Nash Equilibrium and Mixed NE Problem












0















  1. Does the game have a pure Nash equilibrium?

  2. 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!



enter image description here










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  • 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.
    – Don Thousand
    2 days ago










  • 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?
    – Simone Galimberti
    yesterday
















0















  1. Does the game have a pure Nash equilibrium?

  2. 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!



enter image description here










share|cite|improve this question






















  • 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.
    – Don Thousand
    2 days ago










  • 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?
    – Simone Galimberti
    yesterday














0












0








0








  1. Does the game have a pure Nash equilibrium?

  2. 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!



enter image description here










share|cite|improve this question














  1. Does the game have a pure Nash equilibrium?

  2. 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!



enter image description here







game-theory nash-equilibrium






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked 2 days ago









Simone Galimberti

134




134












  • 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.
    – Don Thousand
    2 days ago










  • 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?
    – Simone Galimberti
    yesterday


















  • 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.
    – Don Thousand
    2 days ago










  • 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?
    – Simone Galimberti
    yesterday
















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.
– Don Thousand
2 days ago




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.
– Don Thousand
2 days ago












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?
– Simone Galimberti
yesterday




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?
– Simone Galimberti
yesterday










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