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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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  • $\begingroup$ 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 $3$? $\endgroup$
    – joriki
    Nov 5, 2012 at 18:46
  • $\begingroup$ 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 $\endgroup$
    – user48301
    Nov 5, 2012 at 21:42
  • $\begingroup$ 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? $\endgroup$
    – joriki
    Nov 5, 2012 at 22:47

2 Answers 2

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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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Your answer may be valid only for pure strategy games. Use a LP solver for calculating mixed strategy saddle points.

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