Prisoner's dilemma formulation for children

Question

I am preparing an introductory course on Game Theory for children (between 10 and 17 years old). In the course description, I want to include a prisoner's dilemma in order to catch children's attention and persuade them to attend the course. Therefore, I would like to find a short, direct and attractive-to-children formulation, a "slogan" for my course. The problem is that all of the formulations I have found falls into one of the following issues:

• It includes a reference to "+18" content (death, crimes, etc.).
• It is formulated capitalistically, making money the main protagonist.
• It is a complex and enmeshed formulation, or it is too unreal for a kid's mind.

Can anyone suggest a formulation of the prisoner's dilemma that does not fall into any of these issues?

Answer 1

Here's a silly example:

Give students collections of the same type of thing, where each collection contains "good" objects and "bad" objects -- for example, a stack of Pokemon cards with both rare and common cards. We might assume common cards are worth $1$ and rare cards are worth $5$. Have ready another stack of cards that are all common -- call this the "Free Stack".

Students pair up and play a trading game, as follows:

• Students want to build a nice deck of cards (in the sense of overall point value), and they can get new cards by trading.
• A trade is made when both students select a card from their own deck, placing it face down in front of them. When the cards are revealed simultaneously, the following takes place:
  1. If both cards are rare, then the cards are exchanged and each student takes a card from the Free Stack, adding it to their own deck. This ends the trade.
  2. If both cards are common, then the cards are exchanged and the trade ends.
  3. If the players offer different types of cards (one common and one rare), then the player who offered the common card gets both cards. This ends the trade.

It is obviously advantageous for players to "cooperate" and both offer rare cards. They trade those cards, but they both get +1 from the free card from the Free Stack.

It is not helpful or harmful if they both offer common cards, so both players get +0 for that option.

If they offer different types, then the winner gets +5 because they received the rare card, and the loser gets -5 because they lost the rare card.

Answer 2

I found out about the Prisoners' Dilemma as a kid from a book about the Harry Potter phenomenon, which had a chapter about the problem, but presented as a story about Harry and Draco being accused of breaking school rules. Each was offered the same deal as in the original problem, formulated with House Points being taken away instead of a prison sentence. Maybe you could write a story using these or other characters that kids would be familiar with?

Alternately, the existence of crime and prison sentences are well-known to 10-17-year-olds, so you might not have to modify it at all. Maybe you could play up the second-person formulation ("You are accused of a crime...") to make it more engaging.

Answer 3

I like Nick C's idea more than modifying the typical formulation. The notion of snitching on a friend, regardless of the severity of the "crime", has real-world ramifications beyond the punishment put out by the authorities. Depending on your student population, that is possibly going to spur a conversation that will overshadow the objectives of your lesson.

Here's another non-crime formulation that students will be familiar with:

You and a fellow student are assigned to work on a team project that will give a significant grade in your class. You break the work in half and both agree to do your part over the weekend. Even though it is a major grade, the amount of work for each half of the project is reasonable considering the consequences of a good grade.

If you both do your best work, you will both get 100% but both of you have to do some work over the weekend. If neither of you commit to the project, you will both get 70% but you can both have a free weekend. If one of you commits but the other doesn't, then you will both get an 80% on the project but one of you will work over the weekend while the other doesn't. Your partner won't know whether you decided to do your share of the project until Monday morning, and you won't know what your partner decided. Will you do your share of the project?

This isn't a pure formulation of the Prisoner's Dilemma, because the outcome is being measured in two different currencies (grades and free time) which different students may value differently. But I think any sort of "tragedy of the commons" scenario applied to two players would play out like the Prisoner's Dilemma.

Answer 4

It sounds like you wish to protect your students from the violence and greed of the adult world, while still making the dilemma real enough to keep them engaged.

To that effect, I offer two solutions.

One, replace prison with detention. Make the crime something like using cell phones in class or throwing spitballs.

Two, have them arbitrarily grade each others' work (obviously don't make it their actual grades. It's up to you whether you want to let them think they're grading each other). If they both grade each other well, they both get high grades. If one grades the other poorly, but the other grades the first well, then the first gets a higher score, and the second gets 50%. And whatever numbers you want to formulate in there.

as a side note... I don't think money and prison are taboo, or too much for kids to handle. But I agree that they're kinda clichéd, and somewhat boring because we're desensitized and removed, except for the poor kids for whom the issue is far too close to home

Edit

Following the original prisoner's dilemma, no matter what the opponent does, ratting them out gives you a lighter sentence. Not the best ethics lesson, but this is mathematics. So...

• If they're ratting you out, not ratting them out would give you a E, ratting them out would give you a C.
• If they're not ratting you out, ratting them out would give you an A, and not ratting them out would give you a B.

Answer 5

Use of performance-enhancing drugs in sports is a good example.

