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Game Theory

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Game Theory

Tips: 0.00 INK Postby dealing with it on Mon Mar 29, 2021 1:45 pm

"Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The possible outcomes are:

If A and B each betray the other, each of them serves two years in prison
If A betrays B but B remains silent, A will be set free and B will serve three years in prison
If A remains silent but B betrays A, A will serve three years in prison and B will be set free
If A and B both remain silent, both of them will serve only one year in prison (on the lesser charge)."

-Wiki Prisoner's Dilemma

What is the rational choice for the prisoners?

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Re: Game Theory

Tips: 0.00 INK Postby Sepokku on Mon Mar 29, 2021 3:17 pm

Ayyy, I wrote my business thesis on Game Theory. Obviously, the correct answer is to not say anything, but this also precludes the need to be able to trust your, ahem, "business associate."

Probably goes without saying, but this all neglects to involve the actual legal process. In reality, both prisoners probably get out with no time served. Their bail likely constituted time served and exceeded their maximum sentence. Interesting thought experiment though!

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Re: Game Theory

Tips: 0.00 INK Postby dealing with it on Tue Mar 30, 2021 4:46 pm

The prisoners’ dilemma is interesting because the best possible outcome is not what a pair of rational agents would arrive at.

Let’s say prisoner 1 is considering whether to be silent or betray. In the first scenario, where prisoner 2 chooses to be silent, it is best for prisoner 1 to betray them. In the second scenario, where prisoner 2 chooses to betray prisoner 1, it is best for prisoner 1 to betray prisoner 2. And vice versa. Two rational prisoners will betray one another.

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Re: Game Theory

Tips: 0.00 INK Postby Sepokku on Tue Mar 30, 2021 6:56 pm

True, but if you can trust your partner, wouldn't it be obvious to lie so that you both walk with a lesser sentence? Especially considering you both hurt for tattling on the other. In a scenario where you can be assured that your partner won't out you, and vice versa, it is always preferable to cover for each other.

So once again, if you're going to jail, make sure its with someone you can trust. The best possible outcome is you both cover each other and neither of you gets hit with the larger sentence. HOWEVER, this is (again) also ignoring how the legal process works. In reality, both people probably posted bail and got out with no time served. Their bail likely constituted time served, so they probably pulled a Charlie Sheen and walked with basically no consequences.

Base Game Theory states the best outcome is that neither of you rat the other out. If you cant trust the other, theory would have you out the other. However, how often are you going to be committing felonies with someone you don't know? In reality... You'd only do so with someone you can trust...

edit: If you're looking for good books, Count to a Trillion by John C. Wright is a gold mine for Game Theory. The book itself isn't great, (at times it feels like a poor excuse to example Game Theory), but if you're only interested in Game Theory, the book is very good.

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