Game Theory and the Kingdom of God (A Quirky Series Installment), Part 3: "The Prisoner’s Dilemma"

Of all the non-zerosum "games" the one that has received the most attention is a "game" called the Prisoner's Dilemma (henceforth "PD"). What I love about the PD is what a great lens it gives us to look at life and social interactions. I hope after these next few posts you feel the same.

The classic formulation of the PD is via a story:

Imagine you are criminal with co-conspirator. You both are captured by the police and are being interrogated in different rooms. You cannot communicate with each other. As you are being interrogated you are asked to implicate your partner. If you cooperate with the police and rat out your partner ("It was all his idea! I had nothing to do with it!") you are told that you could go free. If you keep quiet you'll do some time in jail.

What do you do?

The problem is that your partner, in the other room, is also being given the same deal. He's being asked to implicate you to save his own neck. What the police are hoping is that you both crack, revealing vital evidence, as you implicate each other. This way they can send both of you to jail.

That is the classic scenario. Game theorists then specify the following "payoff" structure:

If you both rat each other out, both you and your partner go to jail for 3 years.

If you both stay quiet, both you and your partner go to jail for just 1 year.

If you rat out your partner and he stays quiet, you go free and your partner goes to jail for 5 years.

If you stay quiet while your partner rats you out, your partner goes free and you go to jail for 5 years.

(Ignore the legal feasibility or reality of such a payoff structure, the payoffs are taken as given for point of illustration.)

As we have learned, when we can specify choices ("moves") and players and can quantify outcomes, we can use the idea of a game to analyze the decision making process. How then should we "play" the PD? Should I stay quiet and cooperate with my partner against the police? Or, should I defect on my partner and rat him out?

Ratting out my partner, the "defection" move, looks good. If I rat and my partner say quiet, then I get to go free. Further, if he's ratting me out right now I better rat him out. Because if I say quiet while being ratted out I could go to jail for 5 years. By ratting him out at the same time he's ratting me out we will both go to jail for 3 years, but that is better than going to jail for 5 years.

The point: No matter what my partner does MY BEST MOVE IS TO DEFECT (to rat out my partner).

So far so good. But the problem comes in the symmetry of the situation. Your partner is going through the exact same decision making process. In short, rationality is leading both of you, inexorably, to mutual defection and a shared 3 year jail term. This outcome has perplexed social scientists and game theorists in that we expect rationality to lead to optimal outcomes. The PD is a "dilemma" in that rational play leads to mutual defection and a sub-optimal outcome. That is, both players could have cooperated with each other by staying quiet. In that event, the jail term is only a year. But reason draws the players away from mutual cooperation to mutual defection leading to a worse outcome. And the logic of the players is impeccable. You cannot fault their thinking or strategizing. For just this reason, some game theorists have called the PD the "failure of rationality."

As a psychologist, what is intriguing about the PD is how it illustrates, tragically, failures of trust in our world. PD-type encounters are all around us. We play the PD everyday, with all kinds of people. And, tragically, people "defect" on us and we are left holding the bag or paying the price. Many of us have deep emotional scars because of the way someone treated us in a PD-type interaction: Relational interactions where we trusted a person (or a group of people) or financial interactions where we trusted employers, insurance companies, or people handling our money.

Much more remains to be said about the PD. Much more about trust, multiple player PDs, iterated PDs, free riders, etc. Today I just want to make a point about vulnernability. Trust means you are vulnerable. And it is our vulnerability in the PD that makes us choose the "protective," "cautious," and "paranoid" move: Defection. To trust, to cooperate, just leaves us too vulnerable in this life.

So, how does that fit with the Christian life? Too often, I think I play the game of life cautiously. That is, I don't risk my life serving others, fearing that they will take advantage of me. And here's the thing: I'm totally rational for thinking this. I can feel justified that self-protection is the "best" choice.

But we see God, particularly with Jesus, display this crazy willingness to trust humanity. To trust you, to trust me. And He takes risks when he trusts us. He hasn't played the game conservatively.

And we are called to do the same. To do the crazy thing, to allow rationality to fail. We don't keep a record of wrongs (I Cor. 13). We turn the other cheek. We forgive seventy times seven.

That is a difficult thing to do in this world, to trust. But, like God, I trust. I risk.

So, you can play with me. I won't rat you out.

But you've got to trust me...