3
$\begingroup$

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?

  • 0
    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 $3$?2012-11-05
  • 0
    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 32012-11-05
  • 0
    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?2012-11-05

2 Answers 2

0

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.