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In the Wikipedia example of The Prisoner's Dilemma it states that "all purely rational self-interested prisoners will betray the other, meaning the only possible outcome for two purely rational prisoners is for them to betray each other."

https://en.wikipedia.org/wiki/Prisoner%27s_dilemma

My question is why would they betray each other if they are rational?

Why wouldn't being rational (logical) result in each concluding that there's no reason to think the other would choose differently...therefore the only choice is to stay silent to guarantee the minimum sentence as there is no possibility for the other options?

Randy Zeitman
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  • @InterstellarProbe What is the reasoning that leads to the conclusion that the other will stay silent? ... it's impossible. It's like a card that says "the other side is true" on one side and "the other side is false" on the other.

    The presumption can only be that the other person cannot choose differently than I so we either both confess or both stay silent ... so stay silent.

     – Randy Zeitman May 21 '19 at 21:54
  • If they are clever, the accused may see this offer as a sign of weakness of the prosecutor's case. – Dan Christensen May 22 '19 at 02:24
  • @DanChristensen Sorry but it does not. There's nothing one has to trust. They'll both conclude that there's no reason for one to take to fall for the other and as such the only option is silence. It doesn't matter if they're lifelong friends or strangers. Each one must presume the other can reach the same conclusion. – Randy Zeitman May 22 '19 at 02:30
  • It says at your link, "The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge." These gang members may rationally choose a short sentence over being on the streets with fellow gang members looking for revenge. Or maybe, just maybe out of a sense of loyalty. It could happen. – Dan Christensen May 22 '19 at 02:40
  • @DanChristensen Why would they do anything other than rationally choose the short sentence? – Randy Zeitman May 22 '19 at 15:36
  • Change the game slightly: Suppose these "criminals" are actually spies working to undermine an evil empire (e.g. the Nazis in WW2) that has them arrested. They may rather die a painful death than betray "the cause." Would that be "irrational?" There are just too variables in real life to make simple generalizations. – Dan Christensen May 22 '19 at 19:39
  • @Dan What does betray the cause mean? Spies don't get arrested they get tortured and interrogated and understand there's no bargain to be made. They're not going to choose death because they can be traded. The time for them to choose death is before they are in the hands of the enemy. – Randy Zeitman Jun 04 '19 at 01:22
  • You have lived a very sheltered life. And that is a VERY good thing! The fact is, spies get captured and can be tortured to death for refusing to betray their comrades and their common cause. An extreme example, but I just meant to show that this so-called prisoners' dilemma is not always amenable to simplistic generalizations as above. – Dan Christensen Jun 04 '19 at 02:52
  • Why kill a captured spy on purpose? What simplistic generalization isn't amenable? Why resort to left-handed compliments? – Randy Zeitman Jun 04 '19 at 03:06
  • It is a thought experiment, not a realistic simulation. It is implicit that the sentencing should be the only cost/benefit consideration -- not the possibility of revenge, or affect on reputation, or such. – Graham Kemp Jun 05 '19 at 04:07
  • Why create a human behavior experiment where people act strangely to demonstrate how people normally act? What would you do? I'd very much like to hear the logic of choosing to not keep quiet. – Randy Zeitman Jun 05 '19 at 14:58

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Other answers and comments explain why betrayal is dominant, echoing the standard argument (in the linked wikipedia page) that

the only possible outcome for two purely rational prisoners is for them to betray each other.

Your question suggests a different definition of "rational", one which makes "do unto others" a rational strategy. I think that is a defensible philosophical position.

It's this kind of argument that makes the prisoner's dilemma worth thinking about.

Ethan Bolker
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Confessing is a dominant strategy for both players in the Prisoner's Dilemma.

A few more lines on why confessing is a dominant strategy. Consider yourself in the game. Consider both the possibilities of what the other guy would do (confess, stay silent) and convince yourself that you would pick confessing as it has a better payoff. Since the game is symmetric, the other guy would do the same to you and you'd both end up confessing.

Vizag
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    This statement is true, but begs the question. Making it an answer assumes that a rational person will choose the dominant strategy. The OP is suggesting a different definition of rational. (And perhaps you should explain what "dominant strategy" means.) – Ethan Bolker May 21 '19 at 21:39
  • Yeah thanks Ethan. I thought the same too. And have edited the answer with a few lines of explanation. – Vizag May 21 '19 at 21:42
  • @Vizag Each person understands that if they both confess they get more years than staying silent. As you said it's symmetric ... there's no possibility one will behave differently than the other. This seems to be an XOR situation.

    If the presumption is that the people are rational then self-interest will NOT trump it.

     – Randy Zeitman May 21 '19 at 21:50
  • The key here is this: "You're acting simultaneously and without the knowledge of what the other guy is doing". If you could collude, sure both of you'd pick to stay silent. But you can't. – Vizag May 21 '19 at 21:52
  • Were you able to convince yourself of the fact that confessing is indeed a dominant strategy? – Vizag May 21 '19 at 21:52
  • Two rational prisoners can independently conclude that double-loyalty is the collective best result, but must acknowledge that that only works if they can each trust the other party to not act with self-interest. – Graham Kemp May 22 '19 at 01:36
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I think you're right. Wikipedia says that "all purely rational self-interested prisoners will betray the other". However, in order to show that a prisoner will betray the other, we actually need three assumptions:

  • The prisoner is purely rational.
  • The prisoner is self-interested.
  • The prisoner assumes that the other prisoner's decision is totally independent of her own.

