Gotham Game Theory: The Joker’s Dilemma

The most famous example used to explain game theory is a game called The Prisoner’s Dilemma. A far more fun approach is looking at a game that The Joker introduces to the hit movie The Dark Knight, one of the Batman movies.

In the movie The Joker rigs two ferries with bombs. Ferry A is filled with innocent civilians and Ferry B is filled with prisoners and their police escort. Ferry A has a detonator for the bombs on Ferry B, and Ferry B has the detonator for the bombs on Ferry A. That is the setup, now for the rules.

If Ferry A detonates Ferry B and kills everyone on it, then the passengers on Ferry A survive. If Ferry B detonates first, then they survive. If nobody detonates within 30 minutes, then both ferries explode and everybody dies.

Cleary, if you are on Ferry A then not detonating Ferry B is a bad option as either Ferry B will detonate you or, after 30 minutes, both ferries will explode. Therefore it makes sense for Ferry A to detonate Ferry B as soon as possible. The reverse analysis is true. The result is a race to detonate.

The assured destruction if there is no action is what makes this an easy scenario to solve. Let us answer a slightly modified scenario. Everything is the same as The Joker’s scenario, except that if nobody detonates within 30 minutes, then its a small detonation and everybody lives but loses the use of their legs. If one ferry blows up the other, then as per the original scenario, the surviving passengers are unharmed. Here the regret is one of living as a cripple versus murdering hundreds of others. A difficult decision for most people, but only in terms of valuing your limbs against the guilt of murder. The actual choice, once that value judgement is made, is straightforward.

One more change gets us to seeing the real value of game theory. Let’s assume everybody is guilty and whoever triggers first not only goes free but doesn’t kill the people on the other ferry, they just spend 5 years in jail. If both trigger, the passengers on both ferries go to jail for 3 years. If none trigger then all passengers go free. This is now equivalent to The Prisoner’s Dilemma.

Simplistically, if you never trigger then the worst case scenario is that the other ferry triggers and you go to jail for 5 years. If you do trigger, then the worse case scenario is that the other ferry also triggers and you go to jail for 3 years. Game theory then says to minimise your regret, always trigger.

So what does this mean to you in real life? Assuming you aren’t about to embark with a partner on a crime spree, probably the most important lesson to learn is the value of trust.

The reason that classical game theory does not lead to the cooperative solution of neither side triggering and therefore going free is that there is no trust modeled in the game. If there is no trust then even a small incentive differential can lead to a complete breakdown in cooperation.

Ever wondered why plans developed by the C-suite are often rejected by the rank and file? It could be more about a lack of trust than issues such as communicating, getting buy in, socializing or whatever happens to be the latest fad. This is the power of game theory.

The people of Gotham ignored game theory, only to be saved by Batman. Unless you believe that a superhero will save you, you might be well advised to learn a little bit of game theory yourself.