Split or steal?

April 21, 2012 7:11 PM

Possibly the best filmed example of game theory in action ever.
posted by unSane (127 comments total)

(via Farnam Street, the excellent blog run by Mefi's own sf9719
posted by unSane at 7:14 PM on April 21, 2012

Once I got over the non-ironic insistence on referring to balls, holy cow that was great. The best defence is a good offence, indeed. Nick immediately reframed the question for Ibrahim, totally eliminating from consideration the possibility Ibrahim had to steal.
posted by Homeboy Trouble at 7:22 PM on April 21, 2012 [18 favorites]

I spent yesterday watching lots of Split or Steal clips and they are addictive. It's particularly interesting to see how people rationalize their decisions and how people lie to each other.
posted by Foci for Analysis at 7:27 PM on April 21, 2012 [1 favorite]

This is just about the only time in history I can picture two opponents on a game show ending up being friends.
posted by sonic meat machine at 7:28 PM on April 21, 2012 [2 favorites]

I would not want to be friends with Nick.
posted by euphorb at 7:31 PM on April 21, 2012 [7 favorites]

Damn, I was hoping Ibraham picked Steal.
posted by Ardiril at 7:33 PM on April 21, 2012

That was fantastic, thanks.

For those that missed the Coursera post, I'll note that they're offering a game theory course.
posted by inigo2 at 7:33 PM on April 21, 2012 [1 favorite]

That was amazing. Also, is this seriously a show???
posted by crasiman at 7:33 PM on April 21, 2012

Also, I would love to get Nick at a poker table.
posted by Ardiril at 7:34 PM on April 21, 2012 [2 favorites]

I have never heard of this show before. When the balls first came out, I thought the issue was one of blind chance, so I thought: eh, typical stupid high-stakes game show. Then the host explained that the got to look at their options first. Hoo boy, I thought, that's interesting, what do they think the other person will do?

Then the host explained that they get to talk to each other for a minute before making their choice. Thus making this THE MOST FASCINATING GAME SHOW EVER
posted by shakespeherian at 7:35 PM on April 21, 2012 [23 favorites]

That was great. I think it worked because, as homeboy trouble says, Nick immediately reframed the problem. Instead of, as the host saying moments ago, you could maybe get zero, half, or all, Nick's has reframed it to be you could definitely get zero or maybe get half. A maybe-half is better than a definite-zero, so Ibrahim rationally picks with maybe-half. There's no lure of a maybe-full that would cause you to consider defecting.

Where it could have fallen down was if Nick wasn't convincing, or Ibrahim wasn't convinced. Nick was confident he could bluff Ibrahim in to thinking there was only two options left.
posted by kithrater at 7:37 PM on April 21, 2012 [14 favorites]

There is the risk if Ibrahim got sufficiently angry that he would decide to steal to spite Nick, though.
posted by a womble is an active kind of sloth at 7:42 PM on April 21, 2012 [13 favorites]

Nick's promise to "split the money after the show", along with his patter about being an honest fellow set my bullshit detector ringing. He conceded his chance to sweep the pot but increased his chance to walk with half. Poor Ibrahim was easily bluffed, like most honest men are.

As soon as Nick put forth his proposal, I'd have agreed. Then picked "Steal".

Anyone who tells you they're honest? Isn't.
posted by BitterOldPunk at 7:43 PM on April 21, 2012 [9 favorites]

Big money split or steal clip
posted by Bwithh at 7:43 PM on April 21, 2012 [7 favorites]

Useful background: The Prisoner's Dilemma.
posted by grumblebee at 7:44 PM on April 21, 2012 [4 favorites]

Vincini would have seen through this and chosen steal.
posted by ridogi at 7:45 PM on April 21, 2012 [1 favorite]

I wonder how long it will be until I won't giggle like an 11 year old every time they say balls.
posted by birdherder at 7:46 PM on April 21, 2012 [8 favorites]

I would love to get Nick at a poker table.

That kind of table-talk would likely get him booted out of a game very quickly, I think.
posted by ShutterBun at 7:47 PM on April 21, 2012

Nick's strategy seems sufficiently effective as to make future episodes impossible.
posted by gerryblog at 7:51 PM on April 21, 2012

Nick's strategy seems sufficiently effective as to make future episodes impossible.


On the contrary, it's desperatly vulnerable to a 'steal'. That's why he was trying to hard to persuade Ibrahim that a 'steal' was a losing play.
posted by unSane at 7:54 PM on April 21, 2012 [3 favorites]

Vincini would have seen through this and chosen steal.

Actually, I'm immune to stealing.
posted by shakespeherian at 7:55 PM on April 21, 2012

Split or Steal? Cooperative Behavior When the Stakes are Large

Abstract:
We examine cooperative behavior when large sums of money are at stake, using data from the TV game show “Golden Balls.” At the end of each episode, contestants play a variant on the classic Prisoner’s Dilemma for large and widely ranging stakes averaging over $20,000. Cooperation is surprisingly high for amounts that would normally be considered consequential but look tiny in their current context, what we call a “big peanuts” phenomenon. Utilizing the prior interaction among contestants, we find evidence that people have reciprocal preferences. Surprisingly, there is little support for conditional cooperation in our sample. That is, players do not seem to be more likely to cooperate if their opponent might be expected to cooperate. Further, we replicate earlier findings that males are less cooperative than females, but this gender effect reverses for older contestants because men become increasingly cooperative as their age increases.
posted by Bwithh at 7:56 PM on April 21, 2012 [8 favorites]

On the contrary, it's desperatly vulnerable to a 'steal'. That's why he was trying to hard to persuade Ibrahim that a 'steal' was a losing play.

It would be a more effective strategy if Nick took the time to write out a cheque for the amount, show it to Ibrahim, and then leave it resting on Nick's side of the table. Then Nick picks Steal and hands over the cheque.
posted by kithrater at 7:57 PM on April 21, 2012 [1 favorite]

That was beautiful.

Of course it would never work twice, because the next guy would steal.
posted by empath at 8:00 PM on April 21, 2012 [2 favorites]

It's simpler than game theory but this impressed me when I was ten.
posted by XMLicious at 8:02 PM on April 21, 2012 [1 favorite]

How about this strategy:
You each pick each other's ball. If you don't look at your own balls (so your opponent doesn't have any information about the contents of your balls from your reactions), and you pick the opponent's ball at random, you have a 75% chance of walking away with money (expectation = 37.% of pot), regardless of 'how' your opponent picks which of your balls you should hand over. This requires no trust on either party.
posted by Pyry at 8:02 PM on April 21, 2012 [7 favorites]

I was on flight about ten years ago where they had person TVs for each seat and a small set of channel options, one of which was GSN, which is perfect for me on a flight, really. The only shows I remember from that desperately long flight were Lingo, which I think is still running, and Friend or Foe?, hosted by former VJ Kennedy, which was basically this exact premise. Two teams of two strangers each work together to win the most money, and then the winning team goes through the prisoner's dilemma.

