Do You Want A Dollar? And Other Games Teens Can't Win

[Loss Leader]

For about five years, I played a fairly simple game with the high school students I coached for Mock Trial called "Do You Want A Dollar?"

The rules were simple: everyone takes out a piece of paper, writes their names on it and then answers either yes or no to the question, "Do You Want A Dollar." I would give a dollar to every student who said yes, provided that fewer students wrote yes than no. If a majority wrote yes, nobody would get anything.

I found that high school students could not win this game. I gave them the chance to talk beforehand. I even gave them the chance to talk during. They could not get any money. In five years, and maybe a hundred games with ten to twenty student a game, I gave out a total of 11 dollars.

Repeating the same game with some of the same kids after 1 year in college, they won the maximum possible amount.

What do you think accounted for the poor performance? What other thought experiments would teens fail at? Or do you think my observations are incorrect?

[madurobob]

My guess: high school kids have little need for money and are way to cool to appear to care about a teacher's game. College kids, on the other had, need beer.

I could be wrong, but I'm pretty sure the high school kids could work out the social algebra and the actual algebra pretty easily, but the reward is too trivial. Change the game to "do you want $20" and see if the outcome changes.

[Loss Leader]

My guess: high school kids have little need for money and are way to cool to appear to care about a teacher's game. College kids, on the other had, need beer.

I could be wrong, but I'm pretty sure the high school kids could work out the social algebra and the actual algebra pretty easily, but the reward is too trivial. Change the game to "do you want $20" and see if the outcome changes.


If your guess were right, then most kids would write "no" and I'd be giving out dollars every game. Instead, most kids wrote "yes" almost every time. And, in fact, I played with all sorts of denominations from one dollar up to twenty. I also played with golden dollars and two dollar bills. The majority almost always wrote "yes" and no money was given out.

[Mirrorglass]

I would assume it's because in a high school environment, the kids simply can't trust each other to cooperate. Let's assume 11 out of 20 kids write "no". The other nine get a dollar each, which is great for them - but they've no incentive to give anything to the losers. The end result is that the loser kids get nothing, and feel bad on top of it. They'd much rather everyone lose than just them. It doesn't matter if the group gets to plan ahead; once it comes down to business, no one has any incentive to vote "no".

As for other games, I think any variation of the Prisoner's Dilemma, as well as the Battle of the Sexes, would end up with a bunch of losers, for much the same reasons.

[drkitten]

I would assume it's because in a high school environment, the kids simply can't trust each other to cooperate.

So what changes between high school and college, then?

[Mirrorglass]

So what changes between high school and college, then?

Generally, both lectures and T-shirts become a lot less dry.

[Careyp74]

So what changes between high school and college, then?

Perhaps in College, the kids are at the point where they would like to see the teacher have to give up the money, but still not care about the trivial sum. It is a game to them at that point, and not a matter of some kids getting something that others aren't getting.

[Mark6]

So what changes between high school and college, then?

In my experience, college environment is not nearly as socially competitive as high school. A college may be more competititve academically, but socially high school is a true dog-eats-dog (http://www.paulgraham.com/nerds.html) world. College students have fewer reasons to put down one another, and consequently trust each other more. (The article I linked to explains WHY high-schoolers put down each other so much.)

[Mirrorglass]

Perhaps in College, the kids are at the point where they would like to see the teacher have to give up the money, but still not care about the trivial sum. It is a game to them at that point, and not a matter of some kids getting something that others aren't getting.

Possibly. I personally would think that in college, the likely negative effects of shoving oneself to be a greedy bastard would outweigh the lure of the whole dollar, while in high school, cheating the nerds/jocks/goths/skaters/cheerleaders would, in itself, be a desirable outcome. Basically, college kids already realize it's a good idea to have decent relations to people outside your immediate social circle.

[Mark6]

while in high school, cheating the nerds/jocks/goths/skaters/cheerleaders would, in itself, be a desirable outcome. Basically, college kids already realize it's a good idea to have decent relations to people outside your immediate social circle.
You just repeated what I said

[Mirrorglass]

You just repeated what I said

Yep, it's the magic of cross-posting. Great minds and all that.

[Loss Leader]

I would assume it's because in a high school environment, the kids simply can't trust each other to cooperate. Let's assume 11 out of 20 kids write "no". The other nine get a dollar each, which is great for them - but they've no incentive to give anything to the losers.


I'll point out that I sometimes allowed the kids to plan their votes during the balloting. And they would frequently devise elaborate systems wherein the minority would get their dollars and immediately share them with the majority. No matter what promises they gave each other, someone in the "no" group always crossed over and ruined it for everyone.

It should also be remembered that these were kids on the Mock Trial team. They were not a representative sample of the school. Instead, they were all pretty much nerds and, except for their class years, ran in the same social circles.


It doesn't matter if the group gets to plan ahead; once it comes down to business, no one has any incentive to vote "no".


I would always read the votes out loud. If someone had promised to vote "no," their duplicity was always revealed. This occasioned more that a little yelling. And then the students would have a chance to use that information in future weeks.


Basically, college kids already realize it's a good idea to have decent relations to people outside your immediate social circle.


