The Prisoner's Dilemma, for second-graders

Miscellaneous and Personal Stuff I Must Share
1

The other day, guidance was unexpectedly canceled for my second-grade students, and I had to think of something tout suite to fill time. It was guidance, so I tried an idea I’d been kicking around for awhile: teaching them about the prisoner’s dilemma.

For those unfamiliar with it, it’s a game theory problem. Two dudes are captured and questioned by the police about a crime that they committed together. They’re captured separately and interrogated. The deal the police offer them is like this:
-If neither of you rats the other out, we’ll try you on a lesser crime, and you’ll serve a year in prison for it.
-If both of you rat the other out, we’ll try you both for the main crime, but give you both a lenient sentence for cooperating, and you’ll serve three years in prison.
-If you stay silent and your friend rats you out, then you’ll do the full five years in prison, and he’ll get off totally free.
-Of course, if you rat your friend out and he stays silent, you get off free and your friend does the five years.

The question is, what’s the best course of action?

Midway through teaching them, I realized that I didn’t actually want to encourage them to disobey authority and then refuse to tell authorities about it; that lesson is all kinds of headache for me. Also, I realized that the classic game goes for a low score, which is very confusing to young kids. I went ahead and taught them the basic game anyway, though, revising it for next time.

The revision was more interesting. I changed it to “the sharing game.” Students got a page with instruction and room for four games of five rounds each. For each game, the student chose a partner. It could be someone they’d played with before, or someone new. Both people had to agree on partners in order to play. (This part is a key difference from classic versions of the game in terms of strategy).

A round consisted of both players choosing either a red chip (indicating that they weren’t sharing a toy) or a yellow chip (indicating that they were sharing a toy), and simultaneously revealing their choices. Scoring was as follows:
-If both players shared, they both had a reasonable amount of fun playing together: each got three points.
-If neither player shared, they both had a little bit of fun playing by themselves: each got one point.
-If one player shared and the other didn’t, the one who didn’t share got to play with both toys, getting 5 points, while the one who shared didn’t get to play with either toy, getting zero points.

After five rounds, both players tallied their scores to get a score for the game. They could choose to play again with one other, or to find a new partner for the next game. The goal was to get the highest score in the class over the course of four games recorded on one sheet.

It was pretty interesting how it broke down. First, some of the nicest kids in the class were some of the most vicious players, repeatedly playing red chips on their disbelieving classmates. The temptation of five points overwhelmed everybody, and they would play red chips out of nowhere.

After everyone had played four games, we had a discussion. I asked them to figure out the highest score and how to get it (100 points, achieved by playing red every round against a player who played yellow every round). Everyone agreed that that’d never happen, especially after I reminded them that the goal was to get the highest score possible. We then figured out what you’d get if both players played red each round (20 points), and what you’d get if both players played yellow each round (60 points). Finally, we figured out that the highest score in the class was something like 38 points, and I challenged them to find a way of scoring higher.

Interestingly, it was two of the most aggressive kids in the class who figured it out. First they tried some weird semi-alternating patterns of being nice and being mean, each getting a score somewhere in the forties. But then they tried again and played four full games of nothing but yellow chips, each scoring 60 points. Nobody else was able to come close to their scores.

We had a great discussion afterwards in which I connected it to real life. Yes, sometimes treating other people cruelly results in short-term benefit. But people respond in kind when you do that, and your benefits tend not to last. What’s more, if other people see that you’re the sort who treats others cruelly, they’re not likely to want to have much to do with you, and you’ll have trouble finding anyone to be friends with after awhile. It’s become my go-to metaphor at recess and in class when I need to talk to a kid about social skills.

Anyway, I thought some folks here might be interested in this as a lesson plan idea, and I’m interested in hearing thoughts on modifying it or improving it. (I touched very briefly on the tit-for-tat model, but I’m not sure most second-graders could appreciate it).

2

You could start off by calling it something else. (Or teach it the same day as the planet names to get the giggling all over with at once.)

3

Heh–yeah, I thought of that, too. I first encountered the prisoner’s dilemma many years ago in (I am embarrassed to admit) a Piers Anthony novel, and there it was called the tough-but-fair strategy, so when I told the kids about it, that’s what I called it.

4

I’m glad you realized early on that teaching small children about keeping their mouths shut to the cops wasn’t a great idea. That’s exactly what I was thinking reading the first paragraph.

Imagine of two of your kids actually got interrogated for a crime, and the only thing they’re willing to say is, “Our teacher told us it would be better if we didn’t rat each other out.”

5

Echoing the gladness that you didn’t teach them not to confess to crimes. I think this is a really good activity for kids and I probably would have understood it better when I was reading about it in computer science if I had been taught it in this kind of situation.

6

Not a bad answer. A better one would be “Our teacher told us about the Fifth Amendment. We ain’t talking. She also told us about the 6th Amendment. We want lawyers.”

7

Yeah, well you know how kids simplify things.

8

Brilliant! Do you mind if I share this with my mom? She’s a sixth grade teacher, and I bet she’d love it.

9

We save that lesson for 12th grade Government, where all my kids get a card printed up by the ACLU outlining their rights and what cops can and cannot legally do. :smiley:

10

If the police are going to be such dicks that they try to undermine the friendship between the guys like that, can they really be trusted that they’re telling the truth about how they’ll respond to cooperation?

