think they committed a more serious crime but they don't have enough evidence to convict

警方認為他們涉嫌某件重大犯罪，但卻因證據不足而無法證明兩人有罪

them. They need a confession. They take them and put them in separate rooms so they can't

警方需要其中一人自首招供。警方將兩人分別安置於不同房間避免交談

talk, and play a little game. To try to force a confession the police give

並且進行一項小遊戲。為了順利讓其中一人招供，警方分別給予兩人選擇權

them each a choice. Admit your partner committed the crime, and you will go free. We'll pardon

只要你供出對方的罪行，就能重獲自由之身

you for the minor crime but your partner will have to spend 3 years in prison. If you stay

警方會寬恕你犯下的輕微罪行，但對方會被判入獄3年

silent and your partner lets us know that you were the one who really did it then you're

如果你選擇沉默，而夥伴選擇供出你的話，那麼你就會因此入獄3年

going to have to go away for 3 years. They know that the police don't have any evidence

他們知道警方沒有任何證據

and if they both stay silent then they will only go to prison for 1 year each for the

所以只要兩人都保持沉默，那麼就只會因涉嫌輕微犯罪而被判1年刑期

minor crime. If they both betray each other then they'll both go to prison for 2 years

如果雙方皆選擇背叛對方，那麼兩人都會被判2年刑期

each. OK, each partner can do 1 of 2 things. Stay

好，雙方都有二條路可選，保持沉默或是選擇背叛對方

Silent, or Betray. Staying silent would be cooperating and betraying would be defecting.

保持沉默需要攜手合作，背叛則需出賣對方

If they both stay silent, they each spend a year in prison. If one betrays and the other

如果雙方皆選擇保持沉默，那麼兩人只要坐牢1年；如果背叛對方，對方選擇保持沉默

stays silent, then the betrayer goes free and the silent spends 3 years in prison. If

那麼自己則會重拾自由，對方則需坐牢3年

they both betray then it's 2 years each. So what are they going to do? Well they should

如果互相背叛對方，那麼兩人都要坐牢2年。所以他們會怎麼做？ 他們勢必要攜手合作

cooperate. That's the best option for the group, if we add the total number of years

從刑期的長短來看，這才是對彼此最好的選擇

in prison. But let's take it from Red's perspective.

但是我們試著站在紅小姐的立場來思考

If she thinks blue is going to stay silent, then she should betray so she can go free.

如果她認為男方會保持沉默，那麼她可以選擇供出對方罪刑，那麼自己就能重獲自由

Going free is better than a year in prison. If she thinks he's going to betray her then

重獲自由比吃1年牢飯還要好。如果她認為男方會出賣她的話

she should definitely betray, 2 years in jail is better than 3 and being made a fool of.

那她也應該選擇出賣對方，畢竟2年牢飯比當個笨蛋被害成3年來得好

Blue is in the exact same situation and will think the exact same thing, he should betray

藍先生的處境也一樣，所以也會有相同考量

if she stays silent and he should betray if she betrays.

假設女方保持沉默，自己則應該選擇供出女方罪刑；而假設女方選擇出賣，自己則應該選擇出賣

They should have both cooperated, but from an individual stand point they noticed they

他們必須共同合作，但是從單獨立場來看，如果不曉得對方會怎麼做

could always gain by defecting. If they have no control over what the other person is going

出賣對方才是上策

to do. So they'll both defect to try to better their own situation. But come away not only

所以他們都會試圖出賣對方改善自己的處境，但一旦背叛對方

hurting the group, but themselves. Individually they're worse off than if they both cooperated.

不僅只是整個群體會受影響，自己也會完蛋。如果沒有共同合作，彼此的處境可能會變得更糟

This situation is pretty made up, but it has some real world analogues. A common example

雖然這樣的情境是假設出來的，但現實生活中也時常發生。最常見的例子是市場行銷

is with marketing . Let's say 2 cigarette companies, Red Strikes,

讓我們假設有兩家菸廠，紅A與藍B

and Smooth blue, are deciding how much money they should spend on advertising. Since the

兩廠在商討要花多少錢打廣告

product they each make is identical to one another, advertising has a huge impact on

因為他們的產品幾乎一模一樣，所以打廣告會對銷售帶來顯著的影響

sales. For simplicity let's say their choices are: to advertise a bunch, or not advertise

同樣地，他們有兩個選項：打廣告、或不打廣告

at all. And there's just 100 people in this society and they all smoke. If both don't

假設這個社會上只有一千個人，且全都吸菸

advertise, then just by random chance picking cigarette boxes, 50 people buy Red Strikes

不打廣告的情況下消費者會隨機購買，50人會買紅A廠製

and 50 people buy Smooth blue. At $2 a pack they each make $100. Let's say advertising

另外50人則會買藍B廠製。如果一包菸賣2元，那麼兩廠各能賺進100元

costs $30. If one person advertises and the other does not, then 80 people will buy the

但假設廣告費用是30元，且其中一家打廣告，另一家不打的情況下，會有80人買有打廣告的

cigarettes from the ads and 20 people buy the other ones. The advertiser makes $160

其餘20人買沒打廣告的。紅A廠因打廣告賺進了160元

minus $30 for ads, and comes away with $130. The non advertiser didn't spend money, but

扣除30元的廣告費，能賺到130元。而沒花錢打廣告的B廠則受影響僅賺進40元

only made $40. If they both advertise, again half will buy Red Strikes, and half will buy