This is my best guess. After only three months of dorm living, the concept of "taking one for the team" actually began to make sense to the kids.

Otherwise, I would conclude that there is some degree of maturation that happens in the 18th year that makes the brain more able to override the irrational grab for more (a "yes") with the rational knowledge that a "no" vote will actually lead to more.

I remember an experiment with apes and M&Ms. Shown two numbers, the well-trained apes knew that pointing to the Lower number got them the Higher number of M&Ms. They would pick the number "3" to get "5" candies. However, shown two bowls of M&Ms, they would always pick the larger amount (and be punished with the lower). This persisted no matter how many iterations were done.

[madurobob]

If your guess were right, then most kids would write "no" and I'd be giving out dollars every game. Instead, most kids wrote "yes" almost every time. And, in fact, I played with all sorts of denominations from one dollar up to twenty. I also played with golden dollars and two dollar bills. The majority almost always wrote "yes" and no money was given out.

I disagree. If I'm the high school kid who doesn't care about the game enough to try to negotiate with the class to set up a win, I have two choices: answer "yes" or answer "no". If I answer "no" I am guaranteed I'll get nothing. If I answer "yes" there is at least some small chance I'll get $1.

Thus, nearly all the kids answer "yes".

Still, I'm surprised you got the same result with $20/person offered.

[Mark6]

What exactly do you disagree with? You seem to agree pretty much with what Loss Leader, Mirrorglass and I wrote.

[Mirrorglass]

As an aside, we never did have an exercise like this, but I'm fairly confident my old high school class could have beaten the game, although my junior high class definitely wouldn't have. In our case, most of the cliques, bullying and other social phenomena that could have affected the game had already disappeared between ninth and tenth grade. As such, I think this is more a question of group psychology than individual cognitive maturation.

[madurobob]

What exactly do you disagree with? You seem to agree pretty much with what Loss Leader, Mirrorglass and I wrote.

I disagree that most kids would answer "no" if they don't care enough about the game to actually play (that is, negotiate with the rest of the class). They would answer "yes"

That is, this statement:
If your guess were right, then most kids would write "no"...

I may have misinterpreted, but I understood this to mean that something else was going on, that the kids were answering "yes" not because they don't care about the game, but because they didn't understand it. I suspect they understood just fine; but didn't care.

[Loss Leader]

I suspect they understood just fine; but didn't care.


I don't know, they seemed to care. It's pretty easy to tell when a teenager is bored. They mostly seemed fairly excited by it. It's one of the reasons I did it - it got the energy up for an after-school lecture about the rules of evidence in civil trials.

I remember my wife being horrified when we were out to dinner one summer night and a waitress came up to me and asked, "Can I have a dollar?"

[madurobob]

I don't know, they seemed to care. It's pretty easy to tell when a teenager is bored. They mostly seemed fairly excited by it. It's one of the reasons I did it - it got the energy up for an after-school lecture about the rules of evidence in civil trials.

I remember my wife being horrified when we were out to dinner one summer night and a waitress came up to me and asked, "Can I have a dollar?"

Yeah, I should qualify that "didn't care" with "enough". As in enough to engage with the other lunatic teenagers in the class.

I think we've all come to that conclusion - that your students know how to solve the problem to maximize dollars, but choose not to for social reasons.

[TraneWreck]

I like this game, here's a new wrinkle for you.

When they start talking amongst themselves, deciding how to fill out the papers to make sure they get the maximum amount, if they win, just say, "I'm not giving you the money because you're filthy liars. Clearly you did want the dollar, which is why you spent so much time figuring out how to get it."

[Mirrorglass]

Yeah, I should qualify that "didn't care" with "enough". As in enough to engage with the other lunatic teenagers in the class.

I think we've all come to that conclusion - that your students know how to solve the problem to maximize dollars, but choose not to for social reasons.

I wouldn't put it exactly like that. I'd say most of the students know, or at least can understand how to maximize the dollars, but are not able to coordinate their efforts well enough to actually do it - and that they know this, which ironically is a large reason why they cannot coordinate properly.

[sphenisc]

... No matter what promises they gave each other, someone in the "no" group always crossed over and ruined it for everyone..

Did they provide any explanation of their actions?

[gnome]

I once was part of a team trying to participate in a one-shot prisoner's dilemma at the university.

I was the primary person arguing for a "cooperation" response. They agreed with me to shut me up, then put "Defect" on the paper anyway. :P

[Loss Leader]

Did they provide any explanation of their actions?


"I wanted a dollar."

[Mirrorglass]

I once was part of a team trying to participate in a one-shot prisoner's dilemma at the university.

I was the primary person arguing for a "cooperation" response. They agreed with me to shut me up, then put "Defect" on the paper anyway. :P

Well, that is the best strategy. Repeated Prisoner's Dilemma is another thing, but with one round and no possibility of commitment, there's simply no point in co-operating.

[Loss Leader]

I think we've all come to that conclusion - that your students know how to solve the problem to maximize dollars, but choose not to for social reasons.


I don't think so. I think they knew intellectually how to solve the problem but could not override their irrational greed.

