# Saddle points in zero sum game

We only had one lecture about the subject and already have quite difficult questions, could someone please help me?

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?

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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 $3$? – joriki Nov 5 '12 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 '12 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? – joriki Nov 5 '12 at 22:47

## 1 Answer

The answer is partially yes. The saddles points are (1,3),(2,3) and (3,3) where the numbers indicate the rows and columns respectively. I assumed the row player is the maximizer and the column player is the minimizer.

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