The episode I remember most had a team of an attractive woman and schlubby guy getting to the end, where of course he was enamored and chose to split and she chose to steal because she knew there was no way he was going to screw her over. I think all thew other episodes I saw ended with them splitting.
posted by Navelgazer at 8:02 PM on April 21, 2012

The game probably would let you pick your opponent's ball.
posted by shakespeherian at 8:03 PM on April 21, 2012

Why not? You're allowed to talk, you agree on this strategy, you tell your opponent to pick (for example) the ball at their right, and if they don't, you back out.
posted by Pyry at 8:04 PM on April 21, 2012

In terms of game theory, why should Nick choose to split?

If Ibrahim has been convinced that his choices are nothing, or maybe-half (if Nick is being honest about his strategy), and Ibrahim isn't spiteful, then the only thing he can choose is split. If Nick believes that Ibrahim will act that way, and he's concerned only with making the most money (and not, for example, not being a dick), then why wouldn't Nick choose steal and get all of it?
posted by jcreigh at 8:05 PM on April 21, 2012

Why not? You're allowed to talk, you agree on this strategy, you tell your opponent to pick (for example) the ball at their right, and if they don't, you back out.

In that case, how do you know which one is which? You're back to trusting their word.
posted by shakespeherian at 8:08 PM on April 21, 2012

you don't; it's random. You pick the one on their right; they can pick one on your side.
posted by sonic meat machine at 8:10 PM on April 21, 2012

In terms of game theory, why should Nick choose to split?

He shouldn't, which is why his decision to 'split' at the end is so great. What he's actually done is maximized the OTHER guys expected return.
posted by unSane at 8:12 PM on April 21, 2012 [25 favorites]

You each pick each other's ball. If you don't look at your own balls (so your opponent doesn't have any information about the contents of your balls from your reactions), and you pick the opponent's ball at random, you have a 75% chance of walking away with money (expectation = 37.% of pot), regardless of 'how' your opponent picks which of your balls you should hand over. This requires no trust on either party.

It is 37.5% of the pot in expectation, but only a 50% chance of you walking away with money. Out of four possible outcomes, only two involve you getting money. But if both people are sufficiently competitive, then they're both going to think they can do better than those odds by trying to hornswoggle the other player... that's where the game gets fun.
posted by qxntpqbbbqxl at 8:26 PM on April 21, 2012 [3 favorites]

I wonder how the other player would react if you refused to look at your own balls (*giggle*) and instead just picked one at random. Would they default to "steal" to cover themselves?
posted by Panjandrum at 8:30 PM on April 21, 2012 [3 favorites]

I used to, up until a few months ago, had a co-worker named Hardeep. (I quit, he wasn't fired) I won't even begin to attempt spelling his last name. He had a dark, dark, dark southern Indian complexion, and a glorious full beard. He was about the most extravagantly subcontinental-looking human being I had ever met.

He also had an accent that made him sound like one of the Beetles, and worried constantly about public transport timetables and whether the vegies were local and fresh and how cheaply he could get a leg of mutton, I'm sorry, this is the US, you're all savages over here, lamb to boil and eat with mustard.

It's shocking from a US perspective how quickly some second-generation immigrants, like Hardeep and Ibrahim in the link, become every inch as British as the fair-skinned, light-haired native scions. I really think we're doing something wrong, as that should be the American Dream... the great melting pot. I really do think Europe has the lead, now, and with it the dynamism and energy an immigrant-driven culture provides.
posted by Slap*Happy at 8:31 PM on April 21, 2012 [2 favorites]

Yes, sorry, I meant a 75% chance that somebody walks away with money, compared to the game-theoretic result where you both get nothing because you both play the optimal 'steal'.
posted by Pyry at 8:34 PM on April 21, 2012

Obviously that guy is not an Economist.

One time I did an iterated prisoner's dilemma game during a work training exercise with 20-25 people in my work group. It was ten rounds of cooperate or defect and the training group leader explicitly told us at the start the name of the game was "Win As Much As You Can". Almost everybody in the game cooperated all the way through. There was one guy who cooperated through nine rounds and defected on the tenth.

He won as much as he could for the game on that day in that place for the point in time and space. If he had it to do over again there is no doubt in my mind he would not defect.

Great video!
posted by bukvich at 8:34 PM on April 21, 2012

Oh I gotcha.
posted by shakespeherian at 8:35 PM on April 21, 2012

I wonder how the other player would react if you refused to look at your own balls (*giggle*) and instead just picked one at random. Would they default to "steal" to cover themselves?

Well you'd almost have to under those circumstances. The other player has actively chosen to not care, and your options are all or nothing vs half or nothing.

As for this, yes, the brilliance of it is in Nick promising no choice at all. By removing any trust, putting the entire thing on Ibraham's incentives, he's able to make the small gamble that he can choose the friendlier option without screwing himself over. I love it (though it would likely never work twice.)
posted by Navelgazer at 8:37 PM on April 21, 2012

The interesting phenomenon in that clip is all about psychology, not game theory. I think that Nick wasn't reframing the question for Ibrahim so much as signaling his cooperation in the most effective way possible (without additional time to establish a history of cooperative behavior). Who are you more likely to believe: the person who tells you that they are honest and cooperative and perfect, or the person who admits to a (small) foible, such as Nick's admission of his own greed by insisting that he was going to choose steal?
posted by eviemath at 8:37 PM on April 21, 2012 [4 favorites]

Am I unusual in wanting the outcome in which my opponent and I both win? In preferring the outcome in which I lose to the one in which I have to betray my opponent to win?
posted by namasaya at 8:49 PM on April 21, 2012 [4 favorites]

How do perceptions of profession (and perhaps class?) factor into the Nick vs Ibrahim clip? Nick, as far as I could make out, works for a charity. Ibrahim is a market trader (i.e. runs a stall in a street market or similar, he is not a stockbroker)
posted by Bwithh at 8:54 PM on April 21, 2012 [1 favorite]

I found it interesting that the host emphasised that his promise was "meaningless" in terms of the show. I would want to confirm UK contract law as it applies to oral contracts, but here is what I would do.

1. Agree with opponent that we should share the money, we will both get half. Let them blah blah a bit how they wouldn't lie to me.

2. Confirm in a serious tone that "we have come to agreement, we will share this money. Even shake on it if possible. Say "my word is my guarantee to you".

3. Tell opponent that you have concluded a binding oral contract. It is up to them if they want to pick split or steal, and largely irrelevant. Probably easier to pick split, as the game show will take care of it. Should they select "steal" we'll need to be in touch after the show, deal with bank transfer, taxes, etc. It will be a pain.

4. The even worse pain is if they think they can renege on a binding oral contract witrnessed by millions on TV. "If you think you'll be able to steal my half of our prize money, I will sue you into the ground for breach of contract. Don't be stupid, in the REAL WORLD you don't want to deal with me and my lawyers".
posted by Meatbomb at 8:59 PM on April 21, 2012 [2 favorites]

Yeah I dunno if this was a masterclass by Nick, per se. There's been studies demonstrating the "revenge" principle, where if the amount is a certain amount, people are happier to give themselves and their opponent nothing rather then end up with a smaller amount.
posted by smoke at 9:00 PM on April 21, 2012

In preferring the outcome in which I lose to the one in which I have to betray my opponent to win?