[jasonpatterson]

Or they just wanted to wreck the game for other players to see their reactions?

[madurobob]

I wouldn't put it exactly like that. I'd say most of the students know, or at least can understand how to maximize the dollars, but are not able to coordinate their efforts well enough to actually do it - and that they know this, which ironically is a large reason why they cannot coordinate properly.

Yup, I can agree with that to a certain extent. But, I wouldn't go so far as to say the are unable to coordinate their efforts.

I'm no teacher of teens, but I do have some living in my house. I've seen their ability to work together spontaneously; the "Senior Class Prank", for instance. So, I still don't think its as much of an issue with ability to coordinate as it is with motivation.

Still, what surprises me is that LL says raising the stakes to $20/kid made no difference. I would expect the motivation of $9 to be enough to get kids out of their shells, while $0.49 wouldn't. I wonder at what point the scales tip?

[madurobob]

I don't think so. I think they knew intellectually how to solve the problem but could not override their irrational greed.

I'm.... amazed.

Maybe I am giving the kids I know too much credit.

I'm going to test that this weekend. I'll be camping with a group of 20 or so kids, teaching "outdoor" skills and such. I'm going to try out your "do you want a dollar" game on these 8 to 11 yr olds after supper Saturday night. I'm pretty sure I'll be passing out quarters afterwords, but I'm open to being wrong.

The hard part will be keeping their parents from butting in.

[Dorian Gray]

This isn't prisoners dilemma if you allow them to talk and it depended on more than two people.

[Loss Leader]

This isn't prisoners dilemma if you allow them to talk and it depended on more than two people.


You're right. I started it with a prisoner's dilemma cone of silence. Nobody could communicate at all. However, after several weeks of them not even coming close to winning (I was getting vote returns of 17 yes and 3 no), I started loosening up the rules. First, I reminded them that they had an entire week when I wasn't around to plan. Then, I just let them plan for the first five minutes. Then, I just let them talk as much as they wanted.

At one point, I did it by voice vote, keeping score one at a time on the blackboard. The no and yes votes were tied with one girl left. Amidst screams, exortations, offers to pay her half of all the winnings (four or five bucks), much pointing and begging, she voted yes and nobody got a dollar.

If you try it on your campers, I would start with no talking whatsoever. Maybe you'll have time to play multiple rounds.

[gnome]

Well, that is the best strategy. Repeated Prisoner's Dilemma is another thing, but with one round and no possibility of commitment, there's simply no point in co-operating.

I disagree... going for the DC bonus is a sham--it is rational to imagine the other person mirroring your thinking--and will notice that taking the "obvious" best answer will only lead to DD punishment. CC > DD, so if you presume the other person will follow similar reasoning C>D.

Of course it depends on how cynical you imagine your opponent to be.

[quixotecoyote]

This isn't prisoners dilemma if you allow them to talk and it depended on more than two people.

Call it a prisoner's dilemma variation. There's dozens of 'em in the literature.

[Aepervius]

So what changes between high school and college, then?

1) a tad bit more maturity, ?
2) need pocket money for beer ?
3) socially a different environment ?
4) more trust ?

A combo of all factor might be enoguh.

[rwerdja]

I work with senior citizens once a week for about an hour .. I'm going to try "Do you Want a Dollar?" on them ... it should be interesting to see what they do. It will, no doubt, take the better part of the hour explaining it to them!

[CaptainManacles]

I disagree... going for the DC bonus is a sham--it is rational to imagine the other person mirroring your thinking--and will notice that taking the "obvious" best answer will only lead to DD punishment. CC > DD, so if you presume the other person will follow similar reasoning C>D.

Of course it depends on how cynical you imagine your opponent to be.

No, it doesn't

if your opponent picks C, your best option is DC

if your opponent picks D, your best option is DD

that's the problem with the prisoners dilemma and what makes it such an interesting problem, two reasonable people will get the worst possible outcome every time.

[Mirrorglass]

No, it doesn't

if your opponent picks C, your best option is DC

if your opponent picks D, your best option is DD

that's the problem with the prisoners dilemma and what makes it such an interesting problem, two reasonable people will get the worst possible outcome every time.

Indeed. The only way you'll ever want to choose co-operate is if you can be certain your opponent will choose the same as you, no matter what you choose.

[Loss Leader]

I work with senior citizens once a week for about an hour .. I'm going to try "Do you Want a Dollar?" on them ... it should be interesting to see what they do. It will, no doubt, take the better part of the hour explaining it to them!


My theory is that they will have no problem getting money out of you. They learned long, long ago to sacrifice personal gain for others. Any parent who has ever let a child take the last candy in the bag should be able to play successfully.

And then you have the problem that a dollar probably wouldn't motivate a senior to even feel greed (whereas the high school students would kill for one). Perhaps you can play, "Do You Want To Stand Outside And Yell At Kids On Skateboards?"

[Mirrorglass]

I work with senior citizens once a week for about an hour .. I'm going to try "Do you Want a Dollar?" on them ... it should be interesting to see what they do. It will, no doubt, take the better part of the hour explaining it to them!

