<<Spoilers Below>>

The Dark Knight is a good film.  What made it a great film for me – a man who has just spent a year writing a thesis on game theory – is the amount of game theory contained within it.  The most obvious is the ferry situation.  There has been some extremely good discussion on the blogosphere in regard to the game theory in the movie: here and here are what I found to be the best.  If you are interested in this, I suggest reading those blogs – and the comments – before proceeding with the rest of this post.  It will give necessary background.

The ferry situation could be described as a prisoner’s dilemma or a game of chicken. However, as the two aforementioned blogs point out, the situation is certainly a game of chicken with a twist.  Emphasis on the twist.

Here is my analysis for the situation:

Each boat has a choice of “Detonate” or “Not Detonate.”  However there is a chance that (1) Batman finds a way to prevent the Joker from detonating the boats if they both choose “Not Detonate” – which happens or (2) the Joker was dishonest in that he’d blow up the boats or (3) the Joker’s description of the rules are in some other way dishonest – he’ll blow up the boats anyway, etc.  The entirety of this chance could be represented as a chance node: p = probability that Batman can foil the Joker’s plan or the Joker was dishonest to the benefit of the people on the boat; (1-p) = probability that the game is exactly as the Joker states, or worse.  I assign payoffs as follows: 7 = live without blowing up the other boat; 5 = live with blowing up other boat; 0 = die.  (You could also complicate matters further by adding another payoff of 1 = die but with the dignity of not blowing up the other boat.  It would, however, not change the Nash equilibrium.)

The game tree would appear as:

Hopefully I’ll have a bit more time to work on developing this over the next few days.  Some great fun can be had with it.

– Timothy DeHaut