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    Hi, how would i answer the folowing question??

    In a 2 person simultaneous move game, Player 1 can choose any real
    number and Player 2 can choose any real number.
    The payoffs for each player are:
    Player 1: (-1/2)x^2 + x(e^y)
    Player 2: (-y^2) + 2xy - 2y
    Find any Nash Equilibria of the game and the payoffs
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    is x the real number that Player 1 chose and player 2 y?

    If they maximise Player 1 chooses x = exp(y) and Player 2 chooses y = x-1. By maximising their payoffs w.r.t. the real number they can choose (differentiate the two, and check second order for maximum). But those are two horrible simultaneous equations. 1 solution is x=1 and y=0 with payoffs, 1/2 and 0.

    But there may be others.
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    (Original post by danny111)
    is x the real number that Player 1 chose and player 2 y?

    If they maximise Player 1 chooses x = exp(y) and Player 2 chooses y = x-1. By maximising their payoffs w.r.t. the real number they can choose (differentiate the two, and check second order for maximum). But those are two horrible simultaneous equations. 1 solution is x=1 and y=0 with payoffs, 1/2 and 0.

    But there may be others.
    thanks , i am a little confused...i get the following expressions: y=x-1 and x=e^(x-1), how did you get x=1 and y=0?
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    When you have x-1, the first thing I would try would be x=1
    x=e^(x-1)
    => 1=e^(1-1)
    => 1=e^0
    => 1 = 1, which is true.
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    (Original post by Kasc)
    When you have x-1, the first thing I would try would be x=1
    x=e^(x-1)
    => 1=e^(1-1)
    => 1=e^0
    => 1 = 1, which is true.
    oh thanks
 
 
 
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