Well, just for fun, I'm going to predict the results will be similar to a high school. Senior citizens have no need to get along with all the members of their group, and may well be suspicious/grumpy enough to not trust the others, and will rather play to lose than let others win.

[Spindrift]

You should try a twist on the game. If the yes votes outnumber the no votes, those who voted yes will have to pay you a dollar.

[roger]

You should try a twist on the game. If the yes votes outnumber the no votes, those who voted yes will have to pay you a dollar.
Who would agree to play that game?

[Loss Leader]

You should try a twist on the game. If the yes votes outnumber the no votes, those who voted yes will have to pay you a dollar.


I think you've created a game that rewards sociopaths.

[sphenisc]

"I wanted a dollar."

Then could it be the students who wrote "Yes" were attempting to retain their sense of personal integrity by answering the question honestly, rather than lying in order to achieve financial gain for themselves or others?

I'd suggest that they fully understood the dynamics of game, but that, by their lights, they "won" the game. It's better to play honestly and lose, rather than cheat to win.

You could reduce this conflict in goals by simply asking them to write "Dollar" or "No Dollar" and outlining the consequences, rather than presenting it as an answer to a direct question. I'll predict that you'll lose more money that way. :)

[Spindrift]

I think you've created a game that rewards sociopaths.

No, just a way for a poor teacher to supplement his income off of students who can't seem to figure out how to cooperate.

[gnome]

No, it doesn't

if your opponent picks C, your best option is DC

if your opponent picks D, your best option is DD

that's the problem with the prisoners dilemma and what makes it such an interesting problem, two reasonable people will get the worst possible outcome every time.

We can probably go back and forth indefinitely about it. If it leads to the worst possible outcome, it's obviously not your best option.

If you know that your opponent wants to jump out of that box and is capable of abstract thought, you ask yourself "On what basis can I decide that will yield the best results if my counterpart uses the same basis?" -- with the understanding that your counterpart needs to be able to arrive at the same conclusion independently--this will lead to the conclusion that it is better if you both pick "C" than if you both pick "D".

It is the equivalent in the 20-student "do you want a dollar?" situation... if the students couldn't talk to each other... the best solution would be to submit "yes" or "no" based on a random die roll or other random number generator, calibrated so that if everyone uses the same probability, it will maximize the expected value to each person. (ie expecting just enough "yes" responses to maximize payout)

Someone could do the math here, I'm a bit lazy to.

[Mirrorglass]

We can probably go back and forth indefinitely about it. If it leads to the worst possible outcome, it's obviously not your best option.

If you know that your opponent wants to jump out of that box and is capable of abstract thought, you ask yourself "On what basis can I decide that will yield the best results if my counterpart uses the same basis?" -- with the understanding that your counterpart needs to be able to arrive at the same conclusion independently--this will lead to the conclusion that it is better if you both pick "C" than if you both pick "D".


But if I've concluded my opponent will choose C, thinking it's best for us both to pick C - I'll still pick D, as that way I get an even better payoff. As I've said, picking C is only ever worth it if your opponent will definitely choose the same as you. And in the vanilla Prisoner's Dilemma, such assurances don't exist.

So best possible play yields the worst possible result. It sucks, but it's still best possible play.

[Loss Leader]

So best possible play yields the worst possible result. It sucks, but it's still best possible play.


You guys are talking about the Prisoner's Dilemma as though there's an answer. There isn't. That's what makes it a dilemma.

[Kaylee]

This story:


At one point, I did it by voice vote, keeping score one at a time on the blackboard. The no and yes votes were tied with one girl left. Amidst screams, exortations, offers to pay her half of all the winnings (four or five bucks), much pointing and begging, she voted yes and nobody got a dollar.



makes me think that Jason has probably nailed down the motivation.

Or they just wanted to wreck the game for other players to see their reactions?


I wonder if different social dynamics would make a difference also? Perhaps kids from a small high school where everyone has known each other since kindergarten would react differently than kids from a large high school located in a large city?

---

I work with senior citizens once a week for about an hour .. I'm going to try "Do you Want a Dollar?" on them ... it should be interesting to see what they do. It will, no doubt, take the better part of the hour explaining it to them!

Hmm, how old and how able are they? My apt. building has a lot of senior citizens in it. It seems to me that many seniors' social skills regress as they age. The more mature they get, the more immature they get...

I'm curious what will happen, so I hope you have a follow-up post.

[gnome]

But if I've concluded my opponent will choose C, thinking it's best for us both to pick C - I'll still pick D, as that way I get an even better payoff. As I've said, picking C is only ever worth it if your opponent will definitely choose the same as you. And in the vanilla Prisoner's Dilemma, such assurances don't exist.

So best possible play yields the worst possible result. It sucks, but it's still best possible play.

It's only better if you assume your opponent wouldn't do the same thing. You're breaking the assumption that your counterpart will use a symmetrical reasoning process.

To put it another way... if I played Prisoners Dilemma against myself, we'd get the CC reward. Similarly true if I play PD against someone I know thinks similarly to me. So the best answer really depends on how likely the other person is to think like me.

[SezMe]

I would always read the votes out loud.
Did they know ahead of time that their vote would be a matter of public record?

