CreeperCosmo

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UsernameCreeperCosmo
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 #52
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Hard one (still unanswered): 

You and your best friend have been arrested for several white collar crimes. (Or something else which is more classy than stealing a candy bar) 
Your attorney has told you the police has only got enough evidence to put you and your friend behind bars for 3 years. 
However, the both of you are given the option to confess. If both of you confess you will both serve 10 years, 
if one of you confesses and the other does not, the one who did not confess will serve 20 years. 
Obviously, if you both remain silent you will both serve 3 years. 
You are not allowed to have any communication with your friend. 
Suppose your main priority is to keep yourself out of jail, and your secondary priority is to keep your partner out of jail. 
You have decided that you find it twice as important to keep yourself out of jail as you find it important to keep your partner out of jail. 
(So for example, in your opinion him serving 10 years is equal to you serving 5). 
You estimate the chance of your partner confessing p. 
For which values of p will you choose to confess and for which values will you keep silent? 

HINT: make a formula for the amount of suffering you expect, also taking the suffering for your friends jailtime into account.

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2 Points for every year you're in jail, 1 Point for every year your partner is in jail.

Therefore...

 

Both don't confess- if 50% chance friend will confess

3 years for you (6 points), 3 years for your partner (3 points)

[9] points total

 

Both confess- if 50% chance friend will confess

10 years for you (20 points), 10 years for your partner (10 points)

[30] points total

 

You confess and your friend doesn't- if 50% chance friend will confess

0 years for you (0 points), 20 years for your partner (20 points)

[20] points total

 

Your friend confesses and you don't- 50% chance friend will confess

20 years for you (40 points), 0 years for your partner (0 points)

[40] points total

 

Therefore...

 

If you confess you will have an average of 25 "points"

(30+20)/2=25

 

If you don't you have an average of 24.5 "points"

(40+9)/2=24.5

 

Therefore, in most cases you shouldn't confess :D

CreeperCosmo May 20, 2014
 
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