In the confines of a gameshow? You're not robbing the other guy of his house... it is a game. Why would you prefer the outcome of being duped and going home with nothing over winning?
posted by floam at 9:02 PM on April 21, 2012 [1 favorite]

Am I unusual in wanting the outcome in which my opponent and I both win? In preferring the outcome in which I lose to the one in which I have to betray my opponent to win?

No.

Not only that you are the same as almost everyone around you. In fact, I remember an Adam Curtis documentary which alluded to a study which said there are only two groups of people where, in situations like this, the majority do not choose an outcome where everyone wins.

Psychopaths and Economists.
posted by fullerine at 9:02 PM on April 21, 2012 [38 favorites]

(Although, I'm not sure if I would ever fully recover and accept what happened if I were the guy in the "Big money split or steal clip" posted above. That was pretty brutal!)
posted by floam at 9:03 PM on April 21, 2012

Brilliant gamesmanship on Nick's part. Very cool.
posted by Sticherbeast at 9:10 PM on April 21, 2012

In the confines of a gameshow? You're not robbing the other guy of his house... it is a game.

Are you kidding? Some of these sums involved are huge money; it would have an undeniable impact on someone's life. You really could be effectively robbing someone of the opportunity to own a house or pay a mortgage down.

I mean, generally I'm all for this, and for example I don't understand on Survivor when people get so vindictive about being voted out - the game is essentially built on lying. However, in this case there it is both team-based and mostly not built on lying. I would split every single time; even if I didn't get the money, I would still have my integrity, and I wouldn't need to become a moral pretzel to justify my behaviour every night as I went to sleep.
posted by smoke at 9:10 PM on April 21, 2012 [4 favorites]

In terms of game theory, why should Nick choose to split?

He shouldn't, which is why his decision to 'split' at the end is so great. What he's actually done is maximized the OTHER guys expected return.


The cool thing of Nick's strategy is that he actually breaks his promise (to "steal" and then split the money afterward), but no one cares because the end result of his "split" is the same money distribution.
posted by wanderingstan at 9:10 PM on April 21, 2012 [3 favorites]

(Although, I'm not sure if I would ever fully recover and accept what happened if I were the guy in the "Big money split or steal clip" posted above. That was pretty brutal!)

And that is why I could never watch this show. That was fucking brutal.
posted by crossoverman at 9:15 PM on April 21, 2012 [6 favorites]

The even worse pain is if they think they can renege on a binding oral contract witrnessed by millions on TV.

In the other Split or Steal clip I link to above, both sides say to the other that part of the reason why they won't steal and why the other side should believe that they won't steal, is that the people watching will hate them i.e. there is public recognition by the players of lots of social pressure (and consequences thereof) from the millions watching that they should play fair with each other. One jokes that the audience will probably lynch him if he chose steal, the other says that everyone she knows would be disgusted at her if she chose steal.

Guess what happens next.
posted by Bwithh at 9:19 PM on April 21, 2012

I always wondered what happened to Jasper Carrot.

Gameshows: a failed comics purgatory.
posted by arzakh at 9:19 PM on April 21, 2012

smoke: Sure but I think there's a difference between snatching someone's hypothetical lottery jackpot away and taking something they earned. In that big money clip posted above, I think it would be a lot more painful to be the loser than the winner. The winner will feel bad for a while and get over it. A split would be greatest, but the commenter above said they'd prefer being the victim over the winner. Not I. If I thought there were even moderate odds the other player was going to dupe me I would choose steal. I don't think the winner in the clip is a bad person. The guy had double-crossed her already and his plea seemed forced.
posted by floam at 9:19 PM on April 21, 2012

Yeah that's a good point, Floam, that "Revenge" principle at work. I think talking about oral contract would be they to go, and if Jasper interjected, I would say something to the effect of,
"Oh you're a lawyer are you Jasper? Fantastic, let's make a contract together you and I, and I'll look forward to dragging your sorry arse into court."
posted by smoke at 9:22 PM on April 21, 2012

I don't think the winner in the clip is a bad person. The guy had double-crossed her already and his plea seemed forced.
posted by floam at 9:19 PM on April 21 [+] [!]

According to the info under the youtube video on that page, the winning woman had been backstabbed by someone else (an old lady apparently) in an earlier round over 20,000 pounds, and not by the male contestant she "steals" the money from in this clip (looks like this was the first time they played with each other). The male contestant had lost money in an earlier round to a young guy but it was a much smaller amount and he laughed it off
posted by Bwithh at 9:22 PM on April 21, 2012 [2 favorites]

Nick's effectively changing the game from a prisoner's dilemma into some other sort of coordination game. Most prisoner's dilemmas stipulate away the possibility of money changing hands between the players after payment. What's interesting is that the player's strategy doesn't seem like it should change in that new game. A self-interested actor who is under no obligation to divvy up the money after the first round will just pocket whatever he gets. So the whole thing should play out just like a normal PD. Why is there a difference between Nick saying "trust me, I'll pick the split ball" and "trust me, I'll give you half after the show."?

My guess is that there is a difference: what Nick's doing is exploiting the difference between decisions made in the studio and decisions made outside. You can't trust someone's word when they're inside the game, but when they're outside, a whole different set of moral norms kicks in, and players can be taken at their word. Lying to your friend at the poker table is different from lying to him at the office. That's why they had that little talk about honesty. Fullerine above says that only psychologists and economists would choose to steal, but that's obviously false of you watch enough of these videos, and I suspect that people think different norms are in play because it's a game (they're not really cheating the other person out of money, they're just playing the game. Or on preview, what floam said). Perhaps we should think of Nick exploiting the fact that both players recognize that greedy choices made outside of the game invoke censure and disgust with oneself that act as disutility. By increasing censure for stealing, the utilities of the choices change, and the Nash equilibrium might well change too.

This makes me curious whether there is a reliable "choices-in-game-don't-provoke-censure" effect that might contaminate some experiments in behavioral economics.
posted by painquale at 9:23 PM on April 21, 2012 [24 favorites]

According to the info under the youtube video on that page, the winning woman had been backstabbed by someone else ...

Oh, sorry, my bad. Thanks for setting me straight.
posted by floam at 9:26 PM on April 21, 2012

floam, I would feel bad and wouldn't get over it.

My understanding is that (as fullerine says) the overwhelming flaw in game theory is that people are motivated by much more complex (and attractive) things than self-interest.
posted by namasaya at 9:30 PM on April 21, 2012 [1 favorite]

"You've got your wallet on you?"

"Yep"

"Give me a dollar. In consideration for that dollar I will give you my promise to split any proceeds I receive that result from this game."

Problem solved.
posted by leotrotsky at 9:31 PM on April 21, 2012

floam, I would feel bad and wouldn't get over it.

namasaya, yeah, but if you feel bad and have £100,000, you can just give the guy half of them, or some some to Africa or something. Or therapy or a hot tub and supply of cocaine to last you a long time. Whatever works for you.
posted by floam at 9:35 PM on April 21, 2012

Aww. I thought this thread would be full of hopelessly mangled two by two grids by now as people tried to work out how to use the blockquote tag.
posted by obiwanwasabi at 9:41 PM on April 21, 2012 [3 favorites]

My understanding is that (as fullerine says) the overwhelming flaw in game theory is that people are motivated by much more complex (and attractive) things than self-interest.

