Question

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. Below is the profit matrix for the two firms under combinations of each of the three decisions. The first number in the bracket is the JNJ profit, the second number if the PG profit.

			PG
		High	Medium	Low
	High	(1,1)	(3, 2)	(5, 3)
JNJ	Medium	(2,3)	(4, 4)	(6, 5)
	Low	(3,5)	(5,6)	(7,5)

a) What are each firm’s best responses to each of its rival’s strategies? Explain

b) Does either firm have a dominant strategy? Explain

c) What is the Nash equilibrium in this game?

Answer 1

JNJ/PG	HIGH	MEDIUM	LOW
HIGH	1,1	3,2	5,3
MEDIUM	2,3	4,4	6,5
LOW	3,5	5,6	7,5

a) PLAYER JNJ (PLAYER 1)

If player 1 chooses strategy high, then it is best for player 2 to choose low as he gets the highest pay-off of 3.

If player 1 chooses strategy medium, then player 2 will choose low to get the highest pay-off of 5.

If player 1 choose strategy low, then player 2 will choose medium to get the highest pay-off of 6.

PLAYER PG (PLAYER 2)

If player 2 chooses high, then player 1 will choose low to get the highest pay-off of 3.

If player 2 chooses medium, then player 1 will choose low to get the highest pay-off of 5.

If player 2 chooses low, then player 1 will choose low to get the highest pay-off of 7.

b) Clearly from the above best responses, player 1 has the dominant strategy of choosing low because no matter what strategy player 2 is adopting, he is always choosing strategy low.

c) The nash equilibrium is determined at at 5, 6 where player 1 is choosing low strategy and player 2 is choosing medium strategy.