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#Post#: 28--------------------------------------------------
Q4
DIR By: andrvetch
Date: November 26, 2012, 9:18 am
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(d) I have understood that we have multiple MSNE in this case.
But I I would like to ask to explain the statement in the
answers that the row player mix over the two rows provided
p<=(1/3). I don't understand why this probability 1/3 is here?
(j) Similarly I don't understand why here we don't have any
probability while the story is quite similar to (d).
(g) I have come up with the answer (1/3,1/3,1/3), (1/3,1/3,1/3)
but I can't get the answer (1/2,1/2,0), (1/2,1/2,0) and so on.
Could you please explain how we get this result and why it is
NE?
#Post#: 30--------------------------------------------------
Re: Q4
DIR By: Julia.Wirtz
Date: November 26, 2012, 2:00 pm
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--- Quote from: andrvetch link ---
>
> (d) I have understood that we have multiple MSNE in this case.
But I I would like to ask to explain the statement in the
answers that the row player mix over the two rows provided
p<=(1/3). I don't understand why this probability 1/3 is here?
>
--- End Quote ---
The MSNE is
- P1 plays T with probability p<=1/3 and B with probability
(1-p)
- P2 plays L with probability q=1
p is chosen to make P2 willing to play L.
If P1 would play T with probability p>1/3 then P2 would prefer
to play R.
Remember the definition of a NE: both players must be playing
best response to each other.
#Post#: 31--------------------------------------------------
Re: Q4
DIR By: Julia.Wirtz
Date: November 26, 2012, 2:10 pm
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--- Quote from: andrvetch link ---
>
> (j) Similarly I don't understand why here we don't have any
probability while the story is quite similar to (d).
>
--- End Quote ---
What do you mean with "we don't have any probability "?
Especially in game theory you should try and practice to use
precise terminology. :P
In the solution Abhinay only tells you how to delete strictly
dominated strategies, then he says the solution of the reduced
matrix is similar to (j).
There are two PSNE: (B,L) and (T,R)
The MSNE are:
P1 plays B with probability 1 (to make P2 indifferent between L
and R)
P2 plays L with probability q>=1/2 and R with probability (1-q)
(otherwise P1 does not want to play B)
#Post#: 32--------------------------------------------------
Re: Q4
DIR By: Julia.Wirtz
Date: November 26, 2012, 2:21 pm
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--- Quote from: andrvetch link ---
>
> (g) I have come up with the answer (1/3,1/3,1/3),
(1/3,1/3,1/3) but I can't get the answer (1/2,1/2,0),
(1/2,1/2,0) and so on. Could you please explain how we get this
result and why it is NE?
>
--- End Quote ---
It is a NE because of the same reason as always: Both players
are playing best response to each other.
(If you truly learn and understand this definition, game theory
is a piece of cake ;D)
I guess you need a little intuition to find these results.
First, you should realize, that P1 always wants to do the same
as P2 and vice versa.
As an example, look at the first case: (1/2,1/2,0), (1/2,1/2,0)
Lets call the actions of both players X,Y and Z.
If P1 never plays Z, then P2 never wants to play Z either. So
you can delete column 3 and row 3.
Then you have a 2x2 matrix and you get the probabilities
(1/2,1/2) for X and Y as usual.
The same reasoning goes for the 2 other cases.
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