Game Theory is simply the branch of mathematics that deals with analyzing this sort of choice. It's not an attempt to predict what humans would do in any given situation. I think that unSane is calling this the "best filmed example of game theory in action ever" because Nick is displaying a sophisticated analysis of the situation.
posted by XMLicious at 9:44 PM on April 21, 2012 [3 favorites]

Well, duh - you cheat - you give the opponent either one of your balls, when no one's looking - create a distraction, it's not hard.

Then, no matter which ball picked, one person will pick, "steal", the other, "split"



Or just grow a natural immunity to the poison. I hear that works well, too.
posted by alex_skazat at 9:48 PM on April 21, 2012

And I'm an idiot. Let it be known. And hopefully, that's legally binding.
posted by alex_skazat at 9:49 PM on April 21, 2012

The kind of people who smugly take advantage of the honesty of others make me want to bring back the duel.


painquale: "This makes me curious whether there is a reliable "choices-in-game-don't-provoke-censure" effect that might contaminate some experiments in behavioral economics."

That's an interesting thought. I had a professor you couldn't play Balance of Power against because he would escalate any conflict all the way to nuclear war every time.
posted by ob1quixote at 9:58 PM on April 21, 2012 [2 favorites]

You are just an illustration
This is just a simulation
Lines and pixels on a piece of paper
posted by Apocryphon at 10:01 PM on April 21, 2012

Bwithh: Big money split or steal clip

That was very predictable.
Ya, I guess that means I'm a secret misogynist or something, but it was.
posted by Chuckles at 10:12 PM on April 21, 2012

From the abstract upthread: Further, we replicate earlier findings that males are less cooperative than females, but this gender effect reverses for older contestants because men become increasingly cooperative as their age increases.

So I am a misogynist :) But, I think they have to take looks and charisma into consideration, the basic gender split just isn't that interesting.
posted by Chuckles at 10:15 PM on April 21, 2012 [1 favorite]

I think that unSane is calling this the "best filmed example of game theory in action ever" because Nick is displaying a sophisticated analysis of the situation.

I disagree. I mean, I have no idea what unSane's thoughts were, but I disagree that Nick was displaying a sophisticated game theoretic analysis of the situation. I think he displayed a sophisticated psychological analysis of the situation, but I don't see that game theoretic analysis much entered into the interaction between Nick and Ibrahim or the choices they made. Game theoretically, Nick's promises had no bearing on Ibrahim's choice.

Additionally, game theory makes certain assumptions about player behavior, amount and type of communication between the players, independence of game events, and so on. The minute and a half for the players to talk before having to make the choice of split or steal takes the "golden balls" game out of the classical 2x2 games (eg. prisoner's dilemma) setting. Since the assumptions aren't satisfied, the mathematical theory isn't relevant.
posted by eviemath at 10:28 PM on April 21, 2012 [1 favorite]

painquale: This makes me curious whether there is a reliable "choices-in-game-don't-provoke-censure" effect that might contaminate some experiments in behavioral economics.

It is most interesting, as Adam Curtis points out, that just thinking about game theory at all completely contaminates any situation.
posted by Chuckles at 10:38 PM on April 21, 2012 [1 favorite]

What makes it so much fun is that Nick immediately plays the metagame—that's what creates the sensation that the normal rules are suspended and yet that the game itself is still being fiercely played at the same time.
posted by jann at 10:44 PM on April 21, 2012 [3 favorites]

So I am a misogynist :)

Why would you say that with a smiley face? Isn't that a truth about yourself that you find unpleasant?

I was actually coming in to comment on the top two rated YT comments on that clip, which were nakedly misogynistic. Also: "she should be stabbed in the face with a rusty 10ft rod". Many others. Ugh. All absolutely ignoring the history of that clip in the video description, as well as her post-show interview. Unreal. They'd be cheering if she'd been a man, of course. Or at worst, understanding of her sentiment of having a hard time trusting after she'd been burned the first time.

Linked clip is much less awful to watch!

Somewhat related: I would guess that when both people pick defect, neither side is very upset when they walk him with nothing. When only one person defects, however, the cooperative person feels cheated, even though in both instances they're getting the same $0.
posted by kavasa at 10:58 PM on April 21, 2012 [1 favorite]

That was fun; thanks for posting it. It's a very interesting move, kithrater has it; removing the lure of the maybe-full that would make Ibrahim consider defecting.
posted by LobsterMitten at 11:05 PM on April 21, 2012

Game theoretically, Nick's promises had no bearing on Ibrahim's choice.

I disagree. I think Nick making such a counter-intuitive offer is a commitment device. When he shows that he understands the game theoretical implications, I'm pretty darn sure that he will pick steal.

Now let's look at it from Ibriham's perspective. Jim has just made a credible offer that he will pick steal. My two options are: 1) pick steal myself and get nothing or 2) pick split. If Jim keeps his word, I get half. If he doesn't keep his word, I get nothing. Rationally, I would choose split, as 100% chance of nothing is certainly worse than a positive chance of half.

The really interesting thing is that Nick then proceeds to pick split. Why? My guess is that once he's reframed the question in Ibrahim's mind, Ibrahim will now rationally choose split. Now that Ibrahim is committed to split, Nick has two choices 1) choose steal and a) keep his word or b) not keep his word or 2) switch to split. Choosing 2) has an advantage to 1a) in that there are fewer transactions costs (easier for the game show to give the money directly to Ibraham rather than Nick cutting another check).
posted by alidarbac at 11:06 PM on April 21, 2012 [1 favorite]

The interesting phenomenon in that clip is all about psychology, not game theory

I'm not sure why you think there's a difference. Game theory is essentially a framework that's been adopted to model behavior. In this video Nick is using a commitment device. It'd be even more effective if he revealed which was which (but would be far less amusing in the end).
posted by pwnguin at 11:13 PM on April 21, 2012 [1 favorite]

Since the assumptions aren't satisfied, the mathematical theory isn't relevant.

Yeah, I agree that any connection with game theory is pretty tenuous absent Nick mentioning that it was a factor in how he constructed his strategy. (And even then, one person applying game theory doesn't really click for me as a superlative example of game theory in action, I would imagine something more along the lines of some massive widespread phenomenon, like something in biology, that statistically demonstrates some principle of game theory.)

I was mostly just pointing out that calling game theory flawed because humans don't successfully use it when playing games is kind of like saying that trigonometry is deeply flawed because ships with crews that used trigonometry to navigate crashed into rocks frequently.
posted by XMLicious at 11:15 PM on April 21, 2012

Note at the very end what the two men said: Ibrahim says he'll use the money for a new cover for his yacht, and Nick said he'll get a new oven. Ibrahim had a lot less to lose comparatively by trusting Nick.
posted by zsazsa at 11:24 PM on April 21, 2012

..how cheaply he could get a leg of mutton, I'm sorry, this is the US, you're all savages over here, lamb to boil and eat with mustard.