[Loss Leader]

Did they know ahead of time that their vote would be a matter of public record?


After several iterations, I guess they did.

[The Fallen Serpent]

After several iterations, I guess they did.

That... that is wonderfully wicked.

This is a very interesting social game. I am curious to try it sometime.

[Mirrorglass]

It's only better if you assume your opponent wouldn't do the same thing. You're breaking the assumption that your counterpart will use a symmetrical reasoning process.

To put it another way... if I played Prisoners Dilemma against myself, we'd get the CC reward. Similarly true if I play PD against someone I know thinks similarly to me. So the best answer really depends on how likely the other person is to think like me.

But, if you are playing against yourself, and you know that, and you know you'll both play C, since that's best for everyone - it's still your best move to play D. That way, you get the DC reward, which is the best outcome for you. And you don't care that your opponent is worse off.

[gnome]

But, if you are playing against yourself, and you know that, and you know you'll both play C, since that's best for everyone - it's still your best move to play D. That way, you get the DC reward, which is the best outcome for you. And you don't care that your opponent is worse off.

You're rejecting what I shall call the Kant approach... which is fine, but it doesn't mean I have to.

And I wind up with a better score than you, against myself vs. you against yourself.

[Mirrorglass]

You're rejecting what I shall call the Kant approach... which is fine, but it doesn't mean I have to.

And I wind up with a better score than you, against myself vs. you against yourself.

Yes; that's because you're changing the game. You are considering the outcome where both players get a small victory better than the outcome where you get a large victory and the other player a large loss. In other words, your payoffs are actually different, so you're no longer playing a prisoner's dilemma. In prisoner's dilemma, you do not care about your opponent, and he does not care about you. If you do care, it's not prisoner's dilemma anymore.

As I stated before, in situations where the game is repeated the matter is very different. The Kantian approach works very well in situations like that, with some modification, at least. And such a game is a better representation of reality that a one-time prisoner's dilemma.

But the point is, if you are really playing prisoner's dilemma, then you want to choose defect, no matter what. If you don't, you're playing a different game.

[gnome]

Yes; that's because you're changing the game. You are considering the outcome where both players get a small victory better than the outcome where you get a large victory and the other player a large loss. In other words, your payoffs are actually different, so you're no longer playing a prisoner's dilemma. In prisoner's dilemma, you do not care about your opponent, and he does not care about you. If you do care, it's not prisoner's dilemma anymore.

As I stated before, in situations where the game is repeated the matter is very different. The Kantian approach works very well in situations like that, with some modification, at least. And such a game is a better representation of reality that a one-time prisoner's dilemma.

But the point is, if you are really playing prisoner's dilemma, then you want to choose defect, no matter what. If you don't, you're playing a different game.

Your description of my reasoning is incorrect. I do not choose "C" because I care about my counterpart's results. I choose "C" because I expect the other person to think like me--and that if I decide to choose "D" that he will decide similarly and I'll lose points. Which is easy if it's myself... not so much if I don't know the other person. If so "C" is harder to choose, yes.

I don't think you can argue that you aren't in the Prisoner's dilemma if "D" is the wrong answer. That sounds a bit circular.

[PixyMisa]

But the point is, if you are really playing prisoner's dilemma, then you want to choose defect, no matter what. If you don't, you're playing a different game.
Since that produces a worse outcome than choosing to co-operate, no, you don't.

In game theory you do, but that's just how game theory defines things. Hofstadter's superrationality (http://en.wikipedia.org/wiki/Superrational) is an alternative approach where the obvious fact that it is better to co-operate than to defect is actually taken into account.

[Mirrorglass]

Your description of my reasoning is incorrect. I do not choose "C" because I care about my counterpart's results. I choose "C" because I expect the other person to think like me--and that if I decide to choose "D" that he will decide similarly and I'll lose points. Which is easy if it's myself... not so much if I don't know the other person. If so "C" is harder to choose, yes.

I don't think you can argue that you aren't in the Prisoner's dilemma if "D" is the wrong answer. That sounds a bit circular.

Well yes, I can. You are describing a scenario where you decide the response of both participants - in other words, a scenario where you simply decide what payoff you get. It's obviously not prisoner's dilemma.

I mean, why on Earth would you expect the other person to think like you - no matter what they choose? Do you believe the other person is telepathic?

You can either expect your opponent to choose C, or to choose D (or to randomly alternate between them). But expecting them to always choose the same as you doesn't make any sense.

As I've said, D is the answer that gives you the best payoff, no matter what your opponent chooses. So yes, it's the correct answer if you want to maximize your payoffs. And if you don't want to maximize your payoffs, then you've defined your payoffs incorrectly.

[Mirrorglass]

Since that produces a worse outcome than choosing to co-operate, no, you don't.

For the umpteenth time, no it doesn't. I don't decide my opponent's move in prisoner's dilemma; that's the whole point. I am going to have an idea about what my opponent will do, and then I'll choose the strategy that gives me the best payoff - and that is always defecting.

