# Saddle points in zero sum game

The matrix looks something like this:

\begin{matrix} 3 & 2 & 1 & 4 & 5 \\ 2 & 5 & 1 & 3 & 4 \\ 4 & 5 & 1 & 2 & 3 \\ 3 & 4 & 0 & 5 & 0 \\ 1 & 3 & 0 & 5 & 0 \end{matrix}

Is it true that row will always choose row 1,2 or 3 and column would choose 2 or 4 for the best pay-off? Or how can I determine a saddle point?

• I'm not sure whether these are meant to be the payoffs for row or for column, but in either case neither row $4$ nor row $5$ is dominated by any of rows $1$ through $3$. Could you explain why you think that row would always choose one of rows $1$ through $3$? Nov 5, 2012 at 18:46
• Because the minimum payoff for row would be 1, independent of columns choice, en in rows 4 and 5 the minimum payoff is 0, so i'd suppose row would choose 1,2 or 3
– user48301
Nov 5, 2012 at 21:42
• Now I'm wondering whether you know which player's payoffs these are. You're arguing as if they're payoffs for the row player -- but then it would be column $3$ that dominates columns $2$ and $4$ and not the other way around? Nov 5, 2012 at 22:47