Game Theory: The Dark Knight (Ferry Scene)
Care to play a game?
The Dark Knight is a 2008 superhero thriller movie directed by Christopher Nolan. The movie’s main antagonist is the Joker who holds the assumption that everybody is as corrupted and self-interested as he is. He brilliantly orchestrated plans that put people in impossible situations, in view of forcing them to reveal their true ugly nature. The main protagonist is the Dark Knight, Batman.
A notable scene in the movie is when the Joker threw the city into chaos and triggered a mass evacuation of Gotham City. People were evacuated and placed on ferries. The first ferry was filled with Gotham’s Prison population while the other ferry is filled with innocent law-abiding citizens. Both ferries suddenly grind to a halt. Unexpectedly, the Joker made an announcement that was heard by passengers of both ferries. He made known to the passengers that each ferry is wired to explosive materials and that they were each provided with a detonator device that is designed to blow up the other ferry. There is the assumption that no communication between the two ferries is possible and decisions are to be made simultaneously.
Strategy of the Game
a) If no one presses the detonator button by midnight, the Joker will blow up both ferries.
b) Press the detonator button to live, by blowing up the other boat.
Expected Outcome
The Joker threw at the passengers a dilemma that would test their conscience and will to survive. Given the rules of the game, the payoff matrix is shown below. The highest payoff is 1, which represents survival and the lowest payoff is 0, which represents death.
a) Top-left cell (0,0): Both ferries choose to cooperate; all passengers will die because the Joker will explode both ferries after midnight.
b) Top-right cell (0,1): Prisoners explode the civilians’ ferry and live. There is a payoff of 1 for the prisoners and 0 for the civilians.
c) Bottom-left cell (0,1): Civilians explode the prisoners’ ferry and live. There is a payoff of 1 for civilians and 0 for the prisoners.
d) Bottom-right cell (N/A): It is not possible for both prisoners and civilians to detonate the bomb, as only one ferry will survive if either one detonates the bomb first.
It is expected that either one of the ferries will be blown up before midnight, given that each party has a dominant strategy to detonate. However, this did not happen. After the announcement, the passengers of both ferries were debating whether to press the button and most of them were in favour of doing so. The prisoners thought of their lives not valued by the civilians. On the other hand, the civilians thought that the prisoners were ruthless enough to kill them.
The civilians put the issue to a vote, which resulted in the majority in favour of pressing the detonator button. However, no one person wanted to bear the responsibility of killing a whole ferry of people even though they collectively agreed to the action. The prisoners faced the same issue, with one of them throwing the detonator out to the sea. Each ferry came to realisation that the other party is not going to detonate as the time inches closer to midnight. The Joker failed to achieve his expected result from his social experiment.
This game theory is similar to the Prisoner’s Dilemma in a sense that decisions are made simultaneously without knowing what the other party decides on. However, the choosing of a different strategy would not make either party better off. Therefore, making cooperation unnecessary in this situation. Prisoner’s Dilemma highlights the problem of Pareto-suboptimal solution when each party acts in self-interest, while both can be better of if they were to cooperate.
Morality Beats Survival
The Joker may have specified the payoff matrix wrongly and had a too cynical perception towards people. The unexpected result can be explained if the payoff were as the following:
Payoff of 3: Batman intervenes on time and saves all passengers.
Payoff of 2: Passengers die. It is more acceptable to die than to take the lives of others by pressing the detonator button.
Payoff of 1: Survive by blowing up the other ferry. This option yields the lowest payoff, as passengers fear social stigma and persecution when they survive. Also, their conscience will be very disturbed.
Based on the payoff matrix above, each party has a dominant strategy to cooperate as the payoff to cooperate is higher given whichever strategy the other party chooses. The Nash equilibrium is to cooperate, which is a possible explanation to the end result of the movie scene. Fortunately, Batman did manage to stop the Joker from detonating both ferries and proved to the Joker that people are with a social conscience and not always self-interested.
Burpsi 
I like this post. How you manage to put in Prisoner’s dilemma into this Game Theory. Interesting reads, i wished i take econs. Btw, i msged u on fb just now! Don’t kill me just yet ok 😦
Hey Didi, I thought this piece of work was pretty interesting as well…The Dark Knight has got a number of game theory scenes even right at the beginning, the bank robbery. Regarding the guitar, no worries…I know you have been busy and what not…Just offer me your floor in the UK if I do decide to bunk in 😛 Take care