What linear programming problem gives the solution to this matrix game problem?

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So this game has the following matrix: $$A=\begin{bmatrix} 1 &-1& -2 \\ -1 & 2 & -1 \\ -2 & -1 & 3 \end{bmatrix}$$ So if I know correctly I should consider the following problem:

$$\max e^Tu$$ $$Au \leq e$$ $$u\geq 0$$

Now my problem is that I'm not sure about what $e$ is it the 3-dimensional vector with 1 entries in my case? The other thing I'm not sure about if this is even solveable always? As I'm trying to solve it I always get stuck.

Thanks in advance!

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e is the (column) vector of ones.

The Linear Programming problem you have provided is solvable, and has optimal objective value of 5.