Why can't the English teach their children how to speak? Furthermore why don't the English know the difference between lamb and mutton?
posted by humanfont at 11:28 PM on April 21, 2012 [1 favorite]

Does anyone remember an American gameshow like this from a few years ago? It wad called Friend or Foe and hosted by oldschool MTV host Kennedy.
posted by roll truck roll at 11:31 PM on April 21, 2012

alidarbac and pwnguin, as soon as you start talking about "commitment devices", you're effectively outside the scope of game theory, in my understanding (admittedly, I've only taken a one-week overview course and skimmed a book, so no doubt I'm ignorant of anything beyond the basics), unless that's something that *actually* changes the payoff grid or available options for one or both players. But here, no matter what Nick says or how convincing he is, he still might still choose split or steal, and Ibrahim still had the option of split or steal, and the payoffs were still the same; so from a purely game-theoretic perspective, Nick's assurance that he would choose steal didn't have any effect on the game.
posted by eviemath at 11:47 PM on April 21, 2012

Game theory is essentially a framework that's been adopted to model behavior.

That's not my understand at all. Game theory is a framework for optimizing outcomes without consideration to actual human behaviour. As pointed out above, psychopaths and economists (I would have said sociopaths, but whatever).
posted by Chuckles at 11:55 PM on April 21, 2012

I was actually coming in to comment on the top two rated YT comments on that clip, which were nakedly misogynistic.

I noticed the same thing, and was actually a bit shocked by it, as it's bad even for Youtube standards. If you watch some of the other split or steal videos on Youtube, almost all of the top voted comments are racist, misogynistic, or dickish in some other way. (eg, making fun of someone's weight.)

And then in this video where the woman splits and the man steals, the top two comments are

this guy was playing for all the bros who got stolen

and

HAHAHA! 99% of bitches steal, he got his own back on behalf of all the men who got fucked over by those kitchen dwellers!

So no matter which way it goes, it's an opportunity to mock and demean women.

I don't really want to turn this into "LOL Youtube" but seriously, the (top voted!) comments on these videos are consistently worse than anything else I've seen on Youtube. One actually said "of course he stole. He's black!".
posted by jcreigh at 11:58 PM on April 21, 2012

My lawyer brain immediately defaulted to "contract" for the same reasons mentioned unthread; I think Ibrahim would have a strong argument for the existence of a valid contract formed after Nick conveyed the offer to split in exchange for Ibrahim choosing "split" and Ibrahim accepted by performance (actually choosing split). Thus, Ibrahims's risk in choosing "split" was mitigated.

I'm wondering if there's some sort of agreement the show has the players sign beforehand waiving actions for breach of contract against other players resulting from game play in order to "purify" the play of the game?
posted by Dr. Zira at 11:58 PM on April 21, 2012 [4 favorites]

Nick might not choose Split at the end just to be nice or to make the splitting process easier for the two of them. After he's given Ibraham his spiel and Ibraham has picked his ball, picking Split dominates. If Ibraham picked Split, then it doesn't matter which ball Nick takes: he'll owe half either way. If Ibraham picked Steal, then it's better for Nick to pick Split. He's established that they're playing a game in which the players can transfer money after their first choice: Ibraham might feel guilty and give him some money anyway.

Eviemath, commitment devices are discussed in game theory. By announcing that he will split the money with Ibraham, Nick commits himself to splitting: this commitment changes the payoff grid by introducing disutility (public censure, personal disgust, etc.) if he goes against his word.
posted by painquale at 12:01 AM on April 22, 2012 [2 favorites]

Game theory is essentially a framework that's been adopted to model behavior.

Game theory is a framework for optimizing outcomes without consideration to actual human behaviour.

Game theory is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers." It's a branch of mathematics. It has been applied to model behavior. Arguably with mixed results.
posted by eviemath at 12:03 AM on April 22, 2012

A not-so-big money split or steal clip. Less harrowing somehow.
posted by Homeboy Trouble at 12:03 AM on April 22, 2012 [2 favorites]

[Hey guys, let's try to avoid allowing the worst of YouTube brainless sexist/racist commentary to derail the interesting discussion here... and while we're at it – maybe we can also try to avoid duplicating any of it on our accord?]
posted by taz at 12:08 AM on April 22, 2012 [4 favorites]

alidarbac: The really interesting thing is that Nick then proceeds to pick split. Why? My guess is that once he's reframed the question in Ibrahim's mind, Ibrahim will now rationally choose split.

Ibrahim actually says that he will choose split. To give Nick the money? Because he is not vindictive? Anyway, he does say so.

Dr. Zira: I'm wondering if there's some sort of agreement the show has the players sign beforehand waiving actions for breach of contract against other players resulting from game play in order to "purify" the play of the game?

I was thinking about this.. Surely "I promise I'll choose split" is as legally binding as saying "I'll split the money with you later"? It has me wondering if this whole thing isn't a total setup. Obviously the contestants are coached to be interesting, but where does coaching end and scripting begin :)


jcreigh: And then in this video where the woman splits and the man steals,

He isn't nearly as sad-sack as the other guy. I'm not sure how to judge her by comparison to the other woman, but since I already knew the outcome, it wasn't a good test anyway. These should all be grouped on a page together so you can score your intuition against the real outcome.
posted by Chuckles at 12:10 AM on April 22, 2012

"My lawyer brain immediately defaulted to "contract" for the same reasons mentioned unthread"

Yeah, leotrotsky up thread gave me the strategy I'm pretty sure I'd use:

"I will pay you one dollar for you to pick Split, and at the same time, you will pay me a dollar for me to pick Split. Ok, done. Now, if you pick Steal, I will sue you for my half, and the rest of your money will get lost to lawyers. You can do the same to me if I pick Steal. Honestly, who knows whether this is legally binding? But neither of us want to lose all the money to lawyers to find out, so picking Steal is terrible for either of us."
posted by painquale at 12:10 AM on April 22, 2012 [1 favorite]

Game theory is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers."

And keep in mind that "intelligent rational decision-makers" is a very abstract and technical use of those words. Game theory has been used to analyze the behavior of guppies.
posted by XMLicious at 12:12 AM on April 22, 2012 [2 favorites]

Thanks for the explanation, painquale. I disagree that Nick commits himself to splitting by announcing that he will split the money with Ibrahim, though. He could be lying, as could any player making a deal to choose the split option. I think the same arguments upthread against the influence of public censure, personal disgust, etc. would either apply or not apply in the split after the game scenario. I think that the genius thing about Nick's strategy is that it was more effective in communicating his (real) intentions to Ibrahim than, say, committing to choosing split within the game would have been. In a roundabout way, Nick was demonstrating his willingness to trust in Ibrahim, which made it easier for Ibrahim to trust Nick in return. This could undoubtedly be modeled mathematically, though, as with any mathematical model, one would have to carefully specify the assumptions made (in this case, about human behavior).
posted by eviemath at 12:13 AM on April 22, 2012 [3 favorites]

I really don't think most contestants are thinking about whether oral contracts are binding, or giving small tokens ($1 or whatever) for consideration, etc.

