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Game Theory; Oh man, this stuff is awesome.
Topic Started: Dec 15 2006, 04:47 PM (614 Views)
MFD
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THIEF!
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I always found the Prisoner's Dilemma (the staple Game Theory example) to be more exciting, even when you figure out the answer.

You and your partner in crime are hauled in for questioning by the police for a crime you committed. They can't prove you committed the crime, but they've separated you and your partner nevertheless.

They're offering you a deal. If you squeal on your partner, you'll get a monetary reward, and he'll go to jail for a long time. If you don't squeal, you get to walk.

BUT! You know your partner is being offered the same deal. Which makes the decision more complex. If you both squeal, you'll both go to jail for a medium amount of time. If one of you squeals and the other doesn't, the one who doesn't squeal goes away for a long time, and the squealer gets away with extra money. If neither of you confess, you both get away.

EDIT: I like this game better because it has nothing to do with a stated amount of predictive prowess on either party.
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Juron Pilo
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Yar, I've allready given that game a good run through though.

The ultimate strategy is to pick out a select group of people to conspire with. You probably woln't personally win but someone in that group probably will. :P

edit: are we talking the reiterated model, or the base model, because in the base model the answer is pretty simple and there is only one real answer.
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Huh? Um... that's not how you play. You and your partner don't go in with a set plan, you don't pick a select partner whom you know you can conspire with.

The optimal strategy is to pick the answer with the optimal outcome regardless of your partner's choice.

If you squeal, you either get money, or go to jail for a medium amount of time.

If you don't squeal, you either get away, or go to jail for a long time.

Since getting money is better than getting away, AND since going to jail for a medium amount of time is better than going to jail for a long time, you choose to squeal.

Of course, following this train of thought, your partner will also choose to squeal, but whatever. If he squeals and you didn't, you go to jail for a long time.

EDIT: However, if you play this game alot with the same two actors (say, two countries deciding on an arms treaty), eventually you both will pick the ideal outcome and get away scot-free.
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Juron Pilo
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I'm talking a mass reiterated version with randomly selected partners. See wikipedia article.
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Alan Bates
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So, what do those two boxes look like?
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Juron Pilo
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The wiki article speaks of a glass one...
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MFD
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Well, apparently we're speaking of two different things.

Could you supply a link for the wiki article? You can't say "See wiki article" and not provide a link. That's just poor manners.

Also, I think it's clear that I'm talking about the basic prisoner's dilemma. And the answer's not IMMEDIATELY clear, as I find out every time we mock up a dilemma in class, and I always squeal while my partner does not.
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Alan Bates
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Juron Pilo,Dec 15 2006
02:39 PM
The wiki article speaks of a glass one...

In that case, I pick the one that I know has money in it.
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Arc
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Mystery all the way!
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Blackdeathdraco
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following the rules of that mental challannge, I say since I can have both, why not take both. The second box will either have 1mill or none so i would rather take the 50% chance of getting $1,001,000 then just a posible $0.
When I'm bored, I like to wander around and cast X-Zone on random things.

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Vortex
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The boxes? The answer really is obvious. You kick the guy in the nads, steal all three boxes and then piss on his prone body for effect. Everyones a winner.
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Algasir
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I...

I'm with Vort here.
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Blackdeathdraco
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Now, now. There are only 2 boxes, both opque. One with for sure $1,000 and the other filled with dark smoke and has a 50% chance of holding $1,000,000. And there are only 2 choices: Both or just the unknown.
When I'm bored, I like to wander around and cast X-Zone on random things.

"Sanity is the illusion of the insane." -Me

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Blackdeathdraco,Dec 15 2006
11:27 PM
Now, now. There are only 2 boxes, both opque. One with for sure $1,000 and the other filled with dark smoke and has a 50% chance of holding $1,000,000. And there are only 2 choices: Both or just the unknown.

In this case wouldn't you always take both, seeing as there isn't even a perceived penalty for only taking one?
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Blackdeathdraco
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Henice the pendelum. Normaly, out of the blue with somewhat limited time to think about the options, a person doesn't think about all of the options because they just look at the primary goal or the million dollars, and not the posibility of gaining 1 million +1 thousand dollars.
When I'm bored, I like to wander around and cast X-Zone on random things.

"Sanity is the illusion of the insane." -Me

<A href='http://sigs.guildlaunch.net'><img src='http://sigs.guildlaunch.net/wsig.php/8136909YlbMX.png' border='0'></a>
img src="http://www.animecubed.com/billy/pics/sigs/BDD.jpg"><br>
Be the Ultimate Ninja! Play <a href="http://www.animecubed.com/billy/?BDD">Billy Vs. SNAKEMAN</a> today!
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Blackdeathdraco,Dec 15 2006
10:56 PM
following the rules of that mental challannge, I say since I can have both, why not take both. The second box will either have 1mill or none so i would rather take the 50% chance of getting $1,001,000 then just a posible $0.

Yea, I don't really see the point of doing anything else either, even with the mindreader. It's not like he's 100% correct.
"Death is a primitive concept, I prefer to think of them as battling evil, in another dimension!"
-Gary Gygax

http://tv.zeroboy.net/springtime

Check out Red (White Meteos) and I's livestream!
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LuppyLuptonium
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I'm confused.... Newb read a book about Deal or no Deal?
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Arc
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Blackdeathdraco,Dec 15 2006
07:06 PM
Henice the pendelum. Normaly, out of the blue with somewhat limited time to think about the options, a person doesn't think about all of the options because they just look at the primary goal or the million dollars, and not the posibility of gaining 1 million +1 thousand dollars.

I say be nice and just take one like the guy says...
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Juron Pilo
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http://en.wikipedia.org/wiki/Prisoner's_delimma

Sorry, thought someone already did, although with the amount of times I posted previous I would think it would be obvious what article I was refering to. :P
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Big McStrongmuscle
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...Actually, I crunched the numbers on that box thing. Statistically speaking, the only time its worth taking both boxes is if the Being has a 50.05% chance or less of being correct.

And those personal experiments with the prisoner's dilemma can get really interesting, if you vary the precise constraints. One fun way is to choose the partner anonymously from a known population of the prisoner's friends and enemies.
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