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，警察將你們兩個人抓起來，并把您放在兩個單獨的審訊室中，以便您彼此之間沒有任何溝通。 您以為自己的生活已經結束，但是警察提出了一項協議：

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，他們的句子就會很重，您的句子就會很輕。 如果您互相淘汰，則兩者都將受到重罰。 如果你們兩個都保持沉默，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：

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人的年限，具體取決于您和您的朋友獨立選擇做什么。 第一個數字代表您的入獄時間，第二個數字代表您朋友的入獄時間。

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，而您的朋友只會被服刑一年。

What would you do in this situation?

在這種情況下您會怎么做？

What should you do in this situation?

你應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。 功利主義者可能會說，扣繳稅是更好的選擇，因為它使每個人在監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.

我創建了1000名囚犯，每名囚犯都有50–50個叛逃者或保留者的機會。 然后，我模擬了500對囚犯的互動，并記錄了結果。 我重復了這個實驗200次。

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量大致相同，那么最好隱瞞信息。 大多數時候，回報將對您有利。 叛逃者在監獄中的平均年限為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變得更加有趣。 假設您所在的國家/地區每個人都不互相信任，并且75％的人口屬于叛逃者，而25％的人是叛逃者。

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，因為如果您也要叛逃，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。 假設每個人都過分信任(盡管他們剛剛犯了謀殺罪)。

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！)。 這是因為其他缺陷的可能扣留可能是三年或五年，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，您會怎么做？

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