Basically, if the contestants were all like Mefites, they'd have all that excluded by the rules, but I suspect that with most people, they don't have to. :)
posted by jcreigh at 12:14 AM on April 22, 2012

This was great. If only for the mental image I have of a middle aged British man talking to his wife . . .
"Luv, would you mind turning the tele to me golden balls?"
posted by quadog at 12:44 AM on April 22, 2012

The original book on the subject was called Theory of games and economic behaviors. I know the term commitment device mainly from an anecdote (from economists I think) about negotiating a road intersection in game theoretic terms.

There are many papers that mention commitment device and game theory. It's a relatively straightforward and exceedingly useful modification to allow players communication, and its interesting to see which communications fail. "Trust me, I'm an honest man": not terribly effective. "I'm going to steal" effectively turns it into a dictator game, which he has generously pegged at 50/50.

Drawing the line on what is and isn't game theoretic is difficult. I clearly lump in commitment devices, but one could just as easily call it all some kind of negotiation theory.

I disagree that Nick commits himself to splitting by announcing that he will split the money with Ibrahim, though. He could be lying, as could any player making a deal to choose the split option.

Indeed, this commitment isn't very credible. He could signal his intent by writing a check (half now, half later?). Or Ibrahim could screen him by asking him to reveal his steal ball to him. I think doing so would have made his commitment more credible, but a nightmare in the paperwork.
posted by pwnguin at 12:46 AM on April 22, 2012

Ibrahim says he'll use the money for a new cover for his yacht

I'm pretty sure he was taking the piss.
posted by obiwanwasabi at 12:55 AM on April 22, 2012 [2 favorites]

I disagree that Nick commits himself to splitting by announcing that he will split the money with Ibrahim, though. He could be lying, as could any player making a deal to choose the split option. I think the same arguments upthread against the influence of public censure, personal disgust, etc. would either apply or not apply in the split after the game scenario.

Yes, he could lie about sharing the money. But the point of the commitment device (a public announcement that Ibraham will get half the money) is simply to make the lying option more unattractive, and to communicate to his opponent that the option is unattractive. Some commitment devices genuinely destroy available options, but other commitment devices just make available options more unattractive. Taking disulphram doesn't mean you can no longer choose to drink alcohol; it just makes the experience of drinking alcohol less pleasurable.

But on reflection, I'm interested in this more as a normative exercise about what one should do when confronted with Nick's move. I think you're right that none of this is really what sells Ibraham. Nick basically freaks Ibraham out and makes Ibraham think he's screwed... it's pretty clear Ibraham has no idea what is going on. All these subtle game theoretic models presume that the two players are acting rationally and deliberatively, but Ibraham doesn't do that at all. He doesn't retaliate with the exact same offer, for instance, (no Nick, I'm stealing, and I will give you half) which for all I know is a more rational strategy. That's why I think people are right when they claim that Nick is good at psychology, not game theory... he knew how a panicky Ibraham would act, and that's not exactly the kind of thing that game theory is good at modeling. He got the money because he made Ibraham feel trapped and like he had no other good options, not because he altered the game to make Ibraham coolly recognize the optimal choice.

Or Ibrahim could screen him by asking him to reveal his steal ball to him.

Pretty sure that'd be illegal. Otherwise players could just show each other they're picking Split.
posted by painquale at 1:28 AM on April 22, 2012 [3 favorites]

think you're right that none of this is really what sells Ibraham. Nick basically freaks Ibraham out and makes Ibraham think he's screwed.

Well, I'm assuming Ibrahim is flustered because he was planning to steal.
posted by pwnguin at 1:46 AM on April 22, 2012

Of course it would never work twice, because the next guy would steal.

Why? The next person would have no idea if you were going to really pick split or not.

In terms of game theory, why should Nick choose to split?

This is actually a failure of basic game theory. It's obvious in the long that humans overall will be better off picking 'split', but the fact is, these two are never going to see each other again or deal with each other again. Game theory says they should both pick steal to optimize their individual payoff for that round.

The interesting phenomenon in that clip is all about psychology, not game theory.

No, game theory is still involved. Nick is essentially creating a new game. Ibraham has to now figure out what the chances are he's lying. If he is lying, and planning to pick share then there is a chance he could get everything, so obviously there's no game theory reason for Nick to do that.

If he's telling the truth though, then it gets more complicated, because then game theory obviously tells you that you should pick share. Essentially, he's told Ibraham that he intends to make the game theoretic optimal choice, but then add an extra 'round' to the game and share with him later, so basically he's offering the possibility of money (essentially valued at half the money times the probability he'll really split the cash)

The risk now is if Ibraham decides to be 'irrational' and 'punish' Nick for being a dick. Except it's not irrational in the general altruistic sense where people try to optimize fairness in general. This was only 13k pounds.

----

Anyway, it would be more interesting if the reward was, for example, a million dollars. Or if rather then getting half if they split, they would each get a quarter or 10%. It would be interesting to see where the cutoff is.

Another interesting aspect: What if Nick offers 60%? What if he offers 40%? What if Ibraham had said, "I'll agree, but rather then give me your word you'll give me 50%, you have to give me your word you'll give me 60%, to compensate for the probability you're lying to me."

In the other Split or Steal clip I link to above, both sides say to the other that part of the reason why they won't steal and why the other side should believe that they won't steal, is that the people watching will hate them i.e. there is public recognition by the players of lots of social pressure (and consequences thereof) from the millions watching that they should play fair with each other. One jokes that the audience will probably lynch him if he chose steal, the other says that everyone she knows would be disgusted at her if she chose steal.

Yeah that's an interesting aspect. On the other hand, the viewers also want an interesting show, so they can't get too upset if everyone picks share.

I'm not sure why you think there's a difference. Game theory is essentially a framework that's been adopted to model behavior.

Not at all. As someone (who before your comment) It's just math. It doesn't tell you what people would actually do. Going by game theory, it only makes sense to pick 'steal'
posted by delmoi at 1:52 AM on April 22, 2012

That was an excellent clip. I was almost disappointed they got to talk... Nick had this intense stare like he was going to telepathically sear his plans into Ibrahim's mind.
posted by gryftir at 2:57 AM on April 22, 2012 [1 favorite]

The interesting phenomenon in that clip is all about psychology, not game theory.

I think the interesting thing is that it is about both psychology and game theory. From a game-theoretical point of view, Nick is proposing to adjust the outcomes so that Ibrahim faces equal expected results if he splits or steals; if Ibrahim splits, he'll get half the money either way, and if he steals, half of the time, he gets all the money and half the time he gets nothing. Of course, this depends on Nick's honesty outside the game; Nick's promise to give half of the money isn't as valuable as a game show producer's on-air pledge to give the money; so the split option is less valuable in proportion to Nick's honesty level. However, there are other benefits to the split option; some degree of societal support, to start, and in this specific case, there's a high likelihood that if Nick's initial plan had been acted on (Nick steals and gives the money later), that there would be a news followup and exponentially more societal infamy if Nick cheats outside the game. Also, if Nick is insisting he will steal, the odds for Ibrahim if he chooses steal are perhaps not the 50/50 they formally are.