In game theory you do, but that's just how game theory defines things. Hofstadter's superrationality (http://en.wikipedia.org/wiki/Superrational) is an alternative approach where the obvious fact that it is better to co-operate than to defect is actually taken into account.

As the link itself states, the idea is not without it's critiques. Indeed, it relies on magical thinking - the idea that your opponent's choice depends on your own choice. In simultaneous games, it doesn't, by definition. Attempting to introduce such thinking to the problem simply means discussing a different game, one far less interesting.

The example used in the article is also intentionally massaged to fit the idea. Traditionally, the payoffs in prisoner's dilemma are something like 2-2, 4-0, 0-4, 1-1. That way, the players have a clear incentive to want the 4 over the 2. For reference, see this (http://en.wikipedia.org/wiki/Prisoner%27s_dilemma#Strategy_for_the_classic_pris oner.27s_dilemma) article on the actual prisoner's dilemma.

But in the article, the payoffs are 100-100, 101-0, 0-101, 1-1. The hundred is so high that the one is completely negligible. The players have very little incentive to care whether they're payoffs are 1 or 0, 101 or 100, so the payoffs are effectively 100-100, 100-0, 0-100, 0-0.

Not really prisoner's dilemma at all, since the incentive to defect is completely illusionary. In my opinion, the fact that such a dishonest representation of the game had to be used speaks volumes about the validity of the idea it's supposed to represent. Just try and use the payoffs normally used in the game, and see if it still seems like a good idea to co-operate.

[Gr8wight]

For about five years, I played a fairly simple game with the high school students I coached for Mock Trial called "Do You Want A Dollar?"

The rules were simple: everyone takes out a piece of paper, writes their names on it and then answers either yes or no to the question, "Do You Want A Dollar." I would give a dollar to every student who said yes, provided that fewer students wrote yes than no. If a majority wrote yes, nobody would get anything.

I found that high school students could not win this game. I gave them the chance to talk beforehand. I even gave them the chance to talk during. They could not get any money. In five years, and maybe a hundred games with ten to twenty student a game, I gave out a total of 11 dollars.

Repeating the same game with some of the same kids after 1 year in college, they won the maximum possible amount.

What do you think accounted for the poor performance? What other thought experiments would teens fail at? Or do you think my observations are incorrect?

I suspect a large amount of the difference lies in the fact that high school students are there because they have to be, and really aren't all that interested in the educational aspect of being there. College students, on the other hand, are there because they want to be there, and are more likely to recognise and embrace the "game" for the educational exercise and starting point for discussion that it is.

[Loss Leader]

I suspect a large amount of the difference lies in the fact that high school students are there because they have to be, and really aren't all that interested in the educational aspect of being there.


I would point out that this was after school at the practice for the Mock Trial team. Not only was the activity completely voluntary, but the kids who joined had self-selected themselves as some of the smartest, nerdiest, school-lovingest people in the building.

However, I agree with you that college students would be better at rationally approaching the game as a puzzle to be solved. I found the high school students generally capable of conceptualizing the game rationally, but generally incapable of acting rationally.

[gnome]

For the umpteenth time, no it doesn't. I don't decide my opponent's move in prisoner's dilemma

I'm not deciding my opponent's move. I'm anticipating that my counterpart wants to choose a line of reasoning that benefits from being mirrored rather than suffering from being mirrored.

The example used in the article is also intentionally massaged to fit the idea. Traditionally, the payoffs in prisoner's dilemma are something like 2-2, 4-0, 0-4, 1-1. That way, the players have a clear incentive to want the 4 over the 2. For reference, see this (http://en.wikipedia.org/wiki/Prisoner%27s_dilemma#Strategy_for_the_classic_pris oner.27s_dilemma) article on the actual prisoner's dilemma.

But in the article, the payoffs are 100-100, 101-0, 0-101, 1-1. The hundred is so high that the one is completely negligible. The players have very little incentive to care whether they're payoffs are 1 or 0, 101 or 100, so the payoffs are effectively 100-100, 100-0, 0-100, 0-0.

Not really prisoner's dilemma at all, since the incentive to defect is completely illusionary. In my opinion, the fact that such a dishonest representation of the game had to be used speaks volumes about the validity of the idea it's supposed to represent. Just try and use the payoffs normally used in the game, and see if it still seems like a good idea to co-operate.

FWIW, my reasoning depended on numbers similar to yours, not the scenario where the reward is so close to the temptation.

[Wrathernaut]

I remember an experiment with apes and M&Ms. Shown two numbers, the well-trained apes knew that pointing to the Lower number got them the Higher number of M&Ms. They would pick the number "3" to get "5" candies. However, shown two bowls of M&Ms, they would always pick the larger amount (and be punished with the lower). This persisted no matter how many iterations were done.

