Suppose Nike and Adidas spend enormous sums of money every year to promote their

Question

Suppose Nike and Adidas spend enormous sums of money every year to promote their athletic wear, hoping to steal customers from each other. Furthermore, assume each year they have to decide whether or not they should spend more money on advertising. If neither firm advertises, each of them will earn $5 million. If both advertise, each will earn $2 million in profit. If one firm advertises and the other does not, the firm with the promotions will earn a profit of $3 million and the other firm will earn $0.5 million. Use a payoff matrix to model this problem.

5.   For the problem above:

a) If the probability of an Adidas decision to advertise is 90 percent, what is the expected payoff to Nike’s decision to advertise?

b) If the probability of Adidas not advertising even though Nike does not is 20 percent, what is expected payoff to Nike’s decision to not to advertise?

c) What should Nike do?

Explanation / Answer

5.

a. Nike's pay-off in this case=$(2x0.9+3x0.10)=$2.1

Again $(0.9X0.5+5x0.10)=$0.95<$2.1

b. Nike's pay-off here=$(2x0.80+3x0.20)=$2.2

On the other hand, the pay-off=$(0.5x0.8+5x0.20)=$1.40<$2.2

c. So that Nike would Advertise as expected pay-off for advertise is more than the expected pay-off of not advertising.

Nike Advertise(q=0.80) Not Advertise(1-q=0.20) Addidas Advertise(p=0.90) 2,2 3,0.5 Not Advertise(1-p=0.10) 0.5,3 5,5

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