Joker’s Game Theory in The Dark Knight
In The Dark Knight movie, there is a scene where Joker traps two ferries that carrying people out of Gotham. Each boat has different passengers :
- Boat 1 = Contains the prisoners, several policemen and jail guardian
- Boat 2 = Contains civilians, they are free and look more educated than most people at the first boat
Each of the boat has a bomb placed inside and the detonator to detonate the other bomb, so Boat 1 could detonate the bomb in Boat 2 and vice versa.
With time limit given, they have to choose between to detonate or not, and both of the boat can’t communicate to each other. Yes, this is could be a prisoner’s dilemma or game of chicken because they faced morality problem, they could be a murderer. A lot of sites has discussed this game, including here and here. But I try to do it my way. I’m using the Life Possibility as the parameter.
The trade off matrix
| Life Possibility (in %) | Boat 2 | ||
|---|---|---|---|
| Cooperate | Not Cooperate | ||
| Boat 1 | Cooperate | (0;0) | (0;50) |
| Not Cooperate | (50;0) | (0;0) | |
Explanation :
- Both of them cooperate
- No chance, The Joker will explode them all
- Life possibility is 0%
- One of them doesn’t cooperate
- The Joker will explode the survivors (remember, he’s crazy!), or
- The survivor would be accused as murderer, death penalty is possible
- Life possibility is 50% (for the survivors)
- Both of them don’t cooperate
- That’s the one that The Joker want
- But I’m still thinking about the possibility of how they could explode each other at the same time. If boat 1 detonate it first, boat 2 has no chance to detonate boat 1
- Life possibility is 0%
The trade off matrix after Batman’s Intervention
| Life Possibility (in %) | Boat 2 | ||
|---|---|---|---|
| Cooperate | Not Cooperate | ||
| Boat 1 | Cooperate | (100;100) | (0;50) |
| Not Cooperate | (50;0) | (0;0) | |
Explanation :
- Both of them cooperate :
- Batman has destroyed Joker’s detonator, they are safe
- Life possibility is 100%
- One of them doesn’t cooperate
- The survivor would be accused as murderer, death penalty is possible
- Life possibility is 50% (for the survivors)
- Both of them don’t cooperate
- Still, the life possibility is 0%
Of course they don’t know if Batman has saved them all (or make a new dominant strategy for them) because Batman has thrown Joker’s detonator. That’s a part of dilemma, both of the boats don’t know whether they have the dominant strategy or not. Still, this is a movie (a brilliant movie), where everything run as the spectator expect, and they have chose the best strategy (or the best scenario), to not push the detonator.
– Anton Hermansyah
Tags: Serious Fun
August 5th, 2008 at 7:49 pm
Very briliant decision making analysis from you. You’re my idol like Aris..
August 5th, 2008 at 11:49 pm
That was a really interesting read,very nicely written article.
October 28th, 2008 at 4:43 am
Hello, what entice you to post an article on Joker’s Game Theory in The Dark Knight? This article was extremely interesting, especially since I was searching for thoughts on this subject last Monday.