Like the old joke:

Billy (to Sue): "Look this kid Jimmy is so dumb, he'll always take a nickel instead of a dime!"
Billy (to Jimmy): "Dime or nickel?"
Jimmy: "Nickel!"
Billy gives Jimmy the nickel.
Billy (to Jimmy): "Dime or nickel?"
Jimmy: "Nickel!"
Billy gives Jimmy the nickel.
Billy (to Jimmy): "Dime or nickel?"
Jimmy: "Nickel!"
Billy gives Jimmy the nickel.
Billy (to Jimmy): "Dime or nickel?"
Jimmy: "Nickel!"
Billy gives Jimmy the nickel.
Billy (to Sue): "See! What an idiot." (Billy leaves)
Sue (to Jimmy): "Don't you know, the dime's worth more than the nickel?"
Jimmy: "Yep, but if I take the dime, he'll stop offering me nickels."


That's where the true brilliance of the apes shows through:

Once they pick the smaller bowl M&Ms to get the larger bowl, the scientist's theory is confirmed and the experiment ends.

10x3 > 5

[CaptainManacles]

I'm anticipating that my counterpart wants to choose a line of reasoning that benefits from being mirrored rather than suffering from being mirrored.

You can't make that assumption.

[Mirrorglass]

I'm not deciding my opponent's move. I'm anticipating that my counterpart wants to choose a line of reasoning that benefits from being mirrored rather than suffering from being mirrored.

Yes, I understood that. But once you've anticipated that your counterpart will choose co-operate... it's still your best move to defect.

FWIW, my reasoning depended on numbers similar to yours, not the scenario where the reward is so close to the temptation.

[Loss Leader]

That's where the true brilliance of the apes shows through:

Once they pick the smaller bowl M&Ms to get the larger bowl, the scientist's theory is confirmed and the experiment ends.



It's a funny joke, but I remember the tv program showing them doing it lots and lots of times. I've got to believe it was a Scientific American episode with Alan Alda. Virtually all of my knowledge about cognition comes from Alan Alda and, to a small extent, Charles Rocklet pretending to be Alan Alda.

[gnome]

You can't make that assumption.

Watch me. :p

I can be wrong sometimes, but I can make the assumption.

It happens that if my counterpart is a duplicate of me, or someone who takes my approach to these things, I'll be right.

[gnome]

Yes, I understood that. But once you've anticipated that your counterpart will choose co-operate... it's still your best move to defect.

At this point there's no more misunderstanding to clear up, we just disagree.

But I'm not worried. Greater thinkers than you or I have disagreed on this very point.

[Mirrorglass]

At this point there's no more misunderstanding to clear up, we just disagree.

But I'm not worried. Greater thinkers than you or I have disagreed on this very point.

Frankly, I'm just having trouble understanding what we disagree on.

Are you arguing that the payoff for defecting isn't higher than the payoff for co-operating? Or are you arguing that your opponent's move does depend on your move?

[madurobob]

As I said I would, I tested this on the kids I was camping with this weekend. It was a group of about 30 kids aging from 5 to 13, but I took only the six above 9yrs old for this bit of fun.

I changed the rules slightly for the circumstances. They each had a black or a white pebble (nothing to write on or with in the woods); white for yes, black for no. I also set the payout at 50%. That is, I would pay as long as the white pebbles did not outnumber the black pebbles. I offered $4 per white pebble.

For the first game they had to be silent and they dropped their pebble into my hands so no-one could see what color it was. The result: five white, one black.

For the second game I told them they were allowed to talk, but only about the game (lots of distractions in the woods for a 10 yr old - "look, squirrel!"). I walked away to the latrine for about 5 minutes. When I cam back: 3 white pebbles , 3 black. They "won".

The latrine was close enough for me to hear the conversation. All but one knew the right answer was to have three white pebbles, but no-one wanted to be the one to give a black pebble, because they didn't trust they'd get any reward. There was much yelling. When I walked back there were three white and three black pebbles on the end of the picnic table where I had been standing before. They thought they found the perfect solution until I told them all to open their hands and show me the pebble they had kept - they hadn't thought to get rid of the other pebble! There was more yelling - "I told you so!" and "I wanna change my vote". One kid dropped his pebble on the ground (a gravel pad under the picnic table made up of zilloins of black and white pebbles).

So, they figured it out, but just barely. And, I think if I had insisted each give his pebble to me individually so everyone else would know what color it was the result would have been different. Its interesting how these kids really didn't trust each other, even though they've known each other for a few years and have worked together on several team building exercises that require trusting others on the team.

[Loss Leader]

And, I think if I had insisted each give his pebble to me individually so everyone else would know what color it was the result would have been different.


Fantastic.

[madurobob]

Fantastic.

Well, I found it mildly troubling, and it does point to greed as the motivator. That is, the kids clearly were worried about getting their share if they agreed to answer "no". I assume this was driven by their own feelings of greed (I wouldn't share with them, so I expect them not to share with me).

Doesn't really give me that "warm fuzzy" feeling that we're raising our kids right.

[Loss Leader]

Doesn't really give me that "warm fuzzy" feeling that we're raising our kids right.


I don't think you have anything to be worried about. I think the inability to actually choose to lose is based more in biology than anything else. Some physical maturation of the brain and a little exposure to individual loss scenerios, and they'll be fine. Had you repeated the experiment with the parents, I think you'd have seen no problem. These same children, in ten years, will be horrified to hear how much trouble they had with the game.

I bet you could have made them vote by secret ballot all night and never had to give out a single cent.