However, why the objection to money and capitalism? Real-life actors value money very much and it affects their behavior greatly.

A very realistic and applicable example involving money is what happens when a group of friends goes dining, depending on whether each friend pays for themselves or the bill gets split equally. Suppose a pair of friends are offered a cheap snack that costs 5 units of money or an expensive dish for 25. The friends consider the dish overpriced, valuing it at 20. The snack is fairly priced in their opinion.

If the friends agree to split the bill evenly, the payoff matrix is as follows: $$ \begin{array}{|l|c|c|} \hline & \text{Snack} & \text{Dish} \\ \hline \text{Snack} & 0,0 & -10,5 \\ \hline \text{Dish} & 5,-10 & -5,-5 \\ \hline \end{array} $$ which is typical of the prisoner’s dilemma.

Answer 6

Perhaps:

You and another classmate are together in an obstacle course.

If you both make it to the end within a minute, you each get a free day off from school. If just one of you makes it to the end in a minute, they get a whole week off.

You know that if you had the other student's help, you could easily finish in a minute, but without it, you won't finish in time. Likewise, the other student would complete the course with your assistance, but not without it.

You don't know what the other student will do - even if you helped them, they might not return the favor.

Do you help them?

Answer 7

My suggestion would be to look at the existing literature.

Blake, Rand, Tingley, and Warneken (2015) "introduce a novel implementation of the repeated Prisoner's Dilemma (PD) designed for children to examine whether repeated interactions can successfully promote cooperation in 10 and 11 year olds."

Dealing with younger children (ages 6-11), Fan (2000) reports on a study of "children’s behavior in a prisoner’s dilemma game."

A classic treatment is Tedeschi, Hiester, and Gahagan (1969), which modified the Prisoner's Dilemma Game for a study of children ages 8 to 10.

Multiple papers have been written on how children with autism do or do not cooperate in the Prisoner's Dilemma, if that's a concern.

A journal search for "prisoner's dilemma" children "game theory" came back with about 1000 references. You could limit that to recent studies, or include additional search terms such as "teenager" if you wish. Pick a few studies and read the methodology section for ideas.

References:

Blake, P. R., Rand, D. G., Tingley, D., & Warneken, F. (2015). The shadow of the future promotes cooperation in a repeated prisoner's dilemma for children. Scientific Reports (Nature Publisher Group), 5, 14559. https://doi.org/10.1038/srep14559

Fan, C.-P. (2000). Teaching children cooperation — An application of experimental game theory. Journal of Economic Behavior & Organization, 41(3), 191–209. https://doi.org/10.1016/s0167-2681(99)00072-4

Tedeschi, J. T., Hiester, D., & Gahagan, J. P. (1969). Matrix values and the behavior of children in the Prisoners Dilemma Game. Child Development, 40(2), 517. https://doi.org/10.2307/1127419

Answer 8

Perhaps the problems of "make up" and "traffic" could also be used.

Make-up: Assuming that the chemicals etc., damage your skin in the long run, we may state that constant make-up is "bad". And contrarily no make-up is better in the long run since your skin remains "naturally beautiful".

Given any two individuals with the option of applying make-up or going natural almost everyone will succumb to the lure of make-up. Even though everyone is better off without it in the long run, everyone thinks they'll look better (read attractive) than everybody else - this "race to the bottom" is highly profitable for companies at the expense of the consumers, so to speak. Only a tight cooperation amongst consumers can break out of this cycle and that's very hard to do.

Traffic: Let's say you're in a country where people are semi-literate and if marginally violating a traffic law/discipline gets them going faster, they are going to violate it. Example, lane discipline or "right of way" (i.e., whose turn is it). Those flouting the rules will seem to "move faster" through the system and slowly everyone will do it leading to major traffic issues.

Why did I emphasize semi-literate? You can get the cooperation of the individuals (players in the game) by having them take exams or disseminate information that decreases the likelihood of such traffic violations leading to overall improvement in traffic conditions. Hence, you'll find traffic a lot better in Europe or Canada or USA vs. say the Indian sub-continent, certain African countries and the like.

You could try the same with candies - bring a box of candies to class along with some "health treats". Ask each student to take a single item from the box - either a candy or a healthy option. The candy should be more attractive. To do this though you'll have to have some good candy/chocolates and not some crappy candy i.e., Candy > healthy treat by taste/value. You could add a twist by saying that if you take one candy, the next person after you has the option to take an extra candy.

Another possibility is allowing them to "throw paper balls" in the middle of the class, without penalty or fear of punishment. The option is of a cleaner class vs. a messy one. Even if one student does it, the whole class will devolve into it.

The goal of the Prisoner's dilemma IMHO is simply this: selfishness is worse than cooperation in the long run, even though the former may come out ahead in the short run. Given this POV one could construct numerous examples to show case prisoner's dilemma in a classroom setting.