So Nick has altered the payout structure for Ibrahim in such a way that it is much more in Ibrahim's interest to choose to split. But he also has a psychological upper hand. I have only seen a few clips, but it seems pretty clear that every other final speech is a variant on the theme of how much both contestants desperately want to split the money and can be trusted. So it puts Ibrahim on edge; you can see his double take when Nick's totally standard beginning of "I will absolutely 100%" is followed by the promise to steal, not split. This disrupts Ibrahim's plans (he actually originally grabbed the steal ball), but it also has the effect of refocusing the conversation.

They spend two whole minutes talking about Nick's plan to steal and then give half of the money back; Ibrahim mentions the both split alternative several times, but Nick immediately moves back to his proposal. Nick says a few times that if they both pick steal, they both lose the money, and Ibrahim talks about it as well. But no one ever breathes a word about the possibility that Ibrahim could steal and Nick could split and Ibrahim could walk away much richer. It's such a disorienting approach that everybody lost sight of what would have been Ibrahim's best choice - to steal the money from Nick.
posted by Homeboy Trouble at 3:34 AM on April 22, 2012 [3 favorites]

Prison dilemma
Uncoordinated choice
Psychology here.
posted by nickrussell at 4:23 AM on April 22, 2012

I really do think Europe has the lead, now, and with it the dynamism and energy

Have you looked at the Southern parts of Europe which are struggling with record debt and stalled economies? Spain's unemployment rate is up over 30%, last I looked.
posted by gen at 6:28 AM on April 22, 2012

Nick's strategy seems sufficiently effective as to make future episodes impossible.


On the contrary, it's desperatly vulnerable to a 'steal'. That's why he was trying to hard to persuade Ibrahim that a 'steal' was a losing play.

The conversation has moved on, but I meant everything but the final SPLIT. Promising your opponent that you will absolutely steal, but will split the money if he splits, is pretty close to a maximal strategy for forcing your opponent to split.
posted by gerryblog at 6:58 AM on April 22, 2012

Another strategy would be to convince the other player that you should each select and then switch balls; nobody would give the other player the "steal" ball.
posted by taz at 7:21 AM on April 22, 2012 [7 favorites]

I really do think Europe has the lead, now, and with it the dynamism and energy

Have you looked at the Southern parts of Europe which are struggling with record debt and stalled economies? Spain's unemployment rate is up over 30%, last I looked.

Agreed. In addition, the idea that European countries are ahead of the US in terms of immigration is pretty out there. In 2009, the foreign born represented 12.5 percent of the United States' total population. The percentage of EU residents born outside of the EU is 6.3.

If you think the UK does a better job of integrating immigrants, that may be true. But much of the EU immigration is country-specific and tied to former colonial territories. It's a lot easier for an Indian immigrant to the UK to adapt to their customs and lifestyle than it is for someone from Ghana to adapt to the US.
posted by benbenson at 7:39 AM on April 22, 2012

alidarbac and pwnguin, as soon as you start talking about "commitment devices", you're effectively outside the scope of game theory, in my understanding

On the one hand, this seems like a relatively straightforward signaling game, similar to ones IR people use in which countries/actors try to signal resolve in order to deter/compel. In these games, there are different types of players, and [Ibrahim] observes [Nick]'s behavior to try to figure out whether [Nick] is an [AlwaysSteal] type or a [NotAlwaysSteal] type, while [Nick] tries to influence [Ibrahim]'s judgment by potentially behaving counter to his immediate interests. Put in some prior beliefs, and out will pop any of the few kinds of equilibria for these sort of games.

On the other hand, game theory would be really bad at evaluating specific signals, since their efficacy would depend on exactly what Ibrahim's prior beliefs are and on what exactly the utility structures for each type are. Both of which are more or less unknowable.
posted by ROU_Xenophobe at 8:19 AM on April 22, 2012

Game theory is a framework for optimizing outcomes without consideration to actual human behaviour. As pointed out above, psychopaths and economists (I would have said sociopaths, but whatever).

That's not true at all. Game theoretic implications for bluffing probabilities in poker or how often you should run a blitz in football or tire strategies in racing are pretty well borne out, for example. Game theoretic implications for collective action are well borne out. And so on.

It's true that there are experiments that people have run where they have subjects play simple games like the Centipede Game, in which most sets of players "get it wrong" by cooperating for a bit instead of defecting immediately in the Pareto-inferior Nash equilibrium. It's also true that, ha ha, economics grad students generally "get it right" and lose by doing so.

But, it's not clear what this means for the larger implications of the games. One implication is admittedly that game theory is stupid and just for psychopaths and economists, and is the domain of big fat poopyheads.

A second possible implication is that modelers should be more careful about specifying utility structures that don't just reflect the immediate circumstances around them, but also include sensible assumptions about longer-term possible consequences of their actions. But a third possible implication is that these experiments just aren't very informative about the actual behavior under consideration, mostly because the stakes in the game are usually completely inconsequential -- literally a few dollars or tens of dollars --and they're usually played by undergraduates who've been more or less forced to play. It's entirely possible that their conduct would be quite different if the stakes were higher.

This is actually a failure of basic game theory. It's obvious in the long that humans overall will be better off picking 'split', but the fact is, these two are never going to see each other again or deal with each other again. Game theory says they should both pick steal to optimize their individual payoff for that round.

...and that's not true at all either. Look, I do this stuff "for real" from time to time. For good or ill, this is how I think when I'm wearing my "professional dork" hat. And my first reaction wasn't that "Steal" is immediately attractive. My first reaction, instead, was that any set of risk-averse players would try to coordinate on (split, split) because they'd much rather have a higher probability of obtaining (X/2) than they would a lower probability of obtaining X.
posted by ROU_Xenophobe at 8:47 AM on April 22, 2012 [1 favorite]

Another strategy would be to convince the other player that you should each select and then switch balls; nobody would give the other player the "steal" ball.

I don't quite get it - so I give you my split, he gives me his split, we have the same option (his split or my steal I kept) as when we started except now we know which ball of theirs is which. So you might as well just have both players open one of their balls and show it to the other player, right? And then you don't need to worry about game rules preventing the trade. Just threaten to always steal unless both sides agree to be transparent about which ball is which. Kind of ruins the game though, really. The whole ad-hoc making this into a new game thing seems like it ought to be against the rules entirely.
posted by floam at 8:51 AM on April 22, 2012

The conversation has moved on, but I meant everything but the final SPLIT. Promising your opponent that you will absolutely steal, but will split the money if he splits, is pretty close to a maximal strategy for forcing your opponent to split.

But doesn't it still come down to psychology? I mean, there's nothing to stop your opponent from saying the exact same thing, and then it's just a matter of which one of you does a better job of convincing the other that they're serious.
posted by jcreigh at 9:27 AM on April 22, 2012

a third possible implication is that these experiments just aren't very informative about the actual behavior under consideration, mostly because the stakes in the game are usually completely inconsequential -- literally a few dollars or tens of dollars --and they're usually played by undergraduates who've been more or less forced to play

This seems like it could be true. I've been that undergraduate many many times, and since the amount of money is usually about $10, I have a hard time screwing anyone else over. A higher sum might jog my bare self-interest a little more. Plus, my opponent is usually an anonymous "someone who has recorded their answer earlier," meaning to me that they probably only exist in an experiment script, and this occurred to me the very first time I participated in one of these experiments, so I'm pretty confident it occurs to other undergraduates who walked into the psych building to make beer money for the weekend.
posted by stoneandstar at 11:29 AM on April 22, 2012

I liked delmoi's suggestion of Ibraham demanding that Nick give him 70/30 after the show or else he'll pick steal. It shows that Ibraham wasn't held hostage to Nick: he could hold Nick hostage just the same.

