Suppose Proctor$$ & Gamble$($PG$)$ and Johnson$$ & Johnson$($JNJ$)$ are simultaneously considering new advertising campaigns. Each firm may choose a$$ high, medium, or low level of advertising. What are each$$ firm's best responses to its$$ rival's strategies? Does either firm have a dominant$$ strategy? What is the Nash equilibrium in this$$ game?

Part $2$

If PG picks$$ high, then JNJ should pick

$$

$$

low

medium

high

$$;

if PG picks$$ medium, JNJ should pick

$$

$$

medium

high

low

$$;

and if PG picks$$ low, then JNJ should pick

$$

$$

medium

high

low

$.$

Part $3$

If JNJ picks$$ high, then PG should pick

$$

$$

low

medium

high

$$;

if JNJ picks$$ medium, PG should pick

$$

$$

high

low

medium

$$;

and if JNJ picks$$ low, then PG should pick

$$

$$

high

low

medium

$.$

Part $4$

$$PG$\text{'}$s dominant strategy is to pick

$$

$$

low

high

medium

and$$ JNJ$\text{'}$s dominant strategy is to pick

$$

$$

high

low

medium

$.$

Part $5$

Identify the Nash equilibrium in this game.

Part $6$

A$.$

The Nash equilibrium is for both firms to pick high.

B$.$

The Nash equilibrium is for both firms to pick medium.

C$.$

This game has no Nash equilibria.

D$.$

The Nash equilibrium is for both firms to pick low.

E$.$

The Nash equilibria are for PG to pick medium and JNJ to pick low and for PG to pick low and JNJ to pick medium.