Nash Equilibrium and Mixed NE Problem
0
$begingroup$
- Does the game have a pure Nash equilibrium?
- Find all the mixed equilibria (note, there is at least one)
I'm having some problems solving this exercise about the game between player 1 and 2 in the picture below; from what I understood, checking the best responses of each player to each possible fixed strategy of the other player, there shouldn't be any pure NE in this game. Is this correct? How do I proceed to find the mixed equilibria?
Thank you in advance!
game-theory nash-equilibrium
asked Jan 3 at 16:42
Simone GalimbertiSimone Galimberti
134
$endgroup$
add a comment |
0
$begingroup$
- Does the game have a pure Nash equilibrium?
- Find all the mixed equilibria (note, there is at least one)
I'm having some problems solving this exercise about the game between player 1 and 2 in the picture below; from what I understood, checking the best responses of each player to each possible fixed strategy of the other player, there shouldn't be any pure NE in this game. Is this correct? How do I proceed to find the mixed equilibria?
Thank you in advance!
game-theory nash-equilibrium
asked Jan 3 at 16:42
Simone GalimbertiSimone Galimberti
134
$endgroup$
$begingroup$
The problem has no dominant strategy by symmetry, and by the fact that regardless of what move 1 makes, there is no condition on which player 2 choosing $c$ is better than choosing one of $l$ or $r$. As such, we can remove the middle column. Once you do that, the mixed strategy becomes obvious by symmetry.
$endgroup$
– Don Thousand
Jan 3 at 16:54
$begingroup$
I don't quite understand why you removed the middle column. I understand your reasoning but I thought that, in the process of finding mixed NE, you had to find and remove all dominated columns/rows: Isn't a column/row dominated only when all the payoffs of another column/row are larger?
$endgroup$
– Simone Galimberti
Jan 4 at 9:11
add a comment |
0
0
0
$begingroup$
- Does the game have a pure Nash equilibrium?
- Find all the mixed equilibria (note, there is at least one)
I'm having some problems solving this exercise about the game between player 1 and 2 in the picture below; from what I understood, checking the best responses of each player to each possible fixed strategy of the other player, there shouldn't be any pure NE in this game. Is this correct? How do I proceed to find the mixed equilibria?
Thank you in advance!
game-theory nash-equilibrium
asked Jan 3 at 16:42
Simone GalimbertiSimone Galimberti
134
$endgroup$
- Does the game have a pure Nash equilibrium?
- Find all the mixed equilibria (note, there is at least one)
I'm having some problems solving this exercise about the game between player 1 and 2 in the picture below; from what I understood, checking the best responses of each player to each possible fixed strategy of the other player, there shouldn't be any pure NE in this game. Is this correct? How do I proceed to find the mixed equilibria?
Thank you in advance!
game-theory nash-equilibrium
game-theory nash-equilibrium
asked Jan 3 at 16:42
Simone GalimbertiSimone Galimberti
134
asked Jan 3 at 16:42
Simone GalimbertiSimone Galimberti
134
asked Jan 3 at 16:42
Simone GalimbertiSimone Galimberti
134
asked Jan 3 at 16:42
Simone GalimbertiSimone Galimberti
134
asked Jan 3 at 16:42
Simone GalimbertiSimone Galimberti
134
134
$begingroup$
The problem has no dominant strategy by symmetry, and by the fact that regardless of what move 1 makes, there is no condition on which player 2 choosing $c$ is better than choosing one of $l$ or $r$. As such, we can remove the middle column. Once you do that, the mixed strategy becomes obvious by symmetry.
$endgroup$
– Don Thousand
Jan 3 at 16:54
$begingroup$
I don't quite understand why you removed the middle column. I understand your reasoning but I thought that, in the process of finding mixed NE, you had to find and remove all dominated columns/rows: Isn't a column/row dominated only when all the payoffs of another column/row are larger?
$endgroup$
– Simone Galimberti
Jan 4 at 9:11
add a comment |
$begingroup$
The problem has no dominant strategy by symmetry, and by the fact that regardless of what move 1 makes, there is no condition on which player 2 choosing $c$ is better than choosing one of $l$ or $r$. As such, we can remove the middle column. Once you do that, the mixed strategy becomes obvious by symmetry.
$endgroup$
– Don Thousand
Jan 3 at 16:54
$begingroup$
I don't quite understand why you removed the middle column. I understand your reasoning but I thought that, in the process of finding mixed NE, you had to find and remove all dominated columns/rows: Isn't a column/row dominated only when all the payoffs of another column/row are larger?
$endgroup$
– Simone Galimberti
Jan 4 at 9:11
$begingroup$
The problem has no dominant strategy by symmetry, and by the fact that regardless of what move 1 makes, there is no condition on which player 2 choosing $c$ is better than choosing one of $l$ or $r$. As such, we can remove the middle column. Once you do that, the mixed strategy becomes obvious by symmetry.
$endgroup$
– Don Thousand
Jan 3 at 16:54
$begingroup$
The problem has no dominant strategy by symmetry, and by the fact that regardless of what move 1 makes, there is no condition on which player 2 choosing $c$ is better than choosing one of $l$ or $r$. As such, we can remove the middle column. Once you do that, the mixed strategy becomes obvious by symmetry.
$endgroup$
– Don Thousand
Jan 3 at 16:54
$begingroup$
I don't quite understand why you removed the middle column. I understand your reasoning but I thought that, in the process of finding mixed NE, you had to find and remove all dominated columns/rows: Isn't a column/row dominated only when all the payoffs of another column/row are larger?
$endgroup$
– Simone Galimberti
Jan 4 at 9:11
$begingroup$
I don't quite understand why you removed the middle column. I understand your reasoning but I thought that, in the process of finding mixed NE, you had to find and remove all dominated columns/rows: Isn't a column/row dominated only when all the payoffs of another column/row are larger?
$endgroup$
– Simone Galimberti
Jan 4 at 9:11
add a comment |
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$begingroup$
The problem has no dominant strategy by symmetry, and by the fact that regardless of what move 1 makes, there is no condition on which player 2 choosing $c$ is better than choosing one of $l$ or $r$. As such, we can remove the middle column. Once you do that, the mixed strategy becomes obvious by symmetry.
$endgroup$
– Don Thousand
Jan 3 at 16:54
$begingroup$
I don't quite understand why you removed the middle column. I understand your reasoning but I thought that, in the process of finding mixed NE, you had to find and remove all dominated columns/rows: Isn't a column/row dominated only when all the payoffs of another column/row are larger?
$endgroup$
– Simone Galimberti
Jan 4 at 9:11