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#Post#: 24--------------------------------------------------
Q5
DIR By: Francesco_Longo
Date: November 25, 2012, 1:39 pm
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It's not very clear to me the solution of the case a=2 in the
answer sheet. It says:
"When a=2, there is an infinity of NE's the row player plays top
and the column player playing any mixed strategy and the column
player playing right while the row player plays any mixed
strategy."
1) How can it say that row player plays TOP if this is a
strategy for column player?
2) I don't get the meaning of infinite NE issue.
I find that if a=2, then row column randomizes TOP, BOTTOM with
(1,0) and column player rendomizes LEFT, RIGHT with (0,1). This
should be the MSNE, but it is actually a PSNE.
Can you help me to interpret adequately this result?
Thanks
Francesco
#Post#: 25--------------------------------------------------
Re: Q5
DIR By: Julia.Wirtz
Date: November 25, 2012, 2:24 pm
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1) This is correct. The actions of the row player are "Top",
"Bottom", while the actions of the column player are "Left",
"Right". Easy to get confused, I know.
2) To start with, there are 3 pure strategy NE: (T,L), (T,R),
(B,R).
Then there are 2 cases for proper MSNE:
a)
- Row player plays T with probability 1
- then column player is indifferent between L and R and can mix
with any probability between 0 and 1
- Hence there are infinitely many equilibria of this type
- No matter what probability column player chooses, row player
always weakly prefers to play T, hence this is a NE
b)
- Column player plays R with probability 1
- then row player is indifferent between T and B and can mix
with any probability between 0 and 1
- Hence there are infinitely many equilibria of this type
- No matter what probability row player chooses, column player
always weakly prefers to play R, hence this is a NE.
(You can also understand PSNE as degenerate MSNE with
probabilities 0 and 1. hence the PSNE are really sub-cases of
the MSNE.)
#Post#: 26--------------------------------------------------
Re: Q5
DIR By: Francesco_Longo
Date: November 25, 2012, 8:57 pm
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Thanks for your clear answer.
However I still find very confusing saying "The actions of the
row player are T,B" when he/she rendomizes. I would suggest this
interpretation that I hope can sound correct (please let me know
if not):
"row player supposes that column player plays T with prob p and
B with prob 1-p"
and the way around for column player.
#Post#: 27--------------------------------------------------
Re: Q5
DIR By: Julia.Wirtz
Date: November 26, 2012, 5:09 am
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--- Quote from: Francesco_Longo link ---
>
> However I still find very confusing saying "The actions of the
row player are T,B" when he/she rendomizes.
>
--- End Quote ---
Where does it say this? You should always write something like:
"the row player plays T with probability x and B with
probability 1-x" (or with "any probability" as in the example)
--- Quote from: Francesco_Longo link ---
>
> "row player supposes that column player plays T with prob p
and B with prob 1-p"
>
--- End Quote ---
Unless you have a Bayesian game where the players can have
different types as in Q6, you don't need to specify beliefs.
It's enough to say
"Player 1 plays strategy a, Player 2 plays strategy b".
It is automatically understood that:
- If P2 supposes that P1 plays a, then P2's best response is b
- If P1 supposes that P2 plays b, then P2's best response is a
- So if P1 plays a and P2 plays b, no player has an incentive to
unilaterally deviate, so we have a NE
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