The Prisoner's Dilemma

[packbat]

Another classic game-theory hypothetical for you all:

Yesterday, you and an accomplice pulled off the bank job of the century - a haul large enough for each of you to retire to your favorite island paradise with no extradition to your home country. The money is all untraceably socked away in secret bank accounts, but, unfortunately, the police caught up to you on your way out of town. After a high-speed chase, you both ended up in separate cells in solitary, where you have been stewing away overnight.

This morning, the state attorney visited you in your cell.

"Okay, listen up," he said. "I know you'll just deny it if we ask, but we know you two did it, even if we can't prove it. So I'm going to offer you a deal. Even if both of you say nothing, we can get a year inside for both of you on a reckless endangerment charge for that wild driving last night. I'm willing to drop that charge and let you go if you'll testify against your partner.

"But before you start thinking about altruism and all that, I'm warning you - my partner's right down the hall, offering the exact same deal to your partner. If you clam up and your partner talks, you'll get twenty-five years and your partner will be let off scot free. If you both testify, I'll give you time off for cooperation - fifteen years apiece.

"That's the deal - your choice. Think it over. I'll be back tonight."

Assume that you do not know and have no loyalty to your accomplice - all you want is a minimum sentence for yourself. (You can make up a scenario to explain it if you like - the key part is that you're strangers, only together for one job.)

[Poll #1207554]

(Edit: Anyone interested in further reading may wish to read the Wikipedia Prisoner's Dilemma article.)

(Edit 2: The crosspost to thequestionclub may be found here.)

Comments

[eagon.livejournal.com]

I'd snitch like a motherfucker. No honor among thieves.

[aufdeutschebag.livejournal.com]

Remain silent. He's full of shit.

[si-infuria.livejournal.com]

They wouldn't be offering me shit if they had anything.

[mekkio.livejournal.com]

I'd remain quiet. Even if we have no loyalties between us, if my partner is smart enough to pull off the crime of the century, then he's smart enough to keep quiet and he knows that I am the same.

The cops can't really hold us without a crime. And with the money tucked in a safe place, we can hire a lawyer to make that year in the pen go away.

[bluewolfe.livejournal.com]

So 4 scenarios
I testify, he doesn't, I get off scot free, he gets 25
I testify, he testifies, We both get 10 years
I stay silent, he testifies, I get 25 years
I stay silent, he stays silent, we both get a year.

So it's between 25 and a year, or 10 and nothing. I'm going with the 10 or nothing, which has me testifying. The best case of testifying(0 years) is better than the best of staying silent (1 year) and the worst case of testifying (10 years) is better than the worst case of staying silent (25 years)

Do I have that right?

[bluewolfe.livejournal.com]

was that 15 years off the 25 year sentence? or was that a 15 year sentence. Still, my logic doesn't change much.

[seanseansean.livejournal.com]

i am not a fucking snitch

[brokenbubble.livejournal.com]

i hate the prisoner's dilemma.

[mya87.livejournal.com]

I had the same reasoning. But then it looks like a lot of people are factoring in a third option, that the police are lying. I'm not sure what to make of that.

[bluewolfe.livejournal.com]

Well if this is a game, it'd be bad design to have a random surprise like that in a puzzle. Surprises work in FPS's, but now in puzzles. Save points are not a game mechanic, but a convenience for the player.

[liftup-urhands.livejournal.com]

Agreed.

[mya87.livejournal.com]

that's why i was following that logic you described-- because i thought this was a question about game theory. now i'm just befuddled.

[explodingbat.livejournal.com]

I thought the point of the prisoner's dilemma was that it was played iteratively, in which case you remain silent on your first turn and then do whatever you opponent did previously in each successive turn.

If you ever know that this will be the last game you should always defect because you can't be sure teh other guy won't. Likewise if this is the penultimate game the other guy is going to expect you to defect next turn, so you should defect this turn.

All pretty sordid.

[packbat.livejournal.com]

...dude, that icon's from "Out Of This World"! Awesome!

Oh, and thanks for answering the poll, too. :)

[packbat.livejournal.com]

Thanks for the input!

[packbat.livejournal.com]

Thanks for the input!

[packbat.livejournal.com]

Thanks for the input!

(And yes, you're correct - they can't convict unless one of you snitches.)

[packbat.livejournal.com]

Thanks for the input! There are a number of people who reason that way about the problem (and, obviously, a number of people who reason oppositely).

[packbat.livejournal.com]

15-year sentence, but you're right, your argument remains the same either way.

