So, I’ve watched The Dark Knight for the second time today. And this isn’t a review of Joker, the movie TDK. Instead, this movie will focus on the little insight of game theory to be found in the movie. If you haven’t watched The Dark Knight, consider this a spoiler.

In the movie, there was a scene, where the Joker got two ships to try to blow each other to oblivion. He had cut off communications and power to both ships, and the people in the ferries had to make up their minds whether they should blow the other ship or not. Add to the fact that one ship is ferrying civilians and the other is ferrying convicted prisoners. Nice GT situation, no?

The Joker’s aim, IMO, is MAD - Mutually Assured Destruction (yes, I know I throw that word about very loosely).

So, let’s look at the very basic stuffs. In a very basic situation, the solution of course is to not blow each other to oblivion. Of course that the utility the people from each ship gets is 1 and 0 for being blown away. Below is the Nash equilibrium table.

This is simple to understand. But the above table doesn’t take into account the Joker’s threat to blow both ships up once it hits 12 a.m. And who’d want to even play this game? Why would anyone want to blow up the other ship?

Then came the time limit. That’s when things start to get interesting. The Joker had planned to blow both ships to oblivion if nobody blows another ship up. So, if they don’t blow each other up, the payoff is still 0,0, since they will still die by being blown up by the Joker.

As you can see, in the above Nash equilibrium table, all the non-dominant strategies have been crossed out. So the dominant strategy is, of course  to blow the other ship up, which will then lead to the aforementioned mutually-assured destruction.

This is of course, presumably what the Joker wants. I noticed he loved to see competition amongst people (fighting for a gang member’s position with broken pool sticks). Without any exogenous factors (namely Batman taking down the Joker), both ships would have been blown to hell already, whether by their own doing, or by Joker’s doing.

You may be wondering why I didn’t factor in such as repugnance to take life (as was clearly depicted in the movie) - afterall, that was the given reason why none of the ships blew up. Well, the simple fact is that it makes no difference. The entire scenario was rigged that there is only one winner - Joker.  Only if the disutility from repugnance to take life is high enough for both ships (i.e. equal or more than the utility of one’s own life being taken (which begs the question: what sane mind would find more utility in their life being taken than taking other people’s lives? - Oh don’t talk about the Greater Good. The greater good!¹  - Ah, screw it. I did say ceteris paribus right?)), will both ships not blow each other up and sit there quietly for the Joker to blow them to the high heavens. Ergo, factoring in repugnance is useless in this case².

The rational mind would blow up the other ship as quickly as possible. Which is why, as cfgt says, if the world is filled with game theorists, the world would have ended already.

And speaking of game theory, Gambit, the program used to make the tables above and calculate the Nash Equilibriums was co-written by the husband of my current GT lecturer. Heh. So there. I was bored.

1. a semi related chat log:

   cfgt says:
   doesn’t mean they’re insane
   there’s always the greater good to consider

   Chewxy says:
   yea
   but I stand by the old maxim
   Every man for himself!

   cfgt says:
   so let’s pick someone that we think is important to the world

   Chewxy says:
   Chewxy
   LOL

   cfgt says:
   ok say Chewxy is important to you
   HAAHAHAAHHA

   Chewxy says:
   (so conceited)

   cfgt says:
   and let’s say
   his death
   would result in the world economy crashing
   the country thrown into chaos
   and let’s say
   we like this chewxy

   Chewxy says:
   lol

   cfgt says:
   and let’s say
   you get to choose whether you live or chewxy lives
   let’s say you are an insignificant speck of dust
   LOL

   Chewxy says:
   Chewxy MUST LIVE!!!

   cfgt says:
   LOL. still
   there are plenty of questions
   when it comes to morality
   do I care about the greater good or me and my family and friends

   [↩]

2. also, I am too lazy to make an extensive game. I wanna go back to playing Folklore [↩]

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