Betraying the other player is said to be a dominant strategy.

You have noticed (correctly) that prisoners will instead cooperate if we make these three assumptions:

  • The prisoner is purely rational.
  • The prisoner is self-interested.
  • The prisoner assumes that the other prisoner will always make the same decision that she herself makes (since, after all, the two prisoners are identical).

I don't know of a particular name for a strategy which is best according to these criteria. However, your reasoning reminds me of Eliezer Yudkowsky's "timeless decision theory", which states that if you're in a prisoner's dilemma, and you and the other prisoner are both using timeless decision theory, then you should cooperate (since the other prisoner will make the same decision that you will make).

Tanner Swett
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  • Two rational prisoners can independently conclude that loyalty is the collective best result, but must acknowledge that that only works if they can each trust the other party to not act with self-interest. So, when one prisoner is self-interested... – Graham Kemp May 22 '19 at 01:43
  • @GrahamKemp It has nothing to do with loyalty. It has only to do with logic. The only way one can go free is if one chooses to blame and the other to not blame... which is impossible since each understands the other wants to do the same thing. It's a logical standoff and each is forced to be silent. I see no dilemma. – Randy Zeitman May 22 '19 at 02:02
  • @Tanner Yes, almost. The prisoner will not assume the same decision will be made (if one chooses to accuse then the other will as well ... it's not like quantum entanglement).

    The reason is that each one will presume the other thinks as he/she does, sees the mutual dilemma, and concludes each must shut up and take the year because one staying and one leaving is logically impossible.

     – Randy Zeitman May 22 '19 at 02:11
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Betrayal nets you freedom if the other stays loyal, or two years if the other also betrays.

Loyalty nets you one year if the other is also loyal, or three years if the other betrays.

My question is why would they betray each other if they are rational?

It is in the "self-interested" part of "purely rational self interested."   That aims for freedom and avoids three years but accepts two years as the result of neither party trusting nor caring about the other.

Only if one could trust the other and each cared about the collective best result , then would loyalty be the rational best choice.

The very point of the experiment is that people tend to not be purely self interested or rational in such a scenario. In practice people would stay silent trusting the other to do the same, even though it is in their self-interest to--as the experiment's wording deliberately frames it--'betray' the other.

Graham Kemp
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  • Why is trust needed? What is the logic that has one think that the other will not go through the same logic and conclude it's impossible for both to betray? – Randy Zeitman May 22 '19 at 15:38
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    (It is clearly not impossible for them to both betray). Each knows what is their own thought process, but must measure their trust in the other's response. "I know we should both choose silence as its best for both of us, but my fellow prisoner knows I might do that, do I then trust them to not confess? Can they trust me...?" – Graham Kemp May 22 '19 at 22:51
  • Still again, and I've yet to see an answer ... what trust is needed? Why would one think that the other would not see the same situation? How can both parities conclude that the other will make a different choice? ... how is that possible? – Randy Zeitman Jun 04 '19 at 01:24
  • Do they have reason to trust that the other party is purely rational and not self interested? – Graham Kemp Jun 04 '19 at 01:29
  • Why would criminals who choose to work together not be rational and self-interested. What's the real reason you're saying that? – Randy Zeitman Jun 04 '19 at 01:32
  • Because if they are purely self-interested they would not be interested in the welfare of the other, and anticipate the possibility that the other is the same. The purely rational self-interested choice would not be to stay silent aiming for 1:1 risking 3:0, but rather confess expecting 2:2 but hoping for 0:3. – Graham Kemp Jun 05 '19 at 02:37
  • You say purely but perhaps you mean independently. If there wasn't a dependence then self-interest wouldn't include the other (definition of independence). But since they are, then they have to realize each must choose the same as the other given the offer being made.

    There is no 0:3 ... that would require one both confess and not indict the other.

     – Randy Zeitman Jun 05 '19 at 02:45
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    No, I do mean purely. $~$ If one expects the other to stay silent: it is pure self interest to confess (and thus going free while the other receives 3 years (0:3); pure self interest does not care about harm to the other). $~$ If one expects the other to confess: it is pure self interest to confess (avoiding 3 years and not letting the other go free). $~$ Obtaining a 1:1 sentence is only possible if both trust the other will also think that both remaining silent is the best combined result (ie each has interest in the other's well being and trusts the other to think the same). – Graham Kemp Jun 05 '19 at 03:16
  • The point of the experiment is that people are not purely rational self-interested. In practice people would stay silent because they initially trust others to have some collective interest. Most prefer a joint one year sentence over the thought of going free while another suffers from their choice. [It's why the wording of the experiment frames confession as 'betrayal'.] – Graham Kemp Jun 05 '19 at 03:29
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I USED TO agree that betraying is a good strategy. If Prisoner B thinks that he is better off staying silent, Prisoner A can be free while Prisoner B can stay in jail for 3 years. Now, I agree with Vizag. CONFESSING, HOWEVER, SEEMS LIKE A BETTER STRATEGY. Just consider the combinations and pick the choice to confess. Prisoner B would do the same thing as you.

elipson_-1
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