車去沙灘。

In fact, he's selling exactly the same type of ice cream as you are.

事實上，他賣的東西跟你完全一樣。

You agree that you will split the beach in half.

你們達成協議， 把海灘分成兩半。

In order to ensure that customer's don't 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.

為了讓客人們不用走太遠，你將推車停在中間往南 1/4 哩的地方，也就是你地盤的正中間。

Teddy sets up a quarter mile north of the center, in the middle of Teddy territory.

Teddy 則停在中間往北 1/4 哩的地方，也是他地盤的中間。

With this agreement, everyone south of you buys ice cream from you.

有了這個協議，南邊的客人會來買你的冰棒。

Everyone north of Teddy buys from him, and the 50 percent of beach goers in between walk to the closest cart.

比 Teddy 更北方的客人會去買他的冰棒， 而兩者之間的遊客會走向最接近的推車。

No one walks more than a quarter of a mile, and both vendors sell to half of the beach goers.

沒有人會走超過 1/4 哩，而且兩個冰棒攤都有等量的客源。

Game theorists consider this a socially optimal solution.

賽局論專家認為，這是一個對全社會最佳的結果。

It minimizes the maximum number of steps any visitor must take in order to reach an ice cream cart.

因為它縮短了多數遊客至冰棒攤的距離。

The next day, when you arrive at work, Teddy has set up his cart in the middle of the beach.

隔天你來工作，Teddy 已經把他的推車停好在沙灘的正中間。

You return to your location a quarter mile south of center and get the 25 percent of customers to the south of you.

你一樣到那南方 1/4 哩的地方，得到那些 25% 比你更南方的客戶。

Teddy still gets all of the customers north in Teddy territory, but now you split the 25 percent of people in between the two carts.

而 Teddy 依舊得到整個他北方地盤的客戶，但是現在你們必須平分 25% 的中間客源。

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'll serve the 75 percent of beach-goers to your south, leaving your cousin to sell to the 25 percent of customers to the north.

冰棒戰爭的第三天，你提早抵達沙灘，然後直接在 Teddy 地盤的正中間設攤，期待你可以得到你南方的 75% 客戶，然後把北方那 25%的客戶留給你的好兄弟。

When Teddy arrives, he sets up just south of you stealing all of the southerly customers, and leaving you with a small group of people to the north.

Teddy 到的時候， 他在你南方一點點設攤，偷走所有南方的客源，然後把剩下的一小群的北方客源留給你。

Not to be outdone, you move ten paces south of Teddy to regain your customers.

為了重新得到你的客源，你不甘示弱地往南十步。

When you take a mid-day break, Teddy shuffles ten paces south of you, and again, steals back all the customers to the far end of the beach.

而當你中午小憩片刻時， Teddy 又移到你的南邊十步，再一次偷走所有南方大部份的客源。

Throughout the course of the day, both of you continue to periodically move south towards the bulk of the ice cream buyers, until both of you eventually end up at the center of the beach, back to back, each serving 50 percent of the ice-cream-hungry beach-goers.

一整天下來，為了獲得大量的冰棒買家，你們雙方不斷規律地往南移動，直到雙方都到了沙灘中間，背對背，各服務 50% 渴望冰棒的客戶。

At this point, you and your competitive cousin have reached what game theorists call a Nash Equilibrium - the point where neither of you can improve your position by deviating from your current strategy.

這時候，你和你那愛好競爭的兄弟已經達到了賽局論專家所稱的「納許均衡點」──也就是雙方都無法藉由偏離目前策略的方式，改善自身的處境。

Your original strategy, where you were each a quarter mile from the middle of the beach, didn't last, because it wasn't a Nash Equilibrium.

你們原本的策略是兩個人分別在海灘中間兩側 0.25 英里的位置，但是這個策略已經不具有優勢了，因為它並不符合納許均衡。

Either of you could move your cart toward the other to sell more ice cream.

你們雙方都可以更靠近對方來賣更多的冰淇淋。

With both of you now in the center of the beach, you can't reposition your cart closer to your furthest customers without making your current customers worse off.

你們兩個都在海灘的中心，雙方都無法再改變車子的位置來接近遠方的客人，同時不讓客人流失。

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 sweet treat.

然而你們不再擁有對全社會最佳的結果，因為在沙灘盡頭的客戶必須為了冰棒，走比原來更遠的路。

Think about all the fast food chains, clothing boutiques, or mobile phone kiosks at the mall.

想想所有的速食連鎖店、服飾精品店、或是購物廣場的手機販售門市。

Customers may be better served by distributing services throughout a community, but this leaves businesses vulnerable to aggressive competition.

在一個社區平均的店家分佈可以提供客戶更好的服務，但是這樣會讓那些好鬥的競爭者有機可趁。

In the real world, customers come from more than one direction, and businesses are free to compete with marketing strategies, by differentiating their product line, and with price cuts.

在真實世界裡客戶來自四面八方，但是生意是各種市場策略的自由競爭，像是銷售不同的產品或是提供折扣，

But at the heart of their strategy, companies like to keep their competition as close as possible.

但是各種策略的中心思想， 就是各公司認為和競爭者愈靠近愈好。