I kind of find it hard to believe that a movie based on a comic super hero was one of the best films of 2008. This is partly because not that many good movies were released that year, but also because ‘Batman, the Dark Night’ offers more than just the mindless entertainment you would expect from such a block buster. Most recent super hero films have tried to make the genre more interesting by making their villains more nuanced. Lex Luthor in Superman is a prime example of the well respected society man by day, and evil doing genius by night.

The Joker in the latest installment of the Batman franchise however bucks this trend. He has no visible nuances at all. He’s just plain psychopathic. But it’s his evil deeds that are quite remarkable: He’s not really out for personal gain and greed like most common bad guys. Instead, he’s simply intent on creating mayhem. And not just any sort of mayhem. He also has a penchant for placing his victims in situations where they have to make really difficult choices. This because on one hand, no matter what choice they make, the outcome is most likely always going to be bad. More interestingly though: many times, that choice is also influenced by the decisions of others instead of coming from just one individual. And this is where game theory comes into play.

If you haven’t seen the Batman film or “A Beautiful Mind”, the following may contain spoilers.

Applied Game Theory in Dating

The first time I heard about Game Theory was when I saw ‘A Beautiful Mind’ starring Russell Crowe. It’s a film based on the true life story of John Nash, a brilliant mathematician that slowly turns mad later in his life. But what exactly is game theory? In short, it is about applying mathematics in strategic situations where making a successful choice depends on the choices of others.

In the Beautiful Mind film, Nash, still a student at MIT, finds himself in a bar with three other male friends. At that moment, five gorgeous girls walk into the place. Four of them are brunettes, but the fifth, the most attractive of them all is a blond. Soon enough, the following problem quickly poses itself. If he and his friends only act in their self interest, they will all go for the blond girl. Overcrowding her with too much attention, the blond will surely be put off and won’t give any of the four friends the light of day. At that point, neither will the brunettes anymore as they don’t want to be second choice. The end result: nobody gets what they want.

So Nash proposes that he and his three other friends should cooperate instead. Each one should pick one of the brunettes instead. By going to them immediately, they won’t feel like they were second choice. And even though the blond remains the most coveted prize of them all, in this setup, each individual boy in the group has more chance of success in scoring with one of the lady’s if they simply leave blond aside. Because winning over a brunette is still a way lot better than fighting over one girl and ending up with nothing at all.

The above situation simply demonstrates applied game theory in trying to find an equilibrium in the dating scene. Of course, one can wonder how practical this example is as it assumes all men prefer blondes over brunettes. But the key to remember here is that your success as an individual depends on the choices of others. And that’s what Game Theory is all about: finding the best strategies to success in a situation where you’re not fully in control.

A more practical example of game theory was applied to a case found in the Talmud. It described how to divide a piece of land amongst owners with unequal claims over it. The rules used in these old texts had vexed scholars and scientists for over 2000 years before it was finally explained using game theory in 1980. But back to Batman…

Prisoners Dilemma

The most notable scene in the Batman movie where game theory can be applied is probably the ferry scene. One ferry is filled with ordinary citizens and the other with inmates. Each ferry is given a detonator for the other ship. In order to save themselves, they are given 30 minutes to blow up the other ship. If after that time, no one has pressed the button, the Joker will blow up both ships. To complicate things even further, can the Joker be trusted? He may have rigged it that pressing the detonator will simply destroy, not the other, but their own ferry. This article goes on to explain how the situation plays out and why, all using the ‘prisoners dilemma’ theory.

Pirate Puzzle

Another example is from the first scene: the bank robbery. This one is detailed over here using the pirate puzzle. It’s a puzzle I hadn’t heard of before, though it does seem to be a more complex version based on the following experiment: person A is given a hundred Euros. To keep any of it, person A must first make a deal with person B. He does this by either proposing to give the whole sum to person B, just a percentage of the 100 Euros or nothing at all. If person B agrees, the deal goes through. If B isn’t happy with the deal, persons A and B get nothing at all. In practice, this experiment is a little more nuanced then the pirate puzzle (probably because no one’s lives are at stake).

The Deal

Logic would state that person A keeps 99 Euros for himself and leave just 1 euro for person B. Person B would have to agree because 1 euro is still more than receiving nothing at all. Unfortunately, people don’t always make rational decisions and can at times be a bit vindictive. So the risk for A is that person B may not find it a fair deal at all and will forgo his share of 1 Euro by blowing up the deal. Even though he gains nothing by doing so, B’s psychological loss of 1 Euro is still a lot less than the 99 Euros that person A would lose out on.

As such, it becomes more of a confidence test for person A. If A is not confident at all, he’ll probably split it 50/50 instead. This will ensure he’ll get his cut while still keeping B happy. It’s about as fair a deal as one comes. But the more confident A is, the more likely he’s going to raise his own share and still bring the bacon home. It’s quite possible that he can propose an 80/20 deal and still get away with it.

The big question is, how high can person A rase his share before person B starts feeling vindictive? In this situation, the best strategy for A may very well be to mentally turn the tables around and ask himself what he would do if he were in B’s shoes? What’s the smallest share of money he himself is willing to accept before he would break off the deal? Once he’s figured that out, it becomes a lot easier to figure out how high he can actually go and still get away with it.

You may be thinking to yourself by now that this is all fine and well, but can game theory actually be applied to everyday life situations? Good question. I guess this should give you something to ponder about, the next time you find yourself at the poker table.

And if you’re interested in learning more about game theory, you can always start with the Nash equilibrium.