[gnome]

Frankly, I'm just having trouble understanding what we disagree on.

Are you arguing that the payoff for defecting isn't higher than the payoff for co-operating? Or are you arguing that your opponent's move does depend on your move?

I'm arguing neither. I'm arguing that my reasons for choosing can be mirrored by my opponent. If we are willing to work in tandem by considering this, we can get a better outcome than trying to screw each other. Tacit collusion. Happens all the time. Though, the more players there are, the more difficult this is to achieve.

In fact, this is why an oligopoly is usually undesirable, it is actually feasible for them to collude without explicit conspiring.

[Mirrorglass]

I'm arguing neither. I'm arguing that my reasons for choosing can be mirrored by my opponent. If we are willing to work in tandem by considering this, we can get a better outcome than trying to screw each other. Tacit collusion. Happens all the time. Though, the more players there are, the more difficult this is to achieve.

In fact, this is why an oligopoly is usually undesirable, it is actually feasible for them to collude without explicit conspiring.

That makes sense when the game isn't an individual event, and has actual consequences. It makes perfect sense to make a deal with your opponent, saying you'll both choose to co-operate. But if the game will only be played once - that is, we know there will be no consequences beside the initial payoffs - it doesn't make sense to honor the agreement. I don't care about what outcome we get - the only thing that matters is my payoff.

[CaptainManacles]

Watch me. :p


Okay, sorry, I should rephrase that. You can make that assumption, but if you do you're being irrational and all the conclusions you draw from it will be rejected by everyone else.

These things were worked out decades ago. You're wrong.

[PixyMisa]

For the umpteenth time, no it doesn't.
Yes it does.

As the link itself states, the idea is not without it's critiques. Indeed, it relies on magical thinking
No it doesn't.

It relies on the other party not being an idiot. That's dubious, but it's not magical.

[Mirrorglass]

Yes it does.


No it doesn't.

It relies on the other party not being an idiot. That's dubious, but it's not magical.

Now this is just ridiculous. Let's assume we use the unbalanced payoffs from your example.

You are arguing that choosing co-operate when your opponent chooses co-operate gives a better outcome than choosing defect.

Well, in this case it gives the outcome of 100. Defecting gives 101.

So are you arguing that 100>101? What am I missing here?

Remember, I don't care about my opponent's payoffs, and the game is only played once.

[Random]

“Double your money” is an interesting variant. Each player starts with one hundred dollars (play money or a brawl will break out). Each round, you go around and let people secretly give however much money they want into the pot. After each person has done so, you then count up the total money in the pot, double it, then distribute this money evenly to the players. Do this for a few rounds, see who has the most money at the end.

In a twenty-five player game, each dollar you put in only gives you eight cents back.

[Sophronius]

The reason that this game can't be beaten by most high school classes is because most high school classes are largely populated with greedy, stupid and/or spiteful teens and everybody knows it. There is no point in trying to cooperate simply because half of the class won't understand the problem, half of the class will try to double cross the rest no matter what, and half of the class will actively sabotage the game so as to ruin it for everybody. (yes, that math is correct). Yeh, I know it's been mentioned before in this thread, just wanted to restate it for emphasis.

@mirrorglass: I have been in this discussion before, and I believe the problem here is that people are looking at the PD problem from the wrong angle. They think "the outcome where both parties play nice is better than the one where both parties are greedy, so therefore it is smarter to play nice in the hope that the other player will do so as well". The right way to think about it is of course "assuming I only care about my own gains and I cannot influence the other player, it is always better to be greedy, therefore it is smarter to be greedy."

If there IS a good reason to choose cooperate even though you do not care about the other player, I'd be happy to hear it, but the reasons provided in this thread don't make much sense to me.

[Ladewig]

They could not get any money. In five years, and maybe a hundred games with ten to twenty student a game, I gave out a total of 11 dollars.



Which you could easily get back by holding a Dollar Bill Auction (http://en.wikipedia.org/wiki/Dollar_auction). I wonder how high they would go?

[stilicho]

For about five years, I played a fairly simple game with the high school students I coached for Mock Trial called "Do You Want A Dollar?"

The rules were simple: everyone takes out a piece of paper, writes their names on it and then answers either yes or no to the question, "Do You Want A Dollar." I would give a dollar to every student who said yes, provided that fewer students wrote yes than no. If a majority wrote yes, nobody would get anything.

I found that high school students could not win this game. I gave them the chance to talk beforehand. I even gave them the chance to talk during. They could not get any money. In five years, and maybe a hundred games with ten to twenty student a game, I gave out a total of 11 dollars.

Repeating the same game with some of the same kids after 1 year in college, they won the maximum possible amount.

What do you think accounted for the poor performance? What other thought experiments would teens fail at? Or do you think my observations are incorrect?

Don't you have to use the same test group of high school students in their first year of college together to standardise the control group? I remember instructors trying this sort of game and it was incredibly easy to botch the results by manipulating others in the social group to agree to doing something unexpected.

You have to go into any social situation with the preconception that an experiment is underway and do your best to discover its meaning, those in on it, the expected results, and the potential benefits of negating the expected hypothesis.