Game Theory in the Dark Knight Rises
In action movies such as the Dark Knight Rises, we often see strategic games. How people react to the villains can be further analyzed using game theory. Here are two examples that I found interesting illustrating using game theory:
The movie begins with a scene on the aircraft when a government agent is interrogating criminals for information. The agent sets a “game” for the criminals: they can either confess and stay alive or remain silence and be thrown out of the aircraft. Of course, it is the agent’s option to actually throw the criminals out or not. Let’s simulate payoffs for different strategies. Assume that the payoffs for situation that a criminal remains silence: if the Agent throws him out, then he might have killed someone with the information, thus a -2 payoff for losing the information forever and -1 for the criminal who keeps the secret but loses his life. If the agent does not throw the criminal out of the plane, -1 payoff for the agent for not getting the information and 1 for the criminal who lived. In the case of criminal choosing to confess, the agent gets 1 payoff and criminal gets -1 for giving away information.
| Criminal | |||
| Confess | Not Confess | ||
| Agent | Throw out | 1, -1 | -2, -1 |
| Not throw out | 1, -1 | -1, 1 |
Here, we can see the criminal has a dominant strategy to not confess. In fact, it is obvious that it would be worse off for the agent to throw the criminal out if the criminal does not confess because the information might be lost forever. If the agent keeps the criminals alive, maybe he can get something later through further interrogation. This is in fact what the agent chooses to do in the movie with a fake gun shoot to threat the other eye-folded criminals, which is not effective because it shows that the criminal is clearly not thrown out of the plane.
In the source that I found online, the writer talked more about another game theory example in the movie: Bane threaten the country for blowing up the entire city with nuclear weapon if the national army across the bridge of the Gotham City. Here, the payoff of the army is the entire city regardless because the bomb will blow regardless due to instability of the elements. For Bane, there’s nothing to lose.
| Army | |||
| Cross | Not Cross | ||
| Bane | Blow out | 1, -1000 | 1, -1000 |
| Not blow out | 1, -1000 | 1, -1000 |
Bane seems to be a winner in all strategies here. However, Batman finally rises and saves the world!
source:
-fishsun shadow