Original Sin: Interlude, The Joker's Ferry Game

In my last post we were talking about game theory, specifically zero sum and non-zero sum games. A few days ago in my theories class I was lecturing on game theory, particularly the game called the Prisoner's Dilemma (PD). As we were discussing the PD one of the students asked if the Joker's Ferry Game, from the recent Batman movie The Dark Knight, was a PD. I said, I'd have to think about it. And as I thought about it I kept thinking about this series on Original Sin.

To understand the question about if the Joker's Ferry Game is a PD you may need a refresher on the Prisoner's Dilemma. A classic formulation of the PD is this 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.

The payoffs of the game look like this:



The game is called a "dilemma" because rational play demands that you defect on your partner and rat him out. That is, no matter what "move" your partner plays you always do better if you defect. The problem comes with the symmetry of the situation. The same rational logic governs the play of your partner. Thus, rationality and logic lead you both to the mutual defection cell: You both go to jail for three years. You converge upon the lose/lose cell.

This is frustrating in that if the two players could cooperate and trust each other a better situation is in the offing: Mutual cooperation, where each goes to jail for only one year. It's the win/win cell.

The PD is psychologically interesting because it exposes issues of trust. To play the cooperative move you make yourself vulnerable to what is known as The Sucker's Payoff. If you cooperate you might get defected on and end up going to jail for the maximum of five years. Worse, your partner gets off scotch free for ratting you out. So cooperation is risky.

Okay, so we were talking about all this (trust and self-protection in life) when the Joker's Ferry Game came up. If you've not seen the movie here is the recap:

The Joker has rigged with explosives two ferrys filled with people. Each boat has the detonator to the other boat. That is, you can blow them up and they can blow you up. The Joker then communicates with each boat: You have a choice. You can blow up the other boat and save yourself or, if neither of you act, the Joker will blow both boats up.

So the Joker creates this wicked psychological experiment to see what people will do. He's trying to prove a point to Batman that, at the end of the day, everyone is just like the Joker: A self-interested animal.

So, the question was asked in my class: Is the Joker's Ferry Game a Prisoner's Dilemma? I didn't have an answer but eventually wrote a letter to my class. Here it is:

You'll recall from class that we were talking about the movie The Dark Knight and wondering if the Joker's Ferry Game was, indeed, a Prisoner's Dilemma (PD).

Mathematically, a PD is defined when the payoffs have the following structure:

When higher payoffs (e.g., money) are better:
T > C > D > SP

When lower payoffs (e.g., jail time) are better:
T < C < D < SP

Where T is the payoff for "Temptation to Defect", C is the payoff for "Mutual Cooperation", D is the payoff for "Mutual Defection" and SP is the "Sucker's Payoff."

In the example from class the payoffs fit the PD:

T = 0 Years in Jail
C = 1 Year in Jail
D = 3 Years in Jail
SP = 5 Years in Jail

The question now becomes: What was the payoff structure for the Joker's Ferry game?

To answer this question, we don't need to know the exact payoffs, just the ranking 1 through 4, with 1 being the best outcome and 4 being the worst outcome.

As I fiddled with the payoff matrix it became clear to me that I couldn't rank the outcomes because of this curious fact: We need to know if your prefer morality to survival. If you prefer survival over morality the Joker's game becomes a Prisoner's Dilemma and the rational move is to defect and blow the other ferry up. And the Joker knows this: Rational play means the players/ferrys will converge on mutual defection and blow each other up. The Joker wins: The People of Gotham are amoral animals, just like him.

If, however, you value morality over survival the playoff matrix no longer conforms to the PD.

Interestingly, this angle plays out in the movie. The people on the ferry appear to value their morality over their survival.

Beyond this simplistic analysis of mine you can explore further by seeing internet conversations here, here, and here.

As I thought about all this I realized that the Joker's Ferry Game has some connections with my posts on the Malthusian situation and human sinfulness. The Joker basically sets up a Malthusian choice: It's me or you. And the issue I noted in my letter to the students was that, when push comes to shove, we need to know if the Malthusian pressure for survival can be transcended by human morality.

Let me ask this: If one of those boats blew the other up, would that be evidence for Original Sin? Would the Joker have been proven right? That is, the Joker wants to show Batman that humans are, at root, just as depraved as he is. But I tend to think that if one of the boats did pull the trigger that the Joker's conclusion wouldn't follow for the reasons I've been writing about: There are strong external forces strongly implicated in how the people are behaving. These forces do not excuse the action, but they do make the action comprehensible. The words "weak" and "tragic" seem more applicable than "depraved" or "evil."

To be honest, I have no idea if the Joker's Ferry Game is a Prisoner's Dilemma. It might be more like a game of Chicken. Regardless, it was fun to think about with my students.