11

I agree that second graders are probably too young to be taught the full version of the Prisoner’s Dilemma with its ambiguous morality.

A simple lesson like “snitches need stitches” is more age appropriate.

12

Wow, I am really impressed that you taught your kids this. What’s next, the dilemma of the commons?

13

Well, they are second graders. If they’re being interrogated for a crime, I think prisoner’s dilemma is the least of their worries.

14

If you don’t mind, I’m going to send your game off to the Religious Education coordinator at church.

15

That’s awesome. Take a bow!

16

Isn’t there an experiment similar to this but using candies for sharing?

17

I can’t remember but I think the experiment was like this.
1 child is given 10 pieces of candy.
they are told they can keep all 10 or share whatever number they feel like sharing with another child.
I think the younger kids more often didn’t share or shared very little.
While more of the older kids shared but usually less than 40%.

18

http://scienceblogs.com/notrocketscience/2008/08/children_learn_to_share_by_age_78.php

To find out, Ernst Fehr from the University of Zurich played a series of three decision-making games with 229 children between the ages of 3 and 8. The study used similar methods to those employed by Frans de Waal in his experiments on capuchins, but with some notable differences. For a start, the choices were anonymous. In each trial, a child had to decide between two ways of distributing sweets between themselves and a second child, who was only ever represented by a photo.

Three games

In the first “prosocial game”, the choosing child had to decide between “one sweet each” or “one for me, none for you”. As with the capuchin study, neither choice had greater economic merit for the chooser. Purely selfish individuals that ignore their partners are equally likely to choose either option. This is mostly what children aged 3-6 did, but those aged 7-8 started to choose the “one sweet each” option about 80% of the time.

Were they just trying to help the other kid out or were they more concerned about being unfair and hogging the sweets? The second “envy game” showed that the second explanation was more accurate. This time, the choosing child had to pick between “one sweet each” and “one for me, two for you”. Again, personal gain didn’t dictate a preference and again, children younger than 7 were just as likely to pick both options. But older kids offered their photographic partners one sweet rather than two in 80% of trials; they were more concerned with levelling the rewards than maximising the winnings of the second child.

The final “sharing game” was the only one where sharing involved a personal cost - the first child had to choose between “two for me, none for you” or “one sweet each”, thereby sacrificing one of their own sweets so that their neighbour got one. At 3-4 years of age, only 9% of children chose this unselfish option but at 7-8 years of age, about 45% did.
So humans are very unwilling to share with each other at an early age, but are relatively happy to help other children out as long as they don’t lose anything in the process. As time passes, their capacity for selflessness matures along with their bodies. Between the ages of 6 and 7, a strong sense of fair play kicks and children start caring about what others are getting and whether it’s the same as what they’ve received. They begin to be drawn towards choices that reward everyone equally.

Cliques

When Fehr pooled the decisions of each child across all three games, he found that only about a fifth of the youngest ones made choices which showed that they valued fair play. Among the oldest kids, three times as many made such choices, and a third of them were exceptionally just and made egalitarian decisions in all three games. There were bad seeds too - children who seemed unusually spiteful and offered up as little as possible in all three games. Only 22% of children aged 3-6 behaved like this and among the older children, that proportion fell further to 14% (which is about where it stays in adults).

Not all children were treated equally though. The youngsters clearly preferred to share with those from their own playgroup or school, and were 15-20% more likely to make fair choices in the prosocial game if another child from the same social group stood to benefit. This cliquey justice was even more apparent in the sharing game; when children had to sacrifice one of their own sweets in the name of equality, their willingness to share with others from a different group actually fell with age. And the envy game revealed that these tendencies were stronger among boys than girls.

Fehr says that his results fit with other theories suggesting that selflessness and parochialism (that is, favouritism towards individuals from your own social group) have the same evolutionary roots and evolved hand-in-hand because of frequent conflicts between rival groups. Males tend to bear the brunt of these conflicts and indeed, the boys in Fehr’s study showed a stronger bias towards their own group than the girls did. Culture and education obviously play a role too. As children move toward formal schooling, they develop a better sense of what society expects of them and become more attuned to how they are viewed in the opinions of their peers.

19

Very interesting experiment, canadiankorean–thanks for the link! And I’m glad others like it; feel free of course to share as appropriate.

After the first session of it, I looked up the wikipedia entry on the Prisoner’s Dilemma, and learned something disheartening: in most variants of the game, playing mean is the dominant strategy. The only variant they mentioned in which it was non-dominant was a game with an indefinite number of turns.

I think that my variation–in which players may choose who to play with after each round–changes that, such that the dominant strategy is to play the first game with a tough-but-fair strategy (or possibly even a nice-every-round strategy), and thereafter to play only with other players who chose a similar strategy during the first game. Is this right?

20

Quite possibly, though I’m way too lazy to figure it out exactly. It’s precisely because “playing mean” is a dominant strategy that the game is as important as it is. It describes situations where being selfish is individually beneficial but collectively deleterious, and the interesting question is how is it that we as a society actually manage to usually have most people play fair in such situations even though the “rational” thing to do is play selfish. One of the answers is that we keep track of past games, and punish people who play selfish when we face them again.