The Prisoner’s Dilemma

A couple of recent events influenced the direction of this article. First, I was summoned for jury duty last month. It was the first time I attended a jury summons; I previously found a way to delay the summons and since I’ve moved around so much, I never had to step foot in a courthouse (knock on wood). I figured it was time to complete my civic duty and the eight hours I spent being screened by lawyers was quite fascinating. To keep myself awake throughout the process, I was examining everything from a psychological perspective and analyzing the direction of the questions and how other potential jurors were responding. It turned out to be an interesting day, but I was not selected for the trial.

The second event was listening to a recent episode of The Exemplary DM Podcast. In the episode, the hosts discussed skill challenges and roleplaying scenarios that involved the party interrogating NPCs or the party being interrogated by NPCs. My group has had their fair share of Jack-Bauer 24-style “WE’RE RUNNING OUT OF TIME!” interrogation moments, but I’ve yet to turn the tables on them and have them forced to explain their actions.

I set my mind to work on how a DM could engage the players with a unique challenge that is not decided merely by die rolls. My mind eventually remembered the fascinating principles posed in The Prisoner’s Dilemma. You may not be familiar with the term, but if you have watched The Dark Knight, then you have seen it in action. Below, I present The Prisoner’s Dilemma and discuss how a DM can engage their adventuring group with the game.

The Prisoner’s Dilemma

I learned about The Prisoner’s Dilemma at some point during my college or graduate school career. The Prisoner’s Dilemma was developed out of game theory, and the most common form of the game features prison-sentence payoffs:

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), and the other stays quiet (cooperates), 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?

This situation seems to be displayed in some form or another in every episode of The Closer, Law & Order and CSI: Everywhere my wife watches. The detectives pit one suspect against another to gain more information about a crime or a confession. The suspects are kept in separate rooms and are unaware if their “partner in crime” is cooperating with the detectives. This is The Prisoner’s Dilemma.

It may help to examine The Prisoner’s Dilemma in graphical form, as it truly is a game that two people are playing.

Each Prisoner has two options in the game – he or she can either cooperate with or defect from the other prisoner. If both prisoners remain silent and don’t testify against the other, then they both serve a short 1-month sentence. Cooperation with the other player is the best outcome for both parties.

However, either Prisoner A or Prisoner B can choose to testify against the other, meaning he or she would go free but the other prisoner would receive a 1-year sentence. If Prisoner A and Prisoner B both testify against the other, then they both receive a 3-month sentence. The four possible combinations of outcomes in the game are displayed above.

The dynamics of the game create four possible outcomes for the two players participating in the game, which are displayed to the right. The two players in the game can together reach any one of four outcomes. They can both cooperate, which results in a winning situation for both of them (win-win). One player can defect while the other player cooperates, which results in one player winning more while the other loses more (win more-lose more). The final option is for both players to defect, which results in both player losing (lose-lose).

When the matrix of possibilities is presented in this way, the game may not appear interesting. However, the fun begins when players do not realize they are involved in The Prisoner’s Dilemma. Even if they do realize they are playing The Prisoner’s Dilemma, then they are still in the dark regarding how their fellow player will behave – cooperate or defect. You may now be scheming to create interesting ideas for your adventuring party! And as we’ll see below, The Prisoner’s Dilemma can be reskinned to suit any purpose.

The Genius of The Joker

Heath Ledger (rest in peace) portrays The Joker as a diabolical madman. I’m not a movie critic, so I’ll turn it over to Peter Travers from Rolling Stone (who even drops the term “id” in the review):

Ledger’s Joker has no gray areas — he’s all rampaging id . . . He’s right when he compares himself to a dog chasing a car: The chase is all. The Joker’s sadism is limitless, and the masochistic delight he takes in being punched and bloodied to a pulp would shame the Marquis de Sade. “I choose chaos,” says the Joker, and those words sum up what’s at stake in The Dark Knight.

