I have the following games and have to find all of the Nash equilibria (mixed and pure strategies). See games here
The problem I have is:
Taking the first game (3x2) I tried to see if the strategy "c" is strictly dominated by a mixed strategy between "a" and "b", as "c" never is a best response for player 1. However, I saw "c" is not dominated by any mixed strategy between "a"and "b".
Thus, I'm left with a 3x2 game and have to find all of Nash equilibria in mixed strategies.
This is where I'm having issues, how can I find these equilibria? I tried calculating the expected payoffs to see which probabilities would constitute the equilibria but when I try to calculate the expected payoffs for player 2 I'm left with the result r=2p (with the probabilities for strategies a, b and c being p, r and 1-p-r respectively)
If anyone could tell me how to solve this issue I would greatly appreciate it. Thanks.