The following is a payoff matrix showing profit in millions of dollars when two

Question

The following is a payoff matrix showing profit in millions of dollars when two companies simultaneously decide on various advertising budgets ($1 million, $2 million, or $3 million):

Pizza Hut

$1 mill

$2 mill

$3 mill

$1 mill

$30 / $20

40 / 25

40 / 15

Papa Johns

$2 mill

35 / 25

30 / 30

45 / 20

$3 mill

20 / 40

25 / 35

30 / 25

a.   In the first round of strategy elimination, which ad budget would the companies exclude?

b.   After the first round of elimination, would either company make a second-round elimination?

c.   What would be the likely outcome of this simultaneous advertising decision (i.e. what ad budget would each company end up choosing)?

Pizza Hut

$1 mill

$2 mill

$3 mill

$1 mill

$30 / $20

40 / 25

40 / 15

Papa Johns

$2 mill

35 / 25

30 / 30

45 / 20

$3 mill

20 / 40

25 / 35

30 / 25

Explanation / Answer

(a)

If Pizza hut chooses the advertising budget of $1 million then Papa John will choose advertising budget of $2 million as profit is highest in that case.

If Pizza hut chooses the advertising budget of $2 million then Papa John will choose advertising budget of $1 million as profit is highest in that case.

If Pizza hut chooses the advertising budget of $3 million then Papa John will choose advertising budget of $2 million as profit is highest in that case.

Thus, it can be seen that whatever be the strategy of Pizza Hut, Papa John will never choose the advertisng budget of $3 million.

If Papa John chooses the advertising budget of $1 million then Pizza Hut will choose advertising budget of $2 million as profit is highest in that case.

If Papa John chooses the advertising budget of $2 million then Pizza Hut will choose advertising budget of $2 million as profit is highest in that case.

If Papa John chooses the advertising budget of $3 million then Pizza Hut will choose advertising budget of $1 million as profit is highest in that case.

Thus, it can be seen that whatever be the strategy of Papa John, Pizza Hut will never choose the advertisng budget of $3 million.

So, in first round of strategy elimination, the companies would exclude the ad budget of $3 million.

(b)

Now companies have two strategies - Ad budget of $1 million and Ad budget of $2 million.

If Pizza hut chooses the advertising budget of $1 million then Papa John will choose advertising budget of $2 million as profit is highest in that case.

If Pizza hut chooses the advertising budget of $2 million then Papa John will choose advertising budget of $1 million as profit is highest in that case.

It can be seen that ad budget of Papa John depends on the choice of ad budget by the Pizza Hut.

If Papa John chooses the advertising budget of $1 million then Pizza Hut will choose advertising budget of $2 million as profit is highest in that case.

If Papa John chooses the advertising budget of $2 million then Pizza Hut will choose advertising budget of $2 million as profit is highest in that case.

It can be seen that Pizza hut will never choose the ad budget of $1 million whatever be the ad budget choosen by the Papa John.

So, after first round of elimination, Pizza Hut will make the second round of elimination and it will eliminate the ad budget of $1 million while Papa John will not eliminate any of the remaining strategies.

(c)

Pizza Hut is now left with only one strategy that is ad budget of $2 million.

If Pizza hut chooses the advertising budget of $2 million then Papa John will choose advertising budget of $1 million as profit is highest in that case.

So, the likely outcome of this simultaneous advertising decision is that Pizza Hut will choose advertising budget of $2 million while Papa John will choose the advertising budget of $1 million.

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