I'm trying to solve a two player zero sum game. After writing it in normal form I got the following matrix:
$$ \left( \begin{matrix} 5/4 & -1/4 \\ 5/4 & -1 \\ 2 & 2 \\ 2 & 5/4 \\ -1 & -1/4\\ -1 & -1 \\ -1/4 & 2 \\ -1/4 & 5/4 \\ \end{matrix}\right) $$
Eliminating the dominated rows I get: $$ \left(\begin{matrix} 5/4 & -1/4 \\ 2 & 2 \\ \end{matrix}\right) $$
I try to find mixed strategies $\vec p$ and $\vec q$ for this matrix, such that:
$$ \sum_i p_i = 1 \\ \sum_i q_i = 1 $$
But then, I get the solutions:
$$ \vec p = (0, 0, 1, 0, 0, 0, 0, 0) \\ \vec q = (3/2, -1/2) $$
Which contradicts the condition I want to fulfill.
Solving this game with Sage I get two solutions:
$\vec p = (0, 0, 1, 0, 0, 0, 0, 0), \vec q = (0, 1)$ and $\vec p = (0, 0, 1, 0, 0, 0, 0, 0), \vec q = (1, 0)$
Can somebody explain me why I'm not getting the correct solution?