THIS is the story of two prisoners with a dilemma. But this is also the story of all of us, so listen closely.
It starts with the story of two prisoners. Let’s call them Pedro and Maria. The authorities have enough evidence to implicate Pedro and Maria in a minor crime. They suspect them of committing a greater crime. However, they can only implicate Pedro and Maria of the greater crime if either provides testimony against the other. How can the authorities make them rat each other out?
One clever prosecutor came up with the solution—give them an offer they cannot refuse. To understand the beauty of this offer, let us analyze the situation using game theory.
Game theory is the study of how different rational actors will decide on a situation given the possible outcomes. (In game theory, the situation is called a ‘game,’ the actors ‘players.’) In game theory, the situation Pedro and Maria are in is called the prisoners’ dilemma. It goes like this.
If Pedro and Maria both refuse to testify, they each serve five years for the minor crime. In the language of game theory, we say that they cooperated with each other. Now, if Pedro cooperates and Maria rats on him, then Pedro rots in jail for 20 years while Maria goes free after 3 months. In the language of game theory, we say that Maria has defected. If Pedro defects and Maria cooperates, then Pedro goes free after three months while Maria spends 20 years in jail. If both defect, each will spend 10 years behind bars for their major crime.
But what if they both keep mum? Let’s look at the options open for Maria. If Pedro cooperates, Maria is better off defecting because spending three months in jail is better than serving five years. If Pedro defects, Maria has even more incentive to defect, because serving 10 years is better than serving 20.
Whatever Pedro decides to do, Maria is always better off defecting. And the same is true for Pedro. Hence, by pursuing their best interests, Pedro and Maria will testify against each other and end up serving 10 years.
But surely serving five years is better than serving 10. Why wouldn’t the prisoners agree to cooperate? After all, mutual cooperation brings them to the win-win deal of serving five years. The answer is simple and has already been given—each prisoner is always better off defecting. In other words, the rational decision for each prisoner is to defect.
Letting the prisoners talk to each other just makes it worse, because then Maria will just think that Pedro is trying to get her to cooperate so that he can go free after three months while she rots in jail. In game theory, the technical term for a person who cooperates against his best interest is ‘sucker.’
But what if one prisoner loves the other? Then he will be a sucker for love and potentially serve 20 years. At any rate, his decision will not be a rational one.
But how is the prisoners’ dilemma important if few of us will ever be Pedro or Maria? This is where the power of game theory comes to the fore. Game theory is not interested in the content of the game, only its form. From the standpoint of game theory, prisoners’ dilemma is not about the prisoners but about a game whose structure is such that players who act on their best interest end up in a situation that is less than ideal for everyone involved.
Here’s one example. If both you and your roommate clean the room, then you both get a very clean room. But if you clean but your roommate doesn’t, then he gets a clean room without exerting the effort. To avoid being the sucker, you don’t clean the room. If he cleans, then good. If he doesn’t, then at least you did not waste your effort serving a free loader.
The examples are not always as mundane. Sometimes, it can be explosive. For instance, if both United States and Russia disarm their nuclear warheads now, then the world becomes a safer place. That’s a win-win. But, acting on their best interest, both US and Russia keep their nuclear warheads; both countries defect, because they are better off doing so. The world is less safe as a result.
Similarly, our roads are clogged with cars, our forests are disappearing, and our seas are running out of fish, all because no one wants to be the sucker.
Even the biggest challenge of our time, addressing human-made climate change, is made even more challenging because of its prisoners’ dilemma structure. This explains why countries are slow to act on climate change despite the fact that our survival depends on quick action. In the competitive global economy, no one wants to be the sucker who cooperates while the rest goes on business as usual.
How do we beat the prisoners’ dilemma? By changing the game. Specifically, we beat it by making the rational decision the one that also leads to the best possible outcome. We design the outcomes so that cooperation will not be for suckers, and defection will not go unpunished.
That’s easier said than done. It’s also easier to say in broad strokes than to outline in detail. But we know that with some effort and political will, it is possible. For example, the US and Russia have found a system to simultaneously decrease their number of live nuclear weapons. Some cities have found regulations that work to discourage car use and encourage the use of public transportation, biking, and walking.
When it comes to climate change, we’ve discovered a few game changing strategies. One would be to make renewable energy cheaper. However, we still have a long way to go, and to reach our goal we need more strategies to convince more countries to cooperate on the goal of saving the world. (How funny it is that the world needs encouragement to save itself, but that’s the way it is.)
One step in figuring out what those strategies are is to learn game theory. Only once we realize that we are prisoners of the prisoners’ dilemma can we begin to hack at bars that keep us from being free.
Pecier Decierdo is the resident physicist and astronomer of The Mind Museum.
