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# Game theory: simultaneous move game Watch

1. 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
2. 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.
3. (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?
4. 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.
5. (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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