The Tradition of Raising and Lowering the Flag

What is the importance of Flag Duty, and how bad could it really be at the Royal Military College of Canada?

Game Theory in the Dark Knight

The past few days I’ve had a fever and it’s escalated very high today – I promise to continue posting up to 2 posts per day when I feel better

Anyhow, I have been lucky enough to enjoy the “Dark Knight” in 1080p blue-ray!

While watching it, and especially during the opening sequence that features the clowns robbing a bank, I couldn’t help but notice the unbelievable amount of “game theory” that was being implemented in Joker’s plan.

Game theory attempts to mathematically predict behavior in strategic situations, in which an individual’s success in making choices depends on the choices of others.

Here’s a basic game, called the “Pirate Puzzle”

Three pirates, A, B, and C, arrive from a lucrative hunt with 100 pieces of gold. Pirate A is stronger than pirate B, who is stronger than pirate C.

The strongest pirate present on the boat suggests a way to divide the gold. If the majority of pirates disagree with the deal, the strongest pirate is thrown overboard and then the next strongest pirate comes up with a deal, and so on. On the other hand, if the majority agrees with the strongest pirate, the deal is passed. In addition, Pirates value their life over gold.

How will pirate A take the most gold without losing his life?

No, it’s not an even split. In fact, pirate A only has to give pirate C one gold coin and keep 99 to himself. Why?

Pirate B will most certainly disagree with pirate A’s deal, since he gets nothing. In the case that pirate C votes against pirate A, pirate A will be thrown overboard. When that happens, only pirates B and C remain. Pirate B can easily just take all the gold because even if pirate C disagrees to pirate B’s suggestions, there’s only two pirates and it’s a 50/50 vote. Therefore pirate B gets to keep all his money and pirate C get nothing.

Thus pirate C is happy to get anything at all – 1 gold to be exact.

Let’s examine a case in which there are 4 pirates, A, B, C, and D.

Pirate A needs to give out only 1 gold again. This gold piece goes to pirate C. Why?

Let’s say that pirate C votes against pirate A. Then only pirates B, C, and D are left. Then pirate B only has to give pirate D a gold piece and keep 99 gold pieces for himself – pirate C will be helpless. Therefore, pirate C votes in favor of pirate A because 1 gold is better than nothing.

So now that we have a basic understanding of games, let’s move on to the Dark Knight game.

The original plan of equal division is flawed. Each robber has incentive to increase his share by killing a fellow team member. Once a member performs his job, he loses his negotiating power and value to the team. The Joker plans his strategy by instructing the robbers to take out fellow teammates once their tasks are performed.
Many of the robbers fail to see they can be victim to the same deceit they pull on others. The second robber on the rooftop is a prime example. After his partner disarms the silent alarm, he quickly kills him and then proceeds to perform his own job. He doesn’t see the same thing could happen to him. After he disarms the bank vault, he is greeted with a most unpleasant surprise:

Robber: Where’s the alarm guy?

Vault guy: Boss told when the guy was done, I should take him out. One less share, right? [opens the vault]

Robber: Funny. He told me something similar.

Vault guy: What? No! No! [gets shot in the back]

By now it’s clear the Joker wants everyone dead, and minutes later we learn the Joker has been present on the job all along. The plan finishes with two more deaths both involving the escape vehicle bus.

The Joker, being the “strongest pirate,” was able to sequentially bribe the weaker robbers one by one. In the end, he puts a twist on the game by taking the whole pie.

As you can see, there’s a reason why game theory, as an applied math, is very useful for corporations and economics. With game theory, we can always find the best outcome for ourselves.