3. Consider the following general 2 × 2 zero-sum game, with the payoff numbers a

Question

3. Consider the following general 2 × 2 zero-sum game, with the payoff numbers a, b, c, d all distinct. L M U a b M c d

a) (3 points) Show that if (U, L) are the maxmin strategies then b > a > c.

b) (3 points) Show that if (U, L) are the maxmin strategies then at least one player has a dominated strategy

3. Consider the following general 2 × 2 zero-sum game, with the payoff numbers a,b,c,d all distinct L M Mcd a) (3 points) Show that if (U, L) are the maxmin strategies then b >a>c b) (3 points) Show that if (U, L) are the maxmin strategies then at least one player has a dominated strategy.

Explanation / Answer

Here in each row, we will first isolate minimum value from each row, then select the maximum value from them.

In row 1, as b>a, a will be isolated and considered. In row 1, as the d>c, c will be ilolated and considered. Now we have to select the maximum value from a and c. since a>c, c will be selected.

This is how (U,L) will be the maximin strategy.

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