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Cooperation theory for the classroom

An interactive game theory activity for teaching the prisoner's dilemma

An interactive game theory activity for teaching the prisoner's dilemma.

We encounter cheating in all sorts of contexts, from shirking in the workplace to living with a roommate who doesn't do the dishes. How do we deal with cheaters who reap benefits at our expense? More than a decade ago I developed an interactive game to teach students about the prisoner's dilemma - a classic problem in game theory where individuals are tempted to defect or 'cheat,' and take advantage of cooperators. In this game, students have the opportunity to act out potential strategies in the classic prisoner's dilemma game and give them an intuitive sense of the problem of cooperation: how can cooperation evolve if cheaters prosper?

The game looks something like this: students move around playing a prisoner's dilemma game with their classmates, trying out different strategies, tracking their payoffs on a score sheet. Since developing this game I've used it in many different classrooms, from elementary school kids to graduate students - adjusting a bit for different audiences. The version that I'm publishing here is geared towards college students or advanced high school students, though it's easy to use for younger students as well by dropping the background readings and simplifying the discussion questions. So let's jump right in to how you play the game!

The first thing you need is a little bit of background about the prisoner's dilemma. If you're teaching at the level of high school or above, you might want to describe the original formulation of the prisoner's dilemma, which is about two suspects who are taken into custody. Each of them is offered a reduced sentence if they rat out their partner-in-crime. If neither of them talk, they both get a short sentence. If both of them rat each other out, they get a medium length sentence. But if only one of them talks, then the one who talks goes free and the one who stayed silent gets a long sentence.

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Photo by NBC - © 2012 NBCUniversal Media, LLC

What would you do? Would you rat out your partner or stay quiet? No matter what your partner does, you would be better off talking than staying silent: Either you go free (if your partner stays silent) or you get a medium length sentence (if your partner talks). If you stay silent the best you can do is get a short sentence (if your partner stays silent) and the worst is a long sentence (if your partner rats you out). These outcomes get translated into numerical payoffs and then used in evolutionary computer simulations (like the ones I talk about in my other post How to Walk Away) to see what strategies do best. This dilemma - and the inherent temptation to cheat that is built into it - has formed the basis for decades of research on cooperation and the conditions under which cooperation can thrive vs. the conditions where cheaters prosper.

If you're using this activity in an elementary or middle school classroom, you might want to change the framing a little bit so you're not talking about incarceration and criminality - though if that's how you roll as a K-12 teacher I'm not judging. When I use this activity with younger groups I've called it 'The Apple Tree Game' and simply map the payoffs on to the outcomes for cooperation vs. cheating in getting apples down from a tree. If you cooperate and help each other find and get apples from the tree, you both get 3. If neither of you does anything, you get 0 apples. If one of you sits there while the other does all the work, the lazy cheater runs off with 5 apples and the person who worked to get them is left with nothing AND went through all that effort (so they get -1 apples).

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So, now you've got the basic framing for the prisoner's dilemma game and it's time to play! You'll want to download the activity description so you can use it during your lesson. There are three separate games in this activity. The first one is basic play where students essentially walk around the classroom and silently play the prisoner's dilemma with every classmate who they encounter. In the second game, students can talk to each other as they play, opening up the possibility for coordinating, promising, lying, gossiping and more. In the third game, students have to be silent again and just one thing is altered: they can choose whether they want to keep interacting with the same partner or leave. This last game allows students to use a strategy called Walk Away, which my simulations have shown can favor cooperation in partners playing the prisoner's dilemma (see related blog post on How to Walk Away).

You will need about 1 hour of class time to get the most out of this activity. The first thing you'll want to do is put the prisoner's dilemma payoffs somewhere were students can easily see them so they can calculate their scores as they play. You can just write the payoffs on the board or download this slide with the payoffs on it. If you want you can spend some time talking about the prisoner's dilemma and how it is a social dilemma (i.e., what is individually optimal is not what is socially optimal). But beware, talking a lot about the payoff structure ahead of time can make people less cooperative in the game. (See my note at the end of this blog post about this!)  

Alright, so now you're ready to have your students play. Download the game cards (or you can just have students use the pointy end of their pens for defect and the blunt end for cooperate) and the score sheet below. Don't forget to make enough copies for everyone in your class to have their own score sheet and set of cards (if you're using those). Your students will also need something to write with and something to write on like a notebook. They should also use their notebook to hide their game card/pen behind until they both show one another their behavior for that round.

The game typically goes something like this: you read the instructions (on the activity description), tell them to begin and then the students move around the room playing the prisoner's dilemma game with each other. In game 1 they have a fixed strategy based on their birthday month (either cooperate or defect) and they have one-shot interactions with each other and then move on and find a new partner. This game is a sort of 'warm up' to get students used to the game play, how to calculate the payoffs, and how the prisoner's dilemma works in general. After playing the game, I ask students to write their scores on the board so we can calculate the payoffs for the different strategies. In game 1, defectors always have higher payoffs than cooperators. In the example below, from when I taught this in class a few weeks ago, you can see that defectors have an average of 50 points in game 1 while cooperators only have 17.1!

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In game 2, I let the students choose their own strategy each round and also I let them communicate with one another. This version of the game can get... well... pretty loud. Students make promises to cooperate, yell about who is a defector and who is a cooperator and generally get pretty engaged in the whole game. In this game, cooperators usually do a bit better (above you see they got 20.7) than in game 2, but defectors almost always still win by a large margin (29 points on average in the example above). Because students choose their strategy from round to round, you will need to have students decide if they were mostly cooperating, mostly defecting or a pretty even mix so that you can look at the payoffs of each strategy (mixed got 23.6 points in the example above). (Note: If you're feeling particularly excited about data presentation you can have them report their score on a two dimensional plot where the proportion of cooperation is on the x-axis and the payoff is on the y-axis.)

In game 3, students aren't allowed to talk, but they are allowed to have repeated interactions with one another and decide if/when they want to end those interactions. This makes a lot more strategies possible, including Tit-for-Tat and Walk Away. The video at the top of this post shows students playing this third game. Usually some students discover that if they find another cooperator they can just rapidly rack up points by cooperating and cooperating, and then leaving if their partner defects. Every time I've had students play this, they have discovered this strategy. Except for one time - the most recent time I used it in my Evolutionary Psychology class a few weeks ago. But I did something different that time: I spent 15 minutes before the game emphasizing how defection has the highest payoff no matter what your partner does. So I can't help but wonder whether I influenced them by emphasizing the benefits of selfishness. This fits with research showing that training in economics, and in particular training in the 'self interest model' of human behavior contributes to lower levels of cooperation in the Prisoner's Dilemma game. This seems to be driven by economics students expecting others to behave more selfishly. Despite lower levels of cooperation than usual in game 3, most people in my class still cooperated and cooperators did pretty well anyway, getting about the same payoffs as everyone else (you can see in the picture above cooperators got 70, mixed 68, defectors 70.2).

These three games are just a few variations on the prisoner's dilemma. If you want to teach about general game theory principles and have your students learn how simple rules like Walk Away can promote the evolution of cooperation, then these games may be just what you need. But there are a lot of other things you can teach about using this general kind of framework. Want to teach about the difference between one-shot play and repeated games? Then vary that between the games. Want to teach about how perspective taking changes cooperative behavior? Have them first play without imagining the other person's perspective and then ask them to play imagining how the other person is experiencing the game. The possibilities really are endless! I would love to hear about how you use this game in your classes, what variations you come up with and how it works as a teaching tool, so let me know how it goes!