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av2019


Member

Posted Tue Dec 15th, 2009 11:41am Post subject: Game Theory

I have a question on the last episode of QI they discussed Game Theory. Now my maths is usally pretty rubbish so maybe someone can shed some light on something for me. The bit that I disagree with was when Stephen said that in a situation like the big brother one, one should always chooose to share. Why?? From what I can work out if you share you have a 1/2 chance of winning half the money. if you choose to not share you have a 1/2 chance of winning all the money. Is this right or wrong.

Well even if im wrong im now inventing Game Game Theory Always choose to not share. You have the same odds of winning but you double your winnings. (take note players on Golden Balls)

Anyway thats about it.


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Marty10000


Member

Posted Wed Dec 16th, 2009 2:17am Post subject: Game Theory

ok ill try to explain,
In these situations game theory tries to find the optimum strategy such that when you follow it you gain the greatest reward all of the time. if you move to share all the time and your opponent does the same then you will always get 1/2 the reward, if you chose to take all and you opponent does the same you always get nothing, remember if your opponent is as smart as you they will make the same decision so you should try and play against yourself to work out the optimum strategy.
Of course if everyone played that way it would be best to try and take all all the time but that is called the metagame and is something else entirely.
Hope this helps.


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av2019


Member

Posted Wed Dec 16th, 2009 11:35am Post subject: Game Theory

Thanks for that it explains it in a way I can understand


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Randomisity


Member

Posted Sun Jun 5th, 2011 10:01pm Post subject: Game Theory

I know I'm late to join but I've only just seen the episode and I am sad to report Mr Fry is wrong.

Say in the example there's person A and person B.
If B says I will share the money, then A's best response is to say I'll take the money as then A will get all of the money.
If B says I will take the money A is indifferent between sharing and taking as they will get nothing either way.

Therefore person A should always say take the money as it will always be as good or better than saying share from their view.
Not good from a social view I know, but that's game theory and not real life!


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TheNazgulLord


Member

Posted Sun Aug 7th, 2011 8:22pm Post subject: Game Theory

hope not too late to add something under the property of a mathematician. this is a problem of conditional probability. I dont want to get too technical into this problem (which is actually more a probability problem) so to simplify there are 4 possible outcomes and those are:
1. (A,B) = (h,h)
2. (A,B) = (a,a)
3. (A,B) = (h,a)
4. (A,B) = (a,h)
symbolizing the players by A and B and by h sharing the money and by a keeping all the money. To make it simple by ommitting the mathematics there is 1/4 chance to win half 1/4 chance to win all and 1/2 chance to win nothing as desbribed below

A shares -> B shares -> A wins half (1/4 probability)
A shares -> B keeps -> A wins none (1/4 probability)
A keeps -> B shares -> A wins full (1/4 probability)
A keeps -> B keeps -> A wins none (1/4 probability)

so it is equally probable to win half or all but its generally less probable to win than to lose


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