Posted by: Tom Triumph | November 1, 2011

Students’Dilemma:Prisoners’ Dilemma Offers Insight into Classroom Management

This post is about teaching: For poems, go back one or look at the Poems tab above.  I’ll do another poem in my next post.

Last week in class, students played a series of games in a discussion on game theory, which tied into my lessons on economics, The New Deal, The Great Society and our current economic situation. I had hoped by simulating choices in a game with clear options and weighted consequences, students would better understand the American economic marketplace and the choices the powers-that-be are weighing.  The games were a balance of cooperative and individual win/lose scenarios, all of which can be found on Wikipedia (along with analysis).

While half of my day was spent discussing player options and consequences, the other half was dealing with low level behavior that hints at big things to come. The weather had turned cold, Halloween was next week, and the holidays were knocking; all harbingers of things getting worse. On my drive home, thinking about student behavior and classroom management, I found myself understanding it–and how I should react–through a simple matrix we used throughout our theoretical discussions.

Let me explain….

Note: For those Language Arts teachers who laugh when the thought of math and/or data is mentioned, give yourself some credit and stick with this. Let’s face facts; an essay is nothing but a logic argument on par with any geometric proof.

We were playing Prisoners’ Dilemma. The scenario, from Wikipedia, reads as such:

Two men are arrested, but the police do not possess enough information for a conviction. Following the separation of the two men, the police offer both a similar deal- if one testifies against his partner (defects / betrays), and the other remains silent (cooperates / assists), the betrayer goes free and the cooperator receives the full one-year sentence. If both remain silent, both are sentenced to only one month in jail for a minor charge. If each ‘rats out’ the other, each receives a three-month sentence. Each prisoner must choose to either betray or remain silent; the decision of each is kept quiet. What should they do?

In short, if the student trusts the one across the table from him/her they are best off being silent. Otherwise, rat.

Here is a matrix showing you all of the options.  The top and side are the two players, Rat and Silence being the two options each player has.  The numbers are the number of months they would receive from their choices.

Example PD payoff matrix




3, 3

0, Year


Year, 0

1, 1

So, if both rat each other out they get three months, etc..  Or, looking at relative values it comes down to this:





  win more-lose more


  lose more-win more


When we played the first round, it was a mixed bag based on what students thought they knew about the other student they were playing against.  I had purposely partnered them with random people to stop friend-play  and general foolishness.  Those playing against a “nice” kid assumed they would stay silent, while those known miscreants were assumed to rat.  The results were mixed, because reputation did not often match game play, making it a great community building experience.

Then, we kept playing.

Wikipedia says, “If two players play prisoner’s dilemma more than once in succession and they remember previous actions of their opponent and change their strategy accordingly, the game is called iterated prisoner’s dilemma.”  So, we played “iterated”.  As experience with the game trumped assumptions about the person, patters began to reveal themselves.  We kept playing and playing, with students not knowing when it would end.

For the most part, they began to cooperate.  In most of the later rounds, students began to remain silent for most of their turns, which benefited both players.  This has proven true in controlled experiments.  In our debrief, the main factor that caused players to rat their partner out was boredom–cooperation got boring, and they knew it was “just a game” with nothing at stake.  Otherwise, ratting others out was used when a person felt paranoid that the truce of silence would not last and panicked.  In the following round, the squealer usually returned to silence only to have their partner rat them out, known as “tit for tat” in game theory parlance.  Once that “tat” was done, the game then returned to several rounds of silence-silence.

Then, I told students we were going to do one round.  That was it.  How much do you trust your partner, now?

Nearly every pair ratted each other out.

Knowing that there would be no chance at “tit for tat” they chose the greedy offer.  As one student keenly observed, “there’s no real downside–it’s either three months or you walk.”  He knew silence had a real risk, and not much more of an upside.  Both theorists and controlled experimental data agree: When your timeline is short, being selfish is the best strategy.

