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): a

Answer:

Given,

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):

Papa Johns is the row player and Pizza Hut is the column player. The first term of each cell represents the pay-off of Papa Johns from a particular strategy and the second term represents the pay-off of Pizza Hut. We indicate the optimal choices by underlinning them.

a. In the first round of strategy elimination:

• When Papa Johns chooses $ 1 mill , Pizza Hut chooses $ 3 mill because it gives them a higher pay-off. (240>230>225)
• When Papa Johns chooses $ 2 mill , Pizza Hut chooses $ 1 mill. ( 225 > 215 > 210)
• When Papa Johns chooses $ 3 mill , Pizza Hut chooses $3 mill. (210>200>195)

Thus , Pizza Hut never chooses $2 mill irrespective of what Papa Johns chooses. $2 mill is a strictly dominated strategy for Pizza Hut and will be eliminated in the first round by the iterated elimination of strictly dominated strategies.

The pay-off matrix now becomes :

b. Company make a second-round elimination, After the first round of elimination:

• When Pizza Hut chooses $1 mill , Papa Johns chooses $ 2 mill because it gives them a higher pay-off. (210>200>185)
• When Pizza Hut chooses $3 mill , Papa Johns chooses $ 2 mill. ( 145>140>135)

Thus , Papa Johns always chooses $2 mill irrespective of what Pizza Hut chooses. So , $2 mill is a strictly dominant strategy for Papa Johns. The other two strategies ( $1 mill and $3 mill ) are both strictly dominated strategies for Papa Johns and will be eliminated by the expected iteration of strictly dominated strategies.
The pay-off matrix now becomes :

• When Papa Johns chooses $ 2 mill , Pizza Hut will choose $ 1 mill because it gives them a higher pay-off. ( 225>215)

Thus , the pure strategy Nash Equilibrium for this game is ($2 mill , $1 mill ) and the pay-offs would be (210,225)

c. simultaneous advertising decision:

Thus , the most likely outcome of this simultaneous advertising decision is that Papa Johns will choose $2 mill and Pizza Hut will choose $1 mill and they would end up getting a pay-off of $210 and $225 respectively.