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) Papa Johns will eliminate strategy $3 and Pizza hut will also eliminate $3.

B) Pizza hit will eliminate $1 in second round

C)($1,$2) is a nash equilibrium where Papa Johns will hve budget of $1 and Pizza hit have budget of $2.

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