On my ride home, these findings clarified what was happening in my classroom, and our school overall.  In the classroom, the prisoners’ dilemma has been mutated.  Let’s look at a matrix I gave the kids the next morning:





Does Not

Follow Rules


As Problem


No “Short Term” Fun

Solution Oriented

Long Term Happy

“Short Term” Fun

No Solutions

No Trust




No “Short Term” Fun

Solution Teacher’s

Mixed Happiness

“Short Term” Fun


No Happiness

Along the top is the student’s choices: To follow the rules or not. On the right side are the teacher’s choices: Talk with a student to solve problems, or simply enforce rules and consequences in a black-and-white fashion.

Problem Solvers: Those teachers who have relationships with students, in the long term, find that many of the problems in the class go away.  The problem–both the cause and the effect–are solved.  So, a student might misbehave sitting next to a certain other student, and the solution might be to keep them apart.  Or, at least, the student admits their mistake and accepts the consequences so you can get back to teaching the rest of the class (hey, they are middle schoolers).

Enforcers: They makes rules, enforce with fear, and are only as strong as the consequence.

Note: I am assuming that both sets of teachers are clear in their expectations, and follow through when those expectations are not met.  Problem Solvers are not assumed to be weak pushovers, and Enforcers are not uncaring fascists.  Let’s assume both are kind, caring souls who teach for all of the right reasons, and are good at their jobs, they just possess different philosophies.  Full disclosure, I am a “problem solver” but secretly wish I had more of an “enforcer” in me (although my students think I’m a tad scary).

What’s interesting is that when the trust of the Problem Solver is breached, it pushes that teacher into a tit-for-tat scenario.  Remember what happened in Prisoners’ Dilemma: No one wants to be pushover, so were forced to react before things settled down again.  That teacher might work for solutions, in the long term, but might also feel they have to be more of an Enforcer.   In both Prisoners’ Dilemma and the teacher’s, after being burned a few times that trust gets thin and they rat the other person out more and more.  A student who takes advantage of a teacher trying to work with them to solve problems will find themselves no longer being trusted, and miss out on a great opportunity for long term happiness.  Off to the office with you, kid!

The student’s abuse of the system, in the long run, hurts them.

The day after playing all of the rounds of Prisoners’ Dilemma, I put the matrix above on the board.  They got it, and even added a little it to it.

It got really interesting when we discussed Unified Arts teachers and substitute teachers.  Like the Prisoners’ Dilemma played for one round, everyone ratted each other out.  In the case of classroom management, there was no long term relationship to maintain.  Students see our UA teachers infrequently throughout the week, and substitutes even less.  There is little incentive, other than fear or empathy, to behave.

For further theory, John Kenneth Galbraith lists the five types of power as: 1. Threat, 2. Reward, 3. Expert, 4. Heirarchy, and 5. Respect.  In school, Reward is slippery, built on relationships and easily outstripped by the Reward of your peers laughing with you (which also piggybacks with Respect).  Expert, too, fails during, say, hallway transitions and fire drills.  Yet, a long term relationship can promote Reward, Expert and Respect for the teacher, school and system to the top.  In fact, Respect is the most powerful of the five.

Yet, infrequent adults–subs and the like–rely only on Heirarchy (I’m a teacher and I say so, which is the weakest of the five types of power) and Threat (to the office!)

Now, much of this may be a “duh” moment for you, but I was impressed how this modified Prisoners’ Dilemma predicted classroom management in classrooms that have relationships vs. those that rely only on titles and consequences.  I like things quantified and charted, because I can then predict future events and change how things are done.

For example, getting UA teachers more involved with students at a relationship level–outside the classroom, with teams or TAs–might help at our school.  They are kind, caring individuals with vast depths of knowledge in exactly the things my students want to know more about.  Having permanent substitutes that are working with students daily also builds relationships.

At the very least, create consequences that will instill fear, or at least second thoughts.

I get excited by anything that helps clarify what I can do better, and that makes decisions predictable to a certain degree.  Next post, I’ll go back to poetry.


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