So I have a symmetric game with pay off matrice as
$$ \begin{matrix} P1/P2 & 0 & 1 & 2 & 3 & 4 & 5 \\ 0 & (0,0) & (0,1) & (0,2) & (0,3) & (0,4) & (0,5) \\ 1 & (1,0) & (1,1) & (1,2) & (1,3) & (1,4) & (0,0) \\ 2 & (2,0) & (2,1) & (2,2) & (2,3) & (0,0) & (0,0) \\ 3 & (3,0) & (3,1) & (3,2) & (0,0) & (0,0) & (0,0) \\ 4 & (4,0) & (4,1) & (0,0) & (0,0) & (0,0) & (0,0) \\ 5 & (5,0) & (0,0) & (0,0) & (0,0) & (0,0) & (0,0) \\ \end{matrix} $$
Now I have 3 options
1) Calculate the mixed strategy nash equilibrium of 6x6 game.
2) Eliminate 0 strategy for both players and end up with a 5x5 game and then calculate the mixed strategy nash equilibrium.
$$ \begin{matrix} P1/P2 & 1 & 2 & 3 & 4 & 5 \\ 1 & (1,1) & (1,2) & (1,3) & (1,4) & (0,5) \\ 2 & (2,1) & (2,2) & (2,3) & (0,0) & (0,0) \\ 3 & (3,1) & (3,2) & (0,0) & (0,0) & (0,0) \\ 4 & (4,1) & (0,0) & (0,0) & (0,0) & (0,0) \\ 5 & (5,0) & (0,0) & (0,0) & (0,0) & (0,0) \\ \end{matrix} $$
3)If the row player plays 0 then he has a pay off of 0. Likewise he knows that the column player also has a pay off of 0 if he plays 0 so can I eliminate strategies 0 and 5 for both players and make a 4x4 game and then calculate the mixed strategy nash equilibrium ?
$$ \begin{matrix} P1/P2 & 1 & 2 & 3 & 4 \\ 1 & (1,1) & (1,2) & (1,3) & (1,4)\\ 2 & (2,1) & (2,2) & (2,3) & (0,0)\\ 3 & (3,1) & (3,2) & (0,0) & (0,0)\\ 4 & (4,1) & (0,0) & (0,0) & (0,0)\\ \end{matrix} $$
Whats the approach that I should take ?