The Prisoners Dilemma

A simple game theory exercise explained.

The prisoner’s dilemma is a very simple game theory exercise that is one of the most powerful tools for understanding social problems. Rather than discuss a particular social issue, I’d like to share this exercise with you, since it has applications to most social issues, including both conflict within groups and with other organizations.

What is the Prisoner’s Dilemma?

The prisoner’s dilemma goes like this:

You and your partner in crime are captured by the police. The police put you in separate rooms and interrogate you separately. The police have enough evidence to convict you each for a year in prison. However, they offer you a deal:

If you defect and betray your partner by telling the police he did the crime, you can walk free and he will do three years. If he defects against you and tells the police you did it, you will do three years and he will go free. If you both defect and betray each other, they will have so much evidence they can put you both away for two years.

What would you do?

Applications In Real Life

Before we answer that, let’s look at the applications of the prisoner’s dilemma. While I assume most of my audience law-abiding and free from this exact scenario, the prisoner’s dilemma applies to all social systems where one could gain by harming others, but all of society benefits if we co-operate together.

Take for example a public park. If we all clean up our trash, the park is clean. If everyone cleans up their trash, except me, I save the time and effort of carrying my trash to the trash can, and because I’m only one person, the park is still mostly clean. If no one else cleans up their trash but me, I have to do the work of cleaning up after myself, and still don’t get to enjoy a clean park, because everyone else is throwing their trash on the ground. If everyone throws their trash everywhere, the park is trashy.

The solution most societies use to prisoner’s dilemma-like scenarios is to punish defection. For example, most towns impose a fine on littering. If throwing your trash on the ground comes with a large fee, most people won’t do it. The other way that societies solve prisoner’s dilemmas is through social stigma. If your neighbors know you’re polluting the park, they might shame you or be less likely to invite you to the park with them. The personal benefit of violating the prisoner’s dilemma disappears if society collectively punishes defection.

Relationship Matters

Back to the original scenario. Let’s add one more element: suppose you and your partner in crime have been working together for years and plan to continue working together. After you both get out of jail, you will likely see each other again, work together in the same criminal organization again, and might even find yourself in the same situation of being questioned by the police many more times. What would you do now?

Now suppose, you’ve never even seen this partner before committing a crime together. You don’t know them and will likely never see them again. The job was just a random get-together. If you defect, they’ll go to jail, and they won’t even know it was you who betrayed them. Now, what would you do?

One element that changes the prisoner’s dilemma is how many times you play it. If you and your partner will have multiple rounds of the prisoner’s dilemma, the interest in cooperation goes up. If they know you betrayed them last time, they’ll be less likely to trust you in the future. If they know that you were loyal to them last time, they’ll be more likely to trust you in the future. However, if there is no future, both participants have less reason to be loyal and more reason to act in their own self-interest.

Winning Strategies

So how do you win the prisoner’s dilemma? When AIs have played the prisoner’s dilemma the consistent winning strategy is very simple: tit for tat. First-round, you co-operate. Then, whatever they did last round, you do on the next one. You give people the benefit of the doubt, and then assume that they will continue to act the way they did in the past. If this sounds like a life lesson, that’s because it is.

The winning strategy includes four qualities:

• Nice. The winning strategy must not defect before its partner does.

• Retaliating. The winning strategy must not be nice if the other person isn’t.

• Forgiving. If the other person begins co-operating again, the winning strategy allows them to do so without consequences.

• Non-envious. The winning strategy doesn’t seek to win “more” than their opponent.

The winning strategy to the prisoner’s dilemma changes based on the population you play it with. One might choose a different strategy depending on how trustworthy the larger group seems. If a society is “high-trust,” it means the other members of the group are likely to cooperate. If a society is “low-trust,” it means the other members of the group are likely to defect. Ensuring the group cooperates, trusts each other, and remains loyal is important to any group or leader.

Losing Strategies

From the winning strategy, we can also deduce a losing strategy. I asked ChatGPT-4 to reverse the winning strategy, and it produced the following list:

• Uncooperative: A failing strategy might involve always defecting, regardless of the other player's actions. By always choosing to betray or act in one's self-interest, a player is likely to create a cycle of retaliation and distrust, resulting in both players receiving worse outcomes than if they had cooperated.

• Naive: A player who always cooperates, no matter what the other player does, can also be considered to follow a failing strategy. Such unconditional cooperation is exploitable, as the player will continue to cooperate even if their counterpart consistently defects. In this case, the naive player will suffer the negative consequences, while the defector reaps the benefits.

• Unforgiving: A strategy that never forgives the other player's defection, even if they return to cooperation, can also be considered a failing strategy. Holding grudges and refusing to cooperate after a single betrayal can lead to a cycle of mutual defection, resulting in worse outcomes for both players.

• Inconsistent: A strategy that randomly alternates between cooperation and defection, without any clear logic or pattern, can be highly unpredictable and ineffective. This erratic behavior can make it difficult for the other player to respond effectively, leading to suboptimal outcomes for both parties.

Retaliation

One important aspect of winning strategies is retaliation. If another player defects, you must retaliate. While it might seem “noble” to play co-operatively even when the other side is defecting, this is a losing strategy from a game theory perspective.

If you want cooperation, you are more likely to get it when you show that bad behavior will be punished with tit-for-tat retaliation. Showing that you won’t retaliate invites further bad behavior, since the other player learns there are no consequences for defection. Only once the other player begins cooperating again can you return to doing the same yourself.

The implication of this strategy is a relative morality. There isn’t “one” way you should always treat people. The treatment they receive changes with their behavior. If they act right, cooperate. If they mistreat you, respond accordingly. Social norms function along a prisoner’s dilemma. While it benefits everyone to follow certain rules, if those rules are not enforced cooperation is no longer a winning strategy.