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## #1 2013-07-18 03:07:47

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,016
Website

### Public Goods Problem - Game Theory

Sue and Pete are playing Prisoner's Dilemma with the payoffs from the table below. If both of them cooperate, each will get a bonus of 2A (the public good), if only one cooperates, each will get A, and if no one cooperates there is no bonus. Sue calculated that Pete will cooperate with probability p=0.3. What should be the value of the award A so that Sue is indifferent between cooperating and defecting?

Source:https://brilliant.org/i/zS7vun/
Suggested Guide:https://brilliant.org/competitions/hung … /training/

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #2 2013-07-19 00:40:23

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,016
Website

### Re: Public Goods Problem - Game Theory

Have a look at https://brilliant.org/competitions/hung … ing/#mixed
The probability that Pete choses C is 0.3 while the probabiity that Pete choses D is 0.7
Since, Sue is indifferent between c and d, his expected payoffs must be equal.

0.3(6+2A) +0.7(0+A) = 0.3(12+A) + 0.7(3)

Solving yields, A = 3.9

Thats all, guys!

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #3 2013-07-19 03:33:32

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 106,389

### Re: Public Goods Problem - Game Theory

Hi Agnishom;

Very good!

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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## #4 2013-07-19 04:05:37

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,016
Website

### Re: Public Goods Problem - Game Theory

Thanks

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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