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    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
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    and whats with the topic ?
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    (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

    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?
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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.
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    (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.
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    (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

    Thanks for all your help!
 
 
 
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