The Joker’s Trap
Like everyone else, I went out to see The Dark Knight this weekend. I had just spent the week in LA talking to a lot of people in the movie business about piracy. We waited in line for over an hour and spending a total 0f $60 on tickets and various overpriced snacks, which reaffirmed my belief that Hollywood is going to be just fine. But I would have happily paid twice as much had I known the film was going to be as amazing as it was, and such an eloquent explanation of the fundamental problem with the Prisonerâ€™s Dilemma.
Towards the end of the film The Joker rigs two passenger-filled ferries with explosives (please look away now if you didnâ€™t already see it). The first ferry is filled with upstanding citizens of Gotham. The second contains the most dangerous inmates from Gotham Prison. The Joker has wired each ship with explosives, and left the detonator for each ship on the other ferry. Game theorists in movie theaters everywhere dropped their popcorn – a prisonerâ€™s dilemma with real live prisoners! And Batman!!!
For a great rundown (and some serious maths), see The Quantitative Peaceâ€™s discussion: â€œThe use of the detonator saves the ship while killing everyone aboard the opposing ship. Thus, if any member of Ship A pushes the detonator, then Ship B is destroyed and all of Ship A is saved. Additionally, if either ship fails to use the detonator to destroy its opponent, then both ships will be destroyed by the Joker. Assuming that the actors must make their decision simultaneously, this would lead to the following game:â€
The Joker is convinced one ship will blow up the other, but he makes a huge mistake. He assumes that humans are rational, and only act in their own self interest. As a society we often subscribeâ€”in theory, at leastâ€”to this idea. This theory has been a dominant force in economics, political science, military strategy, psychology, and many other disciplines since the 1950s. It has informed some of the most important decisions the human race has ever made, from the nuclear arms race of the Cold War to the way we share all kinds of resources today. This simple game of two prisoners trying to make decisions based on what the other will do helped shape the structure behind the supposedly dog-eat-dog world we live in.
But in practice the game is flawed. The most basic assumptionâ€”that we all act only in our own self-interestâ€”is simply not true. When econoÂ¬mists test this theory, real people do not always act this way. In real life, in every corner of society, people cooperate with one another in the interest of both the public good and their own private interest. Thatâ€™s why we have nonprofits, nurses, and teachers. If prisoners really thought it was okay to rat on each other all the time, Stop Snitchinâ€™ T-shirts would not exist.
In fact the only rational human beings who only act in their own self-interest are most likely certifiably insane, as indeed The Joker is – which is what makes this movie such a perfect place for this story. But I thought he was smart enough to realize the rest of us play by different rules. Batman understands this, so he rightly guesses that neither ship will blow up the other and beats The Joker. The only way The Joker might have beaten Batman would be by filling at least one boat with exclusively self-interested people, such as the economically rational residents of Arkham Asylum.
This plot line was a really clever way to explain the flaw in the simple Prisonerâ€™s Dilemma game, but it also explained something else about Game Theory beautifully â€“ the importance of diversity. In the movie the diversity is shown in the very different opinions of the prisoners on both ferries about whether or not they should blow up the other ship. In the simple Prisonerâ€™s Dilemma game you only see the prisoners understanding the benefit of cooperating after they have played it a few times, the diversity of ideas about the best thing to do only emerges after a number of games have been played.
But in real life, diversity is key to how we think about these decisions and tackle complex problems. Economic models are useful for sure, but they donâ€™t take into account the diversity of the real world or the human experience. In the Pirateâ€™s Dilemma, people always end up competing with pirates (assuming those pirates are adding value to society in some way) in the long run because cooperating with what society wants is always the best option, fighting is a losing battle. But in the short term itâ€™s difficult for many companies and individuals to see the value in that strategy. For those interested in more on the problems with Game Theory and how they affect all of us, check out The Trap, a great three-part documentary by Adam Curtis, check the intro below, or click here for it on google video.