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

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 14,191
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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?
PD_1.png

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'
'Humanity is still kept intact. It remains within.' -Alokananda

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

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 14,191
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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'
'Humanity is still kept intact. It remains within.' -Alokananda

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

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 81,394

Re: Public Goods Problem - Game Theory

Hi Agnishom;

Very good!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,191
Website

Re: Public Goods Problem - Game Theory

Thanks big_smile


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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