I’m not going to shy away from spoilers since the movie is now three-years old. But if you haven’t seen The Dark Knight, then you probably want to stop reading as I’m about to discuss the ending of the movie.

I originally planned to write at length about how The Joker sets up an elaborate Prisoner’s Dilemma for the resident of Gotham City. But in researching the article, I found two other authors who have already tackled the subject. The first author provides an excellent summary:

A quick re-cap. The Joker has been managed to force Gotham authorities to load two ferries – one with citizens, the other with criminals. While in the water we see that the Joker has rigged each ferry with explosives and given the detonators to each boat. The detonators, we are told, are linked to the other boat’s explosives. Each boat has until midnight to detonate the other ship’s ordinance or BOTH ferries will be destroyed.

Each ferry has to make a choice: kill or be killed – confess or stay silent. And the clock is ticking.

However, if you really want to dive into the The Joker’s version of The Prisoner’s Dilemma, then stop reading this article and first check out this detailed breakdown of The Joker’s Ferry Game. The author created the graphical representation below, and delves into great detail regarding the mathematical and moral implications of The Joker’s Ferry Game. The article culminates with this terrific paragraph, “There are a few other situations in [The Dark Knight] that are prone to game theoretic applications and I have not exhausted the ways in which this game could be modeled.  However, I think this calls for a new villain in the third movie of the trilogy: The Game Theorist.  Much like The Riddler, but deadlier and requiring Batman to use mathematics to fight crime.”

I thoroughly enjoyed The Dark Knight, but as this scene developed, I was screaming in me head, “They’re using The Prisoner’s Dilemma!” The game played by the two boats and the passengers within is fascinating theater. And you can bring the same qualities to your gaming table.

Never Split The Party . . . Except Just This Once

There is no limit to the manner in which The Prisoner’s Dilemma can be applied to roleplaying games. However, one aspect of the game that is crucial is to have each player in The Prisoner’s Dilemma unaware of the other player’s behavior. This logistical problem could be the biggest hurdle when attempting to implement this device. My suggestions for this are below:

  1. The Food Break. Ask half of the party to go out for snacks or take a dinner break. Request that the other half of the group remain at the table for a brief period of time before leaving. The staggered “dinner breaks” will allow you to engage both “players” with The Prisoner’s Dilemma.
  2. The Beer Break. If alcohol is a common fixture around the gaming table, request for half of the party to go out to restock the rations. Keep the remaining members of the party at the table to start The Prisoner’s Dilemma. When the reinforcements arrive, ask the players who originally stayed behind to step outside while you allow the drink-fetchers to “catch up.”
  3. The Get Off My Lawn Manuever. Remember that the DM can swing a great deal of power when it comes to the dynamics at the table. If the DM indicates that one half of the party has to step outside for a few moments, then the players will likely agree to that request. The DM may not wish to go out of their way to take extraordinary measures to split the party to execute The Prisoner’s Dilemma. When in doubt, just ask half of the players to leave the gaming room for a bit.
  4. The Staggered Start. Inform half of the group to arrive at 3PM for the start of the game. Inform the other half to arrive at 4:30PM. Run through The Prisoner’s Dilemma with the first group before the second group arrives. When the second group does arrive, consider using The Food Break, The Dinner Break or The Get Off My Lawn Maneuver.
  5. The Email Fix. A DM could use email between sessions to split the party. The DM would need to trust that his or her players will not collaborate behind the scenes. A long roleplaying scene could be played out over the course of a week or more through email, and the resolution could take place at the gaming table.
  6. The Final Exam. Handouts could be created to disperse to the group at the gaming table. The groups can then be asked to move to separate corners of the room or a different area of the house. The situation posed in The Prisoner’s Dilemma is detailed on the handout, and the groups must return the completed form to the DM before speaking with the other group. This ensures the actions are simultaneous and avoids the groups collaborating on responses.

The D&D Prisoner’s Dilemma

With the tools above to successfully split the party, here are a few ideas for including The Prisoner’s Dilemma in a D&D setting. I have include a graphical representation to aid the understanding of each scenario.

