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.

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10 thoughts on “Original Sin: Interlude, The Joker's Ferry Game”

  1. Ahhh, there's the nugget I was looking for! Is there any obvious reason to suppose that morality-preferrers and survival-preferrers are equally distributed in the population? Is that binary variable completely random, like a coin flip?

    Just looking around, Yogi-Berra-like, evidence suggests that the variable does not have a 50/50 probability structure.

    Of course, the "morality" half of the variable is a contrived option, not a natural one (although that's a hypothesis worth testing, now that I think about it), so natural probabilities do not necessarily apply.

    But the question remains: what is the force that sees to it that survivalists outnumber moralists? Is it natural selection, as would appear to be the case? And what would have to be true about a group of people in order for the ratio of moralists to survivalists to approach 1:1? Wouldn't the individuals have to be purely ambivalent about the choice between morality and survival? That is, wouldn't they have to flip a coin to make their choice, which is the same thing as saying they have to sacrifice their status as moral agents, shifting the responsibility for their decision onto the coin itself?

    Fascinating thread!


  2. (It also suggests reasons that Utopian visions of a shalom society are doomed. Lions might lie down with lambs, but the lions eventually come to their senses. Thanks for the encouragement.)


  3. Luke 16:10 NASB 1995
    "He who is faithful in a very little thing is faithful also in much; and he who is unrighteous in a very little thing is unrighteous also in much.

    Referencing the above verse as a principle of human behavior (quoted from Jesus Himself), how would many Christians in America behave if suddenly subject to a collective life and death crisis???

    Witnessing the undeniable schisms of denominationalism (collective) as well as the strife for power, prominence, and control in church politics (individual), I can't help but assume that MANY of us would resort to extremely degrading behaviors if the stakes were raised from "who's most annointed, "who has more air time" to issues such as food, water, and life/death.

    As Christians, most of us would like to believe we would demonstrate courage and dignity if faced with a life/death crisis. Can a person who frets over losing the lead vocal to another singer for the offering song on Sunday morning suddenly "turn on a switch" and CHOOSE to give up the one piece of bread remaining to that same other person in the midst of a global catostrophic disaster???

    Just another rhetorical question.
    Thanks again!
    Gary Y.

  4. I asked Dr. Beck for his take on "The Dark Knight" after it was released last summer. I'd like to post it (since we're referring to the Joker as an example).

    Hi Gary,
    I liked The Dark Knight very much. My main reaction was how it seemed, to me at least, to be meditation on the goodness and darkness in each of us. And how fragile our morality can be. Also, it seemed to be an interesting meditation on the complexities of human nature and how tragedy can move us in different directions (Joker vs. Two Face vs. Batman)

  5. I asked Dr. Beck for his take on "The Dark Knight" after it was released last summer. I'd like to post it (since we're referring to the Joker as an example).
    Gary Y.

    Hi Gary,
    I liked The Dark Knight very much. My main reaction was how it seemed, to me at least, to be meditation on the goodness and darkness in each of us. And how fragile our morality can be. Also, it seemed to be an interesting meditation on the complexities of human nature and how tragedy can move us in different directions (Joker vs. Two Face vs. Batman)

  6. I just read this series from its beginning. In the fist post of the series, about a Malthusian source for man's sinful behavior, I was reminded of the statement in Hebrews 2:15, which speaks of Christ freeing "those who all their lives were held in slavery by their fear of death." This would tend to support your thesis.

    Yet, the original story of the first sin was sin in the midst of plenty. If, as many believe, Satan is a fallen angel, we should not believe that sin can only come from human necessity in time of scarcity.

  7. One thing to keep in mind in this particular dilemma (The Joker's) are the high odds that pressing the button to blow up the other ship would have more than likely blown their own ship up instead. If anyone on either ship knew The Joker's MO they would have just thrown the remote control overboard from the beginning.

  8. If the Joker promised to do only modest harm to the passengers both boats if they "cooperated," then the PD scheme would apply, absent the self-esteem component, which is always available in PD scenarios and is, therefore, usually assumed not to apply.  One of the reasons the PD itself is so good is that it manages to eliminate the natural sense to consider self-esteem.  The Joker scenario, because the pay-offs include death, just isn't a good a version of the problem that the PD poses.

    The tie-in to original sin, however, is very important.  What IS original sin if not a justification for God's putting us in a world where PD's exist?  What kind of just God creates a universe in which defection is the most rational strategy?  One that is punishing us for something "we" did, or one who is testing us to see if we can redeem ourselves by NOT defecting in life's PD's.  Original sin thus may explain, from a theological standpoint, why nature - let alone the police - presents PDs and tempts us to tragedies of the commons.  Converting such arcana as Nash equilibria to something as accessible as eating the wrong fruit is religion's job.  If politics (but not political philosophy) is the art of the possible, religion (but no theology(!)) is the art of the intelligible.

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