Are you game?

Disclaimer: This post is based on the ending of the movie 'The Dark Knight' which had the late Heath Ledger portray the 'Joker' with psychotic perfection. If you have not seen the movie yet and do not wish for the plot to be revealed, please leave this page now.

For others, here is a quick recap of the climax.



Plot Spoiler Begins:

The Joker loves to play games.Being faithful to his sadistic instincts, he decides to play a game whose high stakes are human lives.

There are two boats marooned off the coast of Gotham City. One of the boats holds the law abiding citizens of Gotham City fleeing from his tyranny, while the other boat holds the law breaking convicts of Gotham City who are being transported to another penitentiary.

Now here is the GAME.

Both the boats, unbeknown to its occupants have been filled with explosives. However, the detonators for the explosives are in the hands of the occupants of the other boat i.e. the convicts hold the detonator to blow up the civilians' boat while the civilians can at the same time blow up the boats holding the convicts. The Joker then, lays down the rules frightened people playing the 'Game'...

1. If you blow up the occupants of the other boat, you live.
2. If by midnight, neither of the boats have blown each other up, the Grand Referee a.k.a the Joker shall blow both of them up.

However, the people of Gotham City, the honorable souls that they are, decide not to blow up each other.

Plot Spoiler Ends

Now this is where the really interesting(?) part of this post begins.

With my recent exposure to Game Theory, I became fascinated with the nature of the game being played by the Joker. So I decided to create a payoff matrix for the game (See below).




As you can see, the Rows represent the decisions taken by the Convicts and the Columns represent the decisions taken by the Civilians. Additionally, in each cell, the first number represents the payoff for the Convicts and the second one represents the payoff for the Civilians.

Now here is the rationale for the payoffs...

minus 2 - The payoff of the guilt of killing somebody.

minus 100 - The payoff for dying :) with the sense of betrayal as you have been killed by the other group.

minus 50 - The pay off for dying but without the sense of betrayal as you would have been killed by the joker.

minus 102 - Dying with both a sense of guilt and betrayal.

As was already mentioned, the result was that neither of them killed each other .

Those familiar with Game theory will smile and say that this payoff matrix is exactly similar to that of the Prisoners' Dilemma. They are absolutely right. The payoff matrix ended up this way coincidentally (Scout's Honor). As this is indeed the Prisoners' Dilemma, the Nash Equilibrium would have ended with both the teams blowing each other up. However, they have played cooperatively and it is interesting to know that in trusting each other, they have also achieved the highest payoffs possible. Another interesting thing to note is that both the teams played cooperatively without any kind of communication except for the fact that if they are still alive, then the other team has not blown them up yet. This help build the trust slowly to the level that they knew that the other group too was playing cooperatively. Thus there are still certain things that Microeconomics can't explain :D.

I myself agree that there are two possible loopholes in my above theory.

1. The Kill/Kill payoff is practically impossible as the chances of it occuring is very less.
2. The Kill/Kill and Don't Kill/Don't Kill payoffs should be much closer.

Now this brings us to the end of this long blog post. I would love to know your viewpoints on my above theory. Please feel free to dissect the payoff matrix and provide your own solution to the above game. What do you think?

ARE YOU GAME?