# Prisoner’s Dilemma – A Game Theory Simulation

Back in the 1970’s I taught a high school social studies course called “War and Peace Studies.”

A recent email exchange reminded me of a simplified version of the Prisoner’s Dilemma that I created for use in the classroom.

The Prisoner’s Dilemma is a fundamental exercise in game theory and serves as a great catalyst for discussions about decision making, communications, ethics and responsibility.

First, the classic example of the Prisoner’s Dilemma from Wikipedia:

Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated the prisoners, visit each of them to offer the same deal. If one testifies for the prosecution against the other (defects) and the other remains silent (cooperates), the defector goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should the prisoners act?

How I adapted for classroom use

Students were divided into two separate locations. (Group A and Group B). Once divided, I managed the game – shuttling between the two rooms. Both groups were given the same goal – “To accumulate as many points as possible without helping or hindering the other group.” In practice, I found that the point incentive generally faded away as groups just focused on their perception of “winning.”

I ran a series of 10 decision rounds. During each 5 minute round both groups were told make a group decision about the choice one of two colors – red or blue. See results chart below. I did not specify how they were to arrive at the decision within their groups. When each group has completed their decision, I shared results back to each group. As the decision rounds accumulated,  players faced the results of cooperation and betrayal.

To add another dimension to the dilemma, periodically (after decision rounds 3 and 6) I invited each group to send a negotiator to a neutral location (usually just the hallway). This was the only communication allowed between the groups. Generally each group was divided over both the instruction to give their negotiator (“bluff ’em” vs “make a deal”) and how to interpret the negotiator’s “report.” Sometimes groups even became mistrustful of their own negotiator.

It usually took about 45-50 minutes to set the game up and go through a series of 7-10 rounds with some negotiation breaks. The homework assignment was to write a reflection “What did I learn about myself during the game?” Loads of great discussion the next day with many great applications to history, current events, group process and ethics.

For great prompts to foster student reflection, see my post “The Reflective Student: The Taxonomy of Reflection.

## 25 thoughts on “Prisoner’s Dilemma – A Game Theory Simulation”

- April 28, 2011

Peter,
Thanks, again, for the information and instructions.

I had a fascinating experience with my students (two different classes of 11th graders, Honors English class). We’d read essays surrounding the question, “Are We Responsible for Others?” over the last month and then listened to the WNYC RadioLab program on altruism before playing your game.

The original directions didn’t include a goal, which threw me until I decided to let it play out. Lack of a stated goal became an interesting wrinkle. When students asked me the goal (which was never at the beginning of the game), I shrugged, and said, “Sounds like you are making the goal yourself.”

Some groups decided the goal was to get the most points; another group decided to be ethical and cooperative and to show integrity (not choosing red after agreeing on blue in negotiations). After three rounds in one class — tied scores — we ended the period, so when we resumed the next morning, I added a wrinkle: anyone who talked the day before could not (for two rounds).

The conversations, with the vociferous voices silenced, became much more thoughtful, less cutthroat. (Made me think about politicians — talkers — and their effect on society — as well as about the silent citizens and their responsibility to step up.)

A couple rounds later I upped the stakes: the win/loss was tied to a GRADE. If a team won, they got a 100% and the other got a 0%; if they tied, each got 50% — kind of like the jail sentence. The conversations were even more thoughtful because the consequences were more real for the other team. (Note: I didn’t tell them how many POINTS the grade was; nor did they ask. It was real enough for them to take it more seriously.)

An especially bright and wise student suggested in negotiations that the teams agree to choose BLUE to maintain the tie until the last round, when they would renegotiate (he knew the other team would pull a red at the last second). Then he had a terrific solution: for Round 10 each team would agree to pick RED, thereby each losing 3 points but STILL maintaining the tie. If one team was dishonest (not choosing red), the dishonesty would NOT HELP the team, as it would if they both agreed to choose blue.

I cannot wait for the all-class discussion on the outcome.

Students’ rationalizations were interesting: when the cutthroat team saw that the other team decided the goal was integrity, they claimed that “they are just picking blue to make us feel bad and look like jerks.”

I replied, “Ah…so THEY are at fault for your decisions?”

Thanks again for this activity!

Camille

- April 28, 2011

Camille,
Thanks for taking the time to share your observations. I’m glad you explored you’re own options – there are many ways to run this activity. It does such a nice job of bringing your essential question to life. “Are We Responsible for Others?”

I’m certain your class conversation will be lively. BTW – if any of your students end up writing reflections, I’d be glad to add them to the post.
~ Cheers, Peter

- September 13, 2011

Hi Peter,
Thanks for posting this. I have a question about the simulation though–assuming RED and BLUE stood in for Cooperate and Defect, was there a reason you didn’t go with the original Cooperate/defect? Were the groups told that they would get points for matching colors? I’m a bit fuzzy on the details here…
Thanks!
Jen

- September 13, 2011

Hi Jen,

I used the colors to make the intent of their choice slightly less obvious in the first round. But since they quickly figure that out, I think you could use most any labels. Let me know how it goes, if you end up trying it another way.

