The Joker's Dilemma

July 2008:

Who knew a comic book film could have instructive examples for the social sciences? Having just returned from the new Batman film, ‘The Dark Knight’ (which on the whole was quite good, though I do miss Anton Furst’s production design from the first film), I was struck by a re-working of the ever popular ‘prisoner’s dilemma’, which for years has been buzzing like flies in the ears of political scientists, economists, and other social scientists.

What is the prisoner’s dilemma you say? The premise is quite simple: two prisoners – who can say why they are there? – have just been incarcerated. As the authorities have insufficient evidence to implicate them, the prisoners are offered a deal by those who are in charge. The deal: an ever so tempting device, nearly always qualified with a catch. The catch: the authorities inform each prisoner separately that if one testifies while the other remains silent, the tattle-tale will go free while the silent one goes to prison for 10 years. If both remain silent, the sentence for both is merely 1 year. If both open their mouths, the sentence for both is 5 years. As the story traditionally goes, rational self-interest kicks in leading both to testify resulting in a Pareto sub-optimal outcome. If co-operation was victorious over self-interest, than the result would be better for all. So ends this bed-time story.

Many, from mathematicians to psychologists, have picked this classic scenario of game theory apart. I am sure their analyses and insights are fascinating and have some element of truth to them. There are countless example of the prisoner’s dilemma, in modified form perhaps, doing its dance in the real world. These range from athletics, to advertising, to the classic arms-race scenario. But what good is a scenario that doesn’t describe the full picture? Enter the Joker.

Madmen have a penchant for popping up as comic-book villains, but the Joker in ‘The Dark Knight’ is especially malicious (and randomly irascible). He introduces another form of the game, far more tormenting, as escape seems futile. It goes like this: two boatfuls of people are told by a mysterious voice that each boat is packed with a melange of things that go boom. They are presented with a detonator that will send the other boat and its occupants to smithereens. The mysterious voice goes on to explain that each boat has 15 minutes to decide if they will blow-up the other and live. If neither destroys the other at the end of the 15 minutes, the voice on the other end will destroy them both. What a game…

In the film, each boating party holds a vote deciding which option to take (the film also introduces another morality element, but like any good economist or rational choice theorist, I will assume that away). Needless to say, the longer they wait to decide, the higher the risk they will be blasted in oblivion by the other boat. Rational choice always gets exciting when it involves groups of people who likely hold different ideologies and belief systems. There is another catch – who is this mysterious voice on the other end? Is it serious, can it be trusted, does it actually exist, can another force stop it? Chance has made its guest appearance.

Humans loathe chance. It makes everything is life more difficult, though this ignores the fact that it is more or less the natural state of things. Remember atrophy? Because we dislike complexity and like to tidy things up, humanity has tried to manage and mitigate chance. We hedge our bets; we look at probabilities to reduce risk. There is even a field of probability theory called stochastic process(es). Stochastic theory rightly acknowledges there is uncertainty in a process, but it tries to discover which possibilities are more likely the others. Has it worked? Consider its use has proliferated in investment banks and other financial institutions as a risk management tool - so much for that example. Will we get better at it? Probably. It is the mysterious element, however, that poses a great challenge.

Call this mystery what you like – a god, nature, the universe, misfortune, the Lucky Charms guy. Are there examples for such mysteriously complex events in the real world? Climate change could be an example. We certainly have an appreciation of the risks and some possibly scenarios – all can be stochastically mapped. What we cannot anticipate is some aggravating factor that is yet unknown, just as industrialists 200 years ago couldn’t have known or anticipated that smoke would cause the world to get warmer if we put enough of it up there. So here we are – two boats voting on what should be done, policy-wise, behaviour-wise, etc, while the clock is ticking with the stakes increasing as we prolong a decision. Can we believe the scientists, will there be a dirty joke the universe will play on us? Pretty much yes to the former, but we hope not for the latter.

And there you have the Joker’s dilemma. As more of these situations proliferate with the growing complexity of the world, the more important (if not difficult) it will be to dodge the dirty jokes. They are like narcoleptics – we just don’t know when they might burst out. Does this get us anywhere? Perhaps not. Perhaps it should merely give a push to the stochastic whiz kids to think of something fast. In reality it is just another descriptor of a collective action dilemma where the stakes have been raised, but I’m still impressed it came across in a superhero film. Here’s hoping that the last joke isn’t on us.