[packbat.livejournal.com]

Right now, I don't think it's possible to keep people from considering factors like that. Besides, people's justifications for a choice are not necessarily identical to the actual causes.

[packbat.livejournal.com]

Thanks for the input!

[packbat.livejournal.com]

It's a nasty little puzzle, isn't it? Thanks for the input!

[packbat.livejournal.com]

The original dilemma is one-shot, but you're right: in the iterated version tit-for-tat is a fairly reliable strategy. I believe Hofstadter talked about it in a Metamagical Themas column.

(Actually, your analysis there suggests a bit of a recursion, a la the surprise-test (or unexpected hanging) paradox (http://plato.stanford.edu/entries/epistemic-paradoxes/). I suppose you can cut it off with a cost-benefit calculation.)

P.S. Thanks for the input!

[absolute-tash.livejournal.com]

The first rule of successfuly surviving an interrogation is "Keep your effing mouth shut!"

[packbat.livejournal.com]

Thanks for the input (and survival tip)!

[absolute-tash.livejournal.com]

I'm getting ready to be interrogated (BDSM thing) very...hmmm...strenously? And i've been researching it as much as I can. Basically everything says shut up. Also, you know, have a high pain tolerance and focus elseware. But the shutting up thing seems to be pretty universal.

[packbat.livejournal.com]

Heh - I haven't done much research, but I know where I've seen "shut up" as advice: it was in The Colditz Story, a nonfiction story about POWs in Germany, WWII, trying to escape from a prison camp. It's a good plan, too - nothing gives as little info to the enemy as nothing. :)

[alchemi.livejournal.com]

The prisoner's dilemma comes up because they both don't have lawyers. Even if the other guys talks, if all they have is him, and he's getting off scott free, it would be pretty easy for a half-decent attorney to rip his credibility to shreds.

I remember a memorable craigslist entry by an anonymous Arizona defense attorney arguing, very persuasively, that most of his/her clients were idiots who made his/her life difficult because they didn't pay any attention to Miranda. The underlying thesis is that it is almost ALWAYS better not to say anything. If you are going to do a deal, only do one with an attorney negotiating it (I mean who says this guy even honors his 'deal' if you do snich).

[ceruleanst.livejournal.com]

Most people arrange the grid of assumptions like this:

He squeals. If I squeal, 15 years. If I don't, 25 years.
He doesn't. If I squeal, 0 years. If I don't, 1 year.

Viewed this way, the advantage of squealing appears to be guaranteed. Assuming a 50% probability of the variable I don't control, confessing has an expected return of 5.5 more years of freedom than the expected return of staying mum, and a lower risk.

But instead, it can be arranged this way:

Allowed to think about the same problem, we will come up with the same answer. If I squeal, 15 years. If I don't, 1 year.
Allowed to think about the same problem, we will come up with different answers. If I squeal, 0 years. If I don't, 25 years.

This is an equally valid way to divide the possibilities. The advantage of one choice is no longer guaranteed. If we assume that there's no way of knowing, and that the probability here is 50% as before, the comparative expected return remains the same, but there are compelling arguments not to treat this like a 50% chance. Hofstadter says that you should assume that your partner is probably as smart as you and therefore will come to the same conclusion as you. Most other people are given to assume that they are probably much smarter than anyone they're paired with. I think the details of the situation will point to which is more likely. In your version, we've just pulled off an epic bank heist together, so it stands to reason that we are comparably clever.

[packbat.livejournal.com]

Thanks for the input! (A lot of people have been talking about the credibility!)

[packbat.livejournal.com]

Thanks for the input! (I remember Hofstadter's analysis of this - I've always thought his analysis was clever, although I know of few whom it convinced.)

[xsickittyx.livejournal.com]

My professor talked about the prisoners dilemma in an econ class. I don't remember what it had to do with economics though. Hmm...

[packbat.livejournal.com]

Economists love game theory, I suppose. And actually, now that I think of it, I think you can make a Prisoner's-Dilemma-equivalent for trade - the 'defect' option (which is "testify" here) corresponds to not holding up your end.

(Thanks for answering the poll!)

If it was someone I knew, my answer would change depending on who they were.

[the-zaniak.livejournal.com]

I'd remain silent. I don't have a lot of reasoning behind it, though. It's hard to tell where your morals would lie when you've just inexplicably found that you're a bank robber, working with someone you don't know very well.

Interesting! Of course, the scenario is completely different when you know your accomplice.

[packbat.livejournal.com]

This is true, and a problem with the hypothetical. Difficult to fix, though. Thanks for the input!