Social Welfare in "The Dark Knight"

In class, we examined that sometimes the Nash equilibrium does not reflect the optimum social welfare. For example, in the minimum income game, Professor Immorlica explained all the reasons that choosing the number 4 would be the best option for everyone. This represented a Nash equilibrium as well as the best social welfare. As it turned out, most people chose the number 1 because they knew that if at least one other person chose a number lower than four, then they would not receive any points. Most people chose to ensure their own profit rather than rely on everyone else to make the decision that was best for society.

In "The Dark Knight," the Joker constructs a situation in which individuals must choose their own life or rely on others to preserve their lives. The Joker claims to have placed a bomb in two boats, one with a large group of convicted prisoners and the other with civilians. He tells each boat that if they press a certain button, the bomb in the other boat will go off. Whoever chooses to press the button first will live because those on the other boat will be dead. The worst Nash equilibrium would point any individual towards pressing the button immediately because no matter what the other boat decides to do, that individual will survive. It is human nature to want to save your own life, a choice that would result in the guilt and burden of knowing you have killed so many other people. If the characters in the film acted as we did in class, acting to increase one's own benefit, each group would have chosen to bomb the other boat. However, viewers of the movie saw a reason to have faith in humanity as each boat decided to let the other live...so everyone survived. This choice on both parts resulted in the best social welfare.

The Joker definitely took prisoner's dilemma to the extreme. The payoff matrix would be

Convicts
pressButton dontPressButton

Civilians pressButton (-5, -5) (0, -5)

dontPressButton (0, -5) (-5, -5)

If both boats pressed the button, both would blow up. If neither boat pressed the button, the Joker would blow them both up. And if either pressed the button before the other, they would survive.

I think you forgot to flip the 0 and -5 in one of the brackets. The payoff matrix should be...

		Convicts
		pressButton	dontPressButton
Civilians	pressButton	(-5, -5)	(0, -5)
	dontPressButton	(-5, 0)	(-5, -5)

here is the same payoff matrix for those of you who hate math:

		Convicts
		press button	don't press button
Civilians	press button	( , )	( , )
	don't press button	( , )	(,)

I don't think it was a faith in humanity that saved the respective boats. I think it was cowardice. No one on the boats had the nerve to push it. Why? Because no one wanted to be responsible for killing a boat filled with people. In the movie, everyone was eager to blow up the other boat, it was just that no one wanted to be the one to do it. Everyone is selfish and wants to do what is in their best interest.

Now we have two scenarios for an individual on one of the boats:

1) Someone else grabs the remote and blows up the boat. He is relieved and glad he is alive.

2) No one else grabs the remote, and therefore in order to ensure his survival he must grab the remote and do it. But he won't, because he is selfish and doesn't want to share the burden of living his entire life knowing what he did.

Either way, the individual won't take the action that the entire crowd wants because he is both selfish and a coward. Not because he has faith that a bunch of convicted felons are truly "good on the inside" or habitants of suburbia have a heightened sense of morality.

I partially agree with Andrew Varrenti.

I agree on the social welfare and believe in humanity.
However, people were reluctant to take action to avoid the responsibility or guilty.

For example, when there was murder in New York, the lady was screaming for help but people were thinking that other people would help or call police and as a result, no one helped nor call the police for help.

The other instance would be when there is empty house without any harm. It will be staying there as it is. However, when there is one broken window, then all the other parts will be quickly broken after that.