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**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'

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

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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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,309

Hi Agnishom;

Very good!

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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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'

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

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