Cheers ~ Peter

- September 13, 2011

I see! Thanks very much. I didn’t realize that last chart was the payoff structure you provided to the students, telling them that their goal was to maximize their group’s points. Assuming that the results chart is a payoff structure (and not a report on how your students behaved) then it all makes perfect sense to me 🙂

- September 13, 2011

(or, NOT telling the students what the goal is, be it maximize points, minimize the other group’s points, maximize the difference in points, etc…) Either way if they’re given the payoff structure, I can see how this runs. If I’m missing something though, please do let me know. I’d like to run this simulation this week because it really does look like it will help more than the online one I’ve used in the past. Thanks very much!

- September 13, 2011

Hi Jen,

I’m glad we got this cleared up. (Maybe I’ll change the labeling to reduce confusion in the future). As far as your question regarding goals: I found that my stated goal didn’t seem to be foremost in their group discussions. They quickly internalized the choice involved in the prisoner’s dilemma and spent more time trying to figure out what the other team would do, than strive for the goal I gave them.

You might try it a few different goals and make that part of the learning experience. It could be interesting to make announced goal changes after certain rounds to see how that impacted behavior.

Best of luck with this in your classroom. Let me know how it goes.

- May 10, 2012

I always thought that if I was confronted with the Prisoner’s dilemma, after being arrested for some crime or other, I would plead that I am innocent and not connected to the other party at all. I would then argue in court that the offer that had been given to both myself and my co-accused was so weighted towards both parties confessing that my co-accused had simply taken the obvious path (guilty or not) to avoid a long sentence.

I would hope that our legal system would want to avoid sending an innocent man to prison at all costs and release me, free of all charges.

- January 8, 2014

Many thanks for posting this Peter. I came across your site while searchng for the results matrix for the four-team/person version of this game that I used an eon ago (pre-Internet). I don’t suppose you’ve come across that version?

- January 8, 2014

Hi Greg,
Glad you like it. haven’t seen the four-team/person version. That would be interesting.
Cheers ~ Peter

- March 31, 2014

I believe that the Program on Negotiation at Harvard Law School has several scenarios developed for four-players.

- March 31, 2014

Hi Glee,
Thanks for that tip. I did the google and found this link at Harvard Law School Prisoner’s Dilemma / Game Theory

Cheers,
Peter

- June 22, 2014

Love the game played it years ago , I saw the solution but was angered and amazed others did not . It was used as a negotiation tool for win win strategies. Limited negotiation rounds and the option not to negotiate was given to both teams. The summary then announced a new team arriving. The question asked was who would they rather play with ?

- June 22, 2014

Chris, I like the addition of a new team. Peter

- January 7, 2015

HI Peter,

I just wanted to thank you for this simulation. I used it in my International Relations classes for 4 years and it was such a fantastic way for the students to understand diplomacy. It was always interesting to me that after the first meeting of the teams, there was always betrayal….I also enjoyed their reactions, when they discovered, that they would have to meet again! Now at a new school, I will use it for my Economics class. It will be used to illustrate how some price fixing schemes can fail. Thanks again for making a complex idea easy to understand and internalize.
Take care,
Lisa

- January 8, 2015

Hi Lisa, Thanks for taking the time to share your experience. I’m always pleased to hear how lesson ideas are used. I’m a big fan of educational simulations. Here’s one I used when I taught sociology. It would be great for economics as well. The Marbles Game – A Society Building Simulation. See rules at the bottom of the page. This is an old website from a course I taught in the 90s.
Have fun, Peter

- October 5, 2016

Peter-

Do you have a matrix for 6 teams? I want to play Blue Green game with about 40 people and 9 per teams sound like too many. Any recommendations? Thanks!

- October 5, 2016

Hi Scott,
No I don’t have a matrix for 6 teams.

I used to run it in a class of 30 students – split into 2 teams of 15. That always worked for me.

The other option, if you had enough space is to split it into two separate games with 2 teams facing off in one area (with 2 rooms) and another game with 2 teams facing off in a different area (with 2 rooms).

- May 31, 2018

I’ve run this with groups of over 100 split into 2 teams where the decision of each team needed to be unanimous. It obviously can take a long time to run it and it becomes a very interesting opportunity for individuals to see how they participate (or don’t) in this kind of setting. One dynamic that is pretty powerful is that one person, who sees the “correct” approach can block the entire team by not voting. Talk about peer pressure!

- May 31, 2018

Over 100 in the groups! I admire your courage. Thanks for sharing that!