Rock Hill, South Carolina|
Alright, every now and then, I come across a topic that deals with mathematics directly or is popular in the field in either a small or large way. When ever I do, I'll post it here. Last time, I talked about a little about the Riemann Hypothesis. This time, I'm gonna talk about Game Theory. You can read more about the specifics on Wolfram, but it's a branch of math that analyzes strategies for finding the best outcome(s) for a situation.
In this branch, there is something called the "Prisoner's Dilemma" which is one of the most popular topics in Game Theory. Try to imagine two people that were just arrested for bank robbing. They are currently in custody and isolated from one another. The detective in charge doesn't have enough evidence to proof their guilt and needs a confession, so he offers both a deal (the same deal). One prisoner at a time, the detective will present the deal. S/he says that they can either stay silent or turn the other prisoner in. If both Prisoner A and Prisoner B stay silent, then they will have to spend 1 year in jail. If Prisoner A turns on Prisoner B while Prisoner B remains silent, then Prisoner A will be set free and Prisoner B will have to spend 10 years in jail. The same thing happens if Prisoner B turns on Prisoner A while Prisoner A remains silent. Now, if they both turn on each other, they will have to spend 5 years in jail. Use this as a visual guide.
They detective will talk to each prisoner individually to obtain their confession. Any response other than silence or confession of the other prisoner's guilt will be ignored. The prisoners are allowed no time to discuss the situation with each other before speaking with the detective. Absolutely no coordination will be allowed. They are forced to make an executive decision.
Now, here's where the Game Theory part kicks in. Each prisoner has to think of what their best possible outcome will be based on how they think the other prisoner will confess.
If Prisoner A turns on Prisoner B, what should Prisoner B do?
If Prisoner A remains silent, what should Prisoner B do?
If Prisoner B turns on Prisoner A, what should Prisoner A do?
If Prisoner B remains silent, what should Prisoner A do?
The prisoners, if they ask themselves these questions, know that the best possible outcome for the individual will result in the other's worse possible outcome. They will also realize that they can both benefit from this deal by spending only 1 year in jail, or they can both spend 5 years by betraying one another. So this dilemma is not so much asking what the prisoners will end up doing in the end, but what the best possible solution for either one or both of them can be.
Anyway, I thought this was really interesting and I hope you've enjoyed reading about it.