The party is exploring ancient ruins. They discover an empty hallway that ends in a locked door. Before the locked door at the end of the hallway are two unlocked doors – one to the right and one to the left. Each room is empty outside of a pressure plate in the center of the room and a lever turned down on the wall furthers away from the hallway. The party learns that both pressure plates must be depressed in order for the levers in each room to work. For example, one player would need to stand on the pressure plate while another pushed the level up; however, this has to happen at the same moment in both rooms. At this point, the party is split between the rooms.

Once the levers are pressed up, the doors to each room with the levers close and a ghostly image appears in both rooms:

You’ve come this far with the help of your friends. But the time for old alliances must come to end. The door you seek is now open, but soon this room will be molten. Press the lever back down if you wish to remain alive, but sadly your friends will not survive. The heat will soon press in, so hurry and commit your sin.

If the message above is a bit too lyrical, then tweak it to be even more obvious – pulling down the lever will result in massive damage and possibly death for the people in the other room. Leaving the lever alone will produce a modest amount of damage for both rooms. If both levers are pulled, then both rooms are flooded with molten lava causing massive damage. If only one lever is pulled, then the room that pulled the lever suffers slight damage but the room that didn’t pull the lever suffers massive damage. The matrix of outcomes is below.

To pull, or not to pull. That is the question.

This matrix is based on actions that result in several different damage expressions for Group A and Group B. The scenario can be edited to place the party in any type of situation, but the outcome variable is damage.

A second example relies on roleplaying with a powerful NPC, which could be a mighty king, an ancient dragon or even one of the gods. The party could have somehow offended one of these major NPCs and end up captured. The party is split in half and each group from the party is taken before the NPC at different times. The NPC offers each group from the party a deal – confess that the other group of players was the guilty party whom offended the NPC and only the guilty will be punished. In a lethal campaign, the punishment could even be death for a number of the players in the party. An example matrix with the outcome of death is presented below.

The stakes in this game are quite higher.

The DM can adjust the punishment to the flavor of the campaign. It could be related to story, for example banishment from the kingdom or to another plane of existence. It could be the challenge level of a quest offered by the NPC as payment for the group’s offense. Be creative with the consequences for the The Prisoner’s Dilemma to tie in outcomes to party goals and PC backstory elements.

Summary

The Prisoner’s Dilemma is classic game theory that can be applied to any D&D campaign. The scenario has been used on a grand scale in The Dark Knight, and can bring some wonderful tension to a campaign. Use the tips above to split up your party into two groups and challenge them with The Prisoner’s Dilemma. Let me know the scenarios you develop and how they work with the players.

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About The Id DM

The Id DM is a psychologist during the weekdays. He DMs for a group of fairly loyal and responsible PCs every other Friday night. In the approximate 330 hours between sessions, he is likely anxious about how to ensure the next game he runs doesn't suck.
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4 Responses to The Prisoner’s Dilemma

  1. Tourq says:

    Since reading your article 5 seconds ago, I have since decided to run a deadly one-shot for my group, ending with The Prisoner’s Dilemma. I’d like for it to be especially ‘potentially’ deadly at the very end, but with only the slightest possibility that all parties make it out alive.

    What I mean is, one choice or the other will result in death, but if the PCs are clever enough, they *might* be able to pull off a third option.

    Hmmm…

    Thanks for the article. I am thus inspired.

  2. The Id DM says:

    Tourq, excellent. Come back and let me know the specifics of your scenario and how it unfolds for your players. :-)

  3. Herrozerro says:

    Much like alot of what i read about game design I love the ideas but dont have much luck in impleminting it in my own games. Though I think for this one Ill need to try harder.

    • The Id DM says:

      I believe you are right that applying The Prisoner’s Dilemma to an RPG takes some effort and energy, but I believe it can be a very worthwhile endeavor. Good luck with implementing the idea in your game.

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