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)?

Explanation / Answer

a. Papa Johns would eliminate $3 mill; Pizza Hut would eliminate $3 mill.

Both would eliminate $ 3 mill because its payoff is lower than as compared to both other strategies of choosing $ 1 mill or $ 2 mill.

b. Papa Johns would not eliminate either; Pizza Hut would eliminate $1 mill.

Papa Johns would not eliminate after eliminating $ 3 mill because there is no perfect strategy in which Papa Johns earns higher payoff irrespective of Pizza Hut decision. On the other hand, Pizza Hut would eliminate $ 1 mill because it provides less payoff as compared to $ 2 mill irrespective of decision of Papa John.

c. Papa Johns would pick $1 mill; Pizza Hut would pick $2 mill.

Pizza Hut left with only $ 2 mill so it will choose $ 2 mill while Papa Johns will choose $ 1 mill because it gives higher payoff.

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