I think there's a little too much bold assertion in this thread about the relation between game theory and psychology. Game theory (and for that matter, probability theory and logic) are related to epistemology and to psychology in a pretty convoluted manner. Linking them all together is a really complicated and contentious task. On their own, game theory and probability theory are studies in pure mathematics or logic, with no normative import and nothing to say about psychology. Then, you can suggest epistemological principles that link the mathematics to normative claims: for example, "if the probability calculus indicates that the probability of P is N, then you should update your credence in P to be N." Then, if you have good reason to assume that people are rational and satisfy the normative constraints, you can use the theory to model people psychologically. But the mathematical theory is not "at the bottom" either: our choice of the mathematical structures to study is motivated by the links to both the epistemological and psychological enterprises. (For example, some probability theorists study "fuzzy credences", and they are motivated to study these both because it seems like it is not always rational to have precisely sharp degrees of belief and because it doesn't seem like we do have sharp degrees of belief.) Each one of these connections -- between the math and the epistemology, and between the epistemology and the psychology, and between the math and the psychology -- is contentious and fraught with all sorts of problematic issues. It's a fascinating area of research.
posted by painquale at 11:41 AM on April 22, 2012 [1 favorite]

It's such a disorienting approach that everybody lost sight of what would have been Ibrahim's best choice - to steal the money from Nick.

It definitely wasn't, because of how committed Nick was to selling his position. He was absolutely convincing, meaning only a vindictive opponent who desired the no-win scenario would have picked Steal.

The final switch-up that Nick pulls is just icing on the cake.
posted by odinsdream at 12:39 PM on April 22, 2012

It definitely wasn't, because of how committed Nick was to selling his position. He was absolutely convincing, meaning only a vindictive opponent who desired the no-win scenario would have picked Steal.

Watching it the first time, I was so offended by the smugness that I would easily have chosen steal out of spite. It was one of the things that got me thinking it was just a giant scripted set up.

In the end the only choice that makes any emotional sense to me is to chose randomly. Which leads to a point that seems to be lost here.. If the game is real at all (as opposed to completely scripted), the producers have eliminated any of the easy outs like randomness or showing your opponent or taking legal action. The point of the show is to create cliched melodrama after all :)
posted by Chuckles at 1:04 PM on April 22, 2012

You people have no idea how many moves ahead Nick was thinking by choosing split.
For instance: it’s going to get him hella laid.
posted by davel at 1:05 PM on April 22, 2012 [5 favorites]

Of related interest:
Evolutionary Game Theory and the Prisoner's Dilemma (brief explanation on Wikipedia)

A friend of mine wrote his dissertation in applied math on this topic.

Here's the short paper summary of his work:
Evolutionary escape from the prisoner's dilemma, by Lee Worden and Simon A. Levin, Journal of Theoretical Biology, Volume 245, Issue 3, 7 April 2007, Pages 411–422. http://dx.doi.org/10.1016/j.jtbi.2006.10.011
(Lee's been on the blue before.)

I believe Martin A. Nowak's lab also looks at related questions.

But basically, Nick's ability to play a metagame (as I mentioned above) and actually alter the dynamics of the game, is the sort of thing that work in applied math from the past fifteen years says we ought to expect in situations like the Prisoner's Dilemma, occurring in dynamic systems.
posted by jann at 3:58 PM on April 22, 2012 [2 favorites]

Anyone who tells you they're honest? Isn't.

Ah, but how about anyone who tells you they always lie?
posted by Twang at 8:17 PM on April 22, 2012

Ah, but how about anyone who tells you they always lie?

Those are mathematicians, and are probably just as familiar with Nash equilibria as Tarski / Godel.
posted by pwnguin at 8:31 PM on April 22, 2012 [1 favorite]

Ah, but how about anyone who tells you they always lie?

See Doctor Who.
posted by XMLicious at 8:34 PM on April 22, 2012

Ah, but how about anyone who tells you they always lie?

Cretans, all of them. At least, that's what they say.
posted by unSane at 9:20 PM on April 22, 2012 [1 favorite]

benbenson: "In 2009, the foreign born represented 12.5 percent of the United States' total population. The percentage of EU residents born outside of the EU is 6.3."

Isn't that apples and oranges? If you're a Slovak in Ireland or a Finn in Portugal you might be an EU resident born inside the EU, but you're still very much a foreigner in your country of residence.
posted by brokkr at 2:29 AM on April 23, 2012 [1 favorite]

brokkr, it's not a great comparison, but neither is any particular EU country to the whole of the United States.
posted by benbenson at 8:48 AM on April 23, 2012

> ...as soon as you start talking about "commitment devices", you're effectively outside the scope of game theory

> Game theory is a framework for optimizing outcomes without consideration to actual human behaviour...

Others have chimed in on this, but commitment strategies are a really important part of game theory research, including the kind performed by cruel and unfeeling economists. Even more interesting are iterated and evolutionary games. What if they had to play this round a hundred times in a row?

The very simplest games might seem psychopathic, but human behavior is rarely a simple game. More complex game theory models actually tell a very optimistic story about human behavior: we crawled out of the Hobbesian jungle by figuring out how to restructure the rules of bad-outcome games like the prisoner's dilemma and make them into cooperative games that benefit everyone. In modern, market-exchange societies, we actually cooperate way more often than we think, even though there are opportunities to defect all the time. Here's one of my favorite papers on the subject, which is part of a really great volume on cooperation in economics.
posted by ecmendenhall at 2:50 PM on April 23, 2012 [3 favorites]

Of course, it takes a certain kind of "cruel and unfeeling" mindset to point out the following:

Imagine that you see a dozen pedestrians walk by a sleeping homeless man who is lying next to a sign that reads, "Please Help" and a cup that contains a few dollar bills. Many people might conclude they are observing selfish behavior when no one puts any money in the cup. Few would recognize that they are witnessing multiple acts of unselfishness as person after person walks by without stealing from the helpless homeless man.

^_^

Now to put the paper in my reading queue.
posted by pwnguin at 12:04 AM on April 24, 2012

Bruce Schneier weighs in.
posted by unSane at 5:35 AM on April 24, 2012

The comment right after Schneier's was very interesting:

This endgame would be even more interesting if you had three choices: Split, Steal and Catch.

If both players split, they get 50% each. Steal beats split (the stealer gets 100%), catch beats steal (the "caught" player goes away with nothing), but split beats catch. If both choose to steal or catch, they both get nothing.

You couldn't do the same trick in this game, as there is always a strategy to beat the other player completely, independent of what he chooses.

Posted by: wasyl at April 24, 2012 7:51 AM

A "fair" game is just so much more satisfying to human psychology. And, if you make the prisoner's dilemma fair, you are left with Rock-Paper-Scissors :)
posted by Chuckles at 1:07 PM on April 25, 2012