走出囚徒困境的方法

You and your friend have committed a murder. A few days later, the cops pick the two of you up and put you in two separate interrogation rooms such that you have no communication with each other. You think your life is over, but the police offer up a deal:

您和您的朋友謀殺了。 幾天后，警察將你們兩個(gè)人抓起來，并把您放在兩個(gè)單獨(dú)的審訊室中，以便您彼此之間沒有任何溝通。 您以為自己的生活已經(jīng)結(jié)束，但是警察提出了一項(xiàng)協(xié)議：

Rat your friend out, and your sentence will be lighter.

把你的朋友趕出去，你的句子就會(huì)輕些。

The catch is that your friend is offered this deal, too.

問題是您的朋友也被提供了這筆交易。

More specifically, if you rat your friend out but your friend says nothing, they get a heavy sentence and you get a light one. If you rat each other out, there’s a heavy penalty for both. If both of you stay silent, the sentences are light for you and your friend.

更具體地說，如果您淘汰了您的朋友，但您的朋友什么也沒說，他們的句子就會(huì)很重，您的句子就會(huì)很輕。 如果您互相淘汰，則兩者都將受到重罰。 如果你們兩個(gè)都保持沉默，那么對您和您的朋友來說句子很輕。

The decisions must be made without communicating with each other, and both you and your friend only have two choices: “defect” and rat them out, or “withhold” information from the cops and stay silent.

這些決定必須在不相互溝通的情況下進(jìn)行，您和您的朋友只有兩種選擇：“瑕疵”并將其淘汰，或者“隱瞞”警察的信息并保持沉默。

Take a look at the following diagram that describes your choices and sentences:

看下面的圖表，它描述了您的選擇和句子：

A punishment diagram for you and your friend.你和你的朋友的懲罰圖。

The matrix describes the number of years the two of you get depending on what you and your friend independently choose to do. The first number represents your prison time and the second represents your friend’s.

該矩陣描述了你們兩個(gè)人的年限，具體取決于您和您的朋友獨(dú)立選擇做什么。 第一個(gè)數(shù)字代表您的入獄時(shí)間，第二個(gè)數(shù)字代表您朋友的入獄時(shí)間。

For example, if you withhold information from the cops, but your friend chooses to rat you out, you get five years in a maximum-security prison but your friend only gets one.

例如，如果您從警察那里隱瞞信息，但您的朋友選擇將您殺了出去，您將在最高安全牢獄中服刑五年，而您的朋友只會(huì)被服刑一年。

What would you do in this situation?

在這種情況下您會(huì)怎么做？

What should you do in this situation?

你應(yīng)該在這種情況下怎么辦？

There’s no easy solution to this problem and there are a lot of interpretations to this. A utilitarian might say withholding is the better option because it minimizes the total number of years either person spends in prison (5 + 1 or 3 + 3 as opposed to 10 + 10). What does probability say?

這個(gè)問題沒有簡單的解決方案，對此有很多解釋。 功利主義者可能會(huì)說，扣繳稅是更好的選擇，因?yàn)樗姑總€(gè)人在監(jiān)獄中度過的總年限最小化(5 + 1或3 + 3，而不是10 + 10)。 概率說什么？

解決困境 (Solving the Dilemma)

I created a population of 1000 prisoners, each with a 50–50 chance of being a defector or withholder. I then simulated an interaction for 500 pairs of prisoners and took note of the outcomes. I repeated this experiment 200 times.

我創(chuàng)建了1000名囚犯，每名囚犯都有50–50個(gè)叛逃者或保留者的機(jī)會(huì)。 然后，我模擬了500對囚犯的互動(dòng)，并記錄了結(jié)果。 我重復(fù)了這個(gè)實(shí)驗(yàn)200次。

Defectors vs. Withholders (50–50 split).偏轉(zhuǎn)器與持倉者(50-50分割)。

As you can see, if the number of defectors and withholders is roughly the same, it’s far better to attempt to withhold information. Most of the time, the payoff will be in your favor. The average number of years a defector spent in prison was 5.75 years vs. a withholders 4.01.

如您所見，如果叛逃者和撤回者的數(shù)量大致相同，那么最好隱瞞信息。 大多數(shù)時(shí)候，回報(bào)將對您有利。 叛逃者在監(jiān)獄中的平均年限為5.75年，而扣留者的平均年限為4.01年。

We can make this a bit more interesting by varying the proportion of defectors and withholders. Say you’re in a country where everyone is untrusting of one another and that 75% of the population is a defector vs. 25% withholder.

我們可以通過改變叛逃者和持股者的比例使這一點(diǎn)變得更加有趣。 假設(shè)您所在的國家/地區(qū)每個(gè)人都不互相信任，并且75％的人口屬于叛逃者，而25％的人是叛逃者。

Defectors vs. Withholders (75–25 split).偏轉(zhuǎn)器vs.保留者(75-25分)。

Your best bet is to withhold information from the police. This makes sense, since if you were to defect as well there’s a much higher probability that you’ll end up with the worst option in the game — 10 years a piece.

最好的選擇是不向警方提供信息。 這是有道理的，因?yàn)?strong>如果您也要叛逃，那么您最終有可能在游戲中遇到最糟糕的選擇，那就是每10年一次。

Let’s try one more. Say everyone is overly trusting (despite the fact that they’ve just committed a murder).

讓我們再試一次。 假設(shè)每個(gè)人都過分信任(盡管他們剛剛犯了謀殺罪)。

Defectors vs. Withholders (25–75 split).偏轉(zhuǎn)器vs.保留者(25–75分割)。

This one is more interesting. It seems that you’d be slightly better off withholding information, but the payoff is wildly inconsistent (and in some cases ends up being worse than defecting!). This is because the possible sentences for withholding while the other defects can be either three or five years while the possible sentences for defecting while the other withholds can be either one or ten years. The difference between 3 and 5 is a lot less than the difference between 1 and 10 — so there’s a lot more variance in the latter scenario.

這個(gè)更有趣。 似乎您最好不隱瞞信息，但是收益卻是完全不一致的(在某些情況下最終要比背叛更糟！)。 這是因?yàn)槠渌毕莸目赡芸哿艨赡苁侨昊蛭迥?#xff0c;而其他缺陷的可能扣留可能是一年或十年。 3與5之間的差異遠(yuǎn)小于1與10之間的差異-因此在后一種情況下存在更多差異。

What would you do in this particular situation?

在這種特殊情況下，您會(huì)怎么做？

If you enjoyed this article, you can follow me on Medium for more content like this. Thanks for reading!

如果您喜歡這篇文章，可以在Medium上關(guān)注我，以獲得更多類似的內(nèi)容。 謝謝閱讀！

翻譯自: https://towardsdatascience.com/a-computational-approach-to-the-prisoners-dilemma-837a799cedf0

走出囚徒困境的方法

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