Simple continuous game or not?
$begingroup$
Two players simultaneously pick a number from [0, 1]. Payoff of the first player (equal to the loss of the second) is the distance between those numbers.
- Does there exist pure-strategy Nash equilibrium?
- Does there exist mixed-strategy Nash equilibrium? How many?
I found value of the game v=1/2, pure optimal strategy for the second player y=1/2 and the mixed optimal strategy for the first player x={0, 1} with probabilities p=(1/2, 1/2).
I am a bit stuck with finding other mixed strategies, could you help me, please?
game-theory nash-equilibrium
asked Dec 21 '18 at 23:35
gillz1gillz1
11
$endgroup$
add a comment |
$begingroup$
Two players simultaneously pick a number from [0, 1]. Payoff of the first player (equal to the loss of the second) is the distance between those numbers.
- Does there exist pure-strategy Nash equilibrium?
- Does there exist mixed-strategy Nash equilibrium? How many?
I found value of the game v=1/2, pure optimal strategy for the second player y=1/2 and the mixed optimal strategy for the first player x={0, 1} with probabilities p=(1/2, 1/2).
I am a bit stuck with finding other mixed strategies, could you help me, please?
game-theory nash-equilibrium
asked Dec 21 '18 at 23:35
gillz1gillz1
11
$endgroup$
add a comment |
$begingroup$
Two players simultaneously pick a number from [0, 1]. Payoff of the first player (equal to the loss of the second) is the distance between those numbers.
- Does there exist pure-strategy Nash equilibrium?
- Does there exist mixed-strategy Nash equilibrium? How many?
I found value of the game v=1/2, pure optimal strategy for the second player y=1/2 and the mixed optimal strategy for the first player x={0, 1} with probabilities p=(1/2, 1/2).
I am a bit stuck with finding other mixed strategies, could you help me, please?
game-theory nash-equilibrium
asked Dec 21 '18 at 23:35
gillz1gillz1
11
$endgroup$
Two players simultaneously pick a number from [0, 1]. Payoff of the first player (equal to the loss of the second) is the distance between those numbers.
- Does there exist pure-strategy Nash equilibrium?
- Does there exist mixed-strategy Nash equilibrium? How many?
I found value of the game v=1/2, pure optimal strategy for the second player y=1/2 and the mixed optimal strategy for the first player x={0, 1} with probabilities p=(1/2, 1/2).
I am a bit stuck with finding other mixed strategies, could you help me, please?
game-theory nash-equilibrium
game-theory nash-equilibrium
asked Dec 21 '18 at 23:35
gillz1gillz1
11
asked Dec 21 '18 at 23:35
gillz1gillz1
11
asked Dec 21 '18 at 23:35
gillz1gillz1
11
asked Dec 21 '18 at 23:35
gillz1gillz1
11
asked Dec 21 '18 at 23:35
gillz1gillz1
11
11
add a comment |
add a comment |
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