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Game Theory - Mixed Strategy

For the following game I had to work out the mixed-strategy Nash equilibrium:

.............Mozart Mahler
Mozart ..(2,2).....(0,0)
Mahler ....(0,0).....(1,1)

The answer that I came out with was (1/3Mozart, 2/3Mahler), (1/3Mozart, 2/3Mahler).
I found it odd that they'd not play both Mozart with a greater probability since it gives them both a higher pay-off. So I thought I'd verify my answer. Any help would be brilliant, thanks :smile:
Reply 1
Avatar for BJP
BJP
OP
13
Bump? :smile:
Reply 2
Avatar for Makubex
Makubex
and whats with the topic ?
Reply 3
Avatar for py0alb
py0alb
3
Original post by BJP
For the following game I had to work out the mixed-strategy Nash equilibrium:

.............Mozart Mahler
Mozart ..(2,2).....(0,0)
Mahler ....(0,0).....(1,1)

The answer that I came out with was (1/3Mozart, 2/3Mahler), (1/3Mozart, 2/3Mahler).
I found it odd that they'd not play both Mozart with a greater probability since it gives them both a higher pay-off. So I thought I'd verify my answer. Any help would be brilliant, thanks :smile:



It looks to me like there is no need for a mixed strategy as the pure Mozart/Mozart strategy is strictly dominant. Are you sure you copied the payoffs down correctly?
Reply 4
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BJP
OP
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Original post by py0alb
It looks to me like there is no need for a mixed strategy as the pure Mozart/Mozart strategy is strictly dominant. Are you sure you copied the payoffs down correctly?


Yeah, just checked. The question does ask for a mixed-strategy. If there was need for one, is the one I've found correct, do you know? Thanks a lot.
Reply 5
Avatar for py0alb
py0alb
3
Original post by BJP
Yeah, just checked. The question does ask for a mixed-strategy. If there was need for one, is the one I've found correct, do you know? Thanks a lot.


If you look at the 1st player's payoffs, you get 2L = (1-L), and if you look at the 2nd player's payoffs you get 2U = = (1-U), so you find L and U both = 1/3

so (1/3 2/3), (1/3 2/3) is the mixed NE. Note that because both players would be better off playing (1,0), this is an unstable equilibrium. It's a bit of a stupid question really, seeing as its a case where you wouldn't need to find a mixed strategy.

Something like
21 00
00 12
would be better.
Reply 6
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BJP
OP
13
Original post by py0alb
If you look at the 1st player's payoffs, you get 2L = (1-L), and if you look at the 2nd player's payoffs you get 2U = = (1-U), so you find L and U both = 1/3

so (1/3 2/3), (1/3 2/3) is the mixed NE. Note that because both players would be better off playing (1,0), this is an unstable equilibrium. It's a bit of a stupid question really, seeing as its a case where you wouldn't need to find a mixed strategy.

Something like
21 00
00 12
would be better.


Yeah, I take your point about it being a weird question.

But, my mixed strategy was correct? That's good :smile:

Thanks for all your help!

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