Goofy answer when trying to solve the prisoner's dilemma (probability stuff)

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SUMMARY

The forum discussion centers on solving the prisoner's dilemma using probability to find the optimal strategy for the row player. The user attempts to equate the expected payoffs for strategies Deny (D) and Tattle (T) but encounters an inconsistency in their calculations, leading to an impossible probability of p=4/3. The discussion highlights the presence of a dominant strategy where both players should choose to "tattle," rendering the user's approach of avoiding dominated alternatives unnecessary.

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Homework Statement


Trying to find optimal solution for row player. Deny=D Tattle=T. I am trying to do this without knocking out dominated alternatives.

D T
D -1,1 -10,0

T 0,-10 -6,-6

Homework Equations

The Attempt at a Solution


DD=p(-1)+(1-p)(-10) =-1p-10+10p =9p-10
DT=p(0)+(1-p)(-6) =-6+6p

9p-10=-6+6p
3p=4
p=4/3 (Huh?)

I do not know if my arithmetic is off, or I cannot solve the game by setting both equations equal because of the (0,-10) and (-10,0) scenarios.

Thanks for the help.

Homework Statement


Homework Equations


The Attempt at a Solution


Homework Statement


Homework Equations


The Attempt at a Solution

 
Last edited:
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It's not clear to me why you are doing that. There clearly is a dominant solution- both prisoners "tattle".
 

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