## Related questions with answers

Set up the payoff matrix. You must decide whether to attack your opponent by sea or air, and your opponent must simultaneously decide whether to mount an all-out air defense, an all-out coastal defense (against an attack from the sea) or a combined air and coastal defense. If there is no defense for your mode of attack, you win 100 points. If your attack is met by a shared air and coastal defense, you win 50 points. If your attack is met by an all-out defense, you lose 200 points.

Solution

VerifiedThe goal is to set up the payoff matrix.

$A$ stands for an all-out air defense, $C$ stands for an all-out coastal defense and $AC$ for a combined air and coastal defense.

Entries $p_{11}$ and $p_{22}$ are $100$ because there is no defense.

Entries $p_{21}$ and $p_{12}$ are $-200$ because my attack is met by an all-out defense.

Entries $p_{13}$ and $p_{23}$ are $50$ because my attack is met by a shared air and coastal defense.

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