如果兩家都花錢打廣告，那麼消費者的購買機率又回到50: 50

Smooth blue. But since they both spent $30 on advertising, they only come away with only

但因為花了30元打廣告的關係，最終兩家都只賺進70元

$70 each. Same deal, both people cooperating and not

一樣的概念，選擇攜手合作且不打廣告的話就能夠達到

advertising is the most preferable situation, but both company can see that advertising

雙贏的局面。但是對兩家來說，打廣告能幫公司賺進更多錢

will always make them more money. But unlike the prisoner's in jail, these companies

但不同於入獄服刑的犯人，這兩家公司能夠進行溝通協調

can talk and try to influence each other. From here Blue would be better off if Red

並且嘗試影響對方。只要雙方都沒打廣告，兩邊都有錢賺

didn't advertise. Red wouldn't go for that because that would be worse for them.

但是對紅A廠來說，甚麼都不做的情況下銷售可能變差

Blue could try to convince Red that they would both not advertise, the only other situation

藍B廠可以選擇說服A： 兩邊都不打廣告的話，對兩邊都好

where they're both better off. But without any real obligation to each other, there's

但如果沒有實質約束的話

nothing that's stopping them from trying to advertise to gain more of the market anyway.

就沒有甚麼能夠阻止對方打廣告賺大錢

If you think your opponent's going to not advertise, you're better off advertising.

所以如果覺得對手不會打廣告，那你最好選擇打廣告

Although we're still making assumptions to make this situation work too. With this model

畢竟這只是我們假設出來的情境。在這樣的情境下

we're assuming they only play once. The game changes when the players have a chance to

我們只假設發生一次。當玩家們有機會建立關係，遊戲規則就會改變。只要一起合作

build a relationship and work together to get more gains over time, or punish each other

就能一起賺大錢；當然也可以搞對方，選擇不配合

by not cooperating. Also to make the model work we have to make

為了讓這模擬情境能夠運作，我們必須制定遊戲規則來規範玩家

up rules for the players. Assume they're basically computer programs with predictable actions.

假設玩家都是電腦，且所有行為都是設定好的

These guys are creepier than they were in my head. They were supposed to be cute.

沒想到電腦卻會讓人感到可怕，它們應該是善良可愛的才對

For the prisoner's dilemma and other similar models, we're assuming they are Rational Agents.

在囚徒困境和類似情境中，我們假設登場人物都是理性動物

A rational agent is a hypothetical person that will always pick the option that they

理性動物能透過思考來選出自己認為是最好的答案

predict will work out best for them. They're not really thinking about the gains of someone

且不會管他人是死是活

else. Seems selfish but it something that real people will generally do too. People

聽起來很自私但這對人類來說是很平常的事

always want what's best for themselves and we don't like to made a fool of.

人們會總是希望選擇對自己好的選項，而且不喜歡他人被玩弄股掌間

But if you put real people in the prisoner's dilemma, people don't always defect like the

但如果將一個人放在囚徒困境中，他並不會每次都照模擬走，選擇背叛對方

model predicts. In one study, 40 people playing prisoner's

某項研究報告顯示，將40個人放在囚徒困境中

dilemma games, through a computer, without ever meeting or talking, only playing each

透過電腦模擬，在沒有見面、交談的情況下，若任一位玩家只能只玩一次

opponent once, these are one off games, using a payoff matrix that looks like this, cooperated

讓全部玩家都玩過之後，結果就會像這張得失矩陣一樣，合作機率為22%

an averaged 22% of the time. These people never cooperated. These are people always

這項表示玩家遊戲中不曾與他人合作，而這項表示玩家總是選擇合作

cooperated. These guys cooperated on half of their games and everyone else is in between.

這項表示玩家在遊戲過程中有一半情形是選擇與他人合作，其他則成不規則分布

This is a lot of cooperation coming from a model that predicts no cooperation.

在原本預測不會合作的情境下，竟出現了許多次合作

The largest group did act like rational agents, but most people tried to cooperate at least

雖然最大群體的確有像同理性動物般地做出決定，但大多數的人卻最少會嘗試與他人進行合作一次

once. It's because there's more to real people.

因為人類不僅擁有理性思維

We are social creatures and even in a one off scenario with no guarantees and obligations

人類是社交型動物，即是在沒有保證、沒有任何義務、沒有任何機會與他人建立關係的單次情境下

and no chance to build a relationship, we're still thinking about how the group might decide.

我們仍會思考別人可能做出甚麼選擇

We're actually thinking from the perspective of the group, and making an optimistic decision.

我們會站在群體的觀點思考，然後做出一個正面樂觀的決定

Cooperating an average of 20% of the time might not seem very optimistic, but remember

合作的機率是20%，聽起來雖然不太樂觀

this is with absolutely no communication or obligations.

但記得這機率的先決條件是完全無法溝通、或是責任歸屬

Anyways, that's not really the point. Using the rational agent is still useful. The model

這不是今天的重點。用理性動物來情境演練還是有效的

is just trying to point out the dilemma of certain specific situation where people actually

這情境只是要演算某種特定情形的結果為何，但事實上人們會不自覺的只想到自己

hurting themselves when counter-intuitively, they're only thinking about themselves...

然後選擇傷害對方

and that's why we're modelling using the cold robotic psychopaths.

這就是為什麼我們要設定玩家為冷血無情的心理病態