In the next matrix, why is (55,0) not a Nash Equilibrium? My book says that the next matrix has no Nash Equilibriums. Still, Im a little confused about row 3, column 2.
Reasoning from player 2's perspectivo, he could say "if player 1 chooses row 3, I Will choose column 2, and that is convenient for both of us". So how is that not supposed to be a Nash Equilibrium?
Although I undestand that if I reason from player 1's perspective, he would go like this: "If player 2 chooses column 2, I Will pick row 1"
I kind of understand that I have already said why is (55,0) not a Nash Equilibrium (because being player 1 , i wouldn't pick that option), but not entirely...
$$
        \begin{pmatrix}
        (35,25) & (80,0) \\
        (30,10) & (60, 0)\\
        (45,-10) & (55,0)\\
                 \end{pmatrix}
$$

In short, an NE has to take views of "all" players. Any player deviating from NE "unilaterally" won't get greater payoffs. So, at (55, 0), even though it's a better choice for player 2, it's not an optimal option for player 1. Furthermore, if player 2 chooses column 2 to play, player 1, instead of choosing row 3, can choose row 1 to obtain greater(than 50) payoff 80 for himself.
