Question

Suppose 2 companies are competing for a percentage of the market share, and the table below represents the market share change for company B as well as three strategies that companies A and B might employ.

A. If Company A offers a discount price and Company B offers a free gift with purchase, what will be the change in market share for company B?

B. Company A will want to maximize the minimum payoff, thereby employing the Maximin approach to the game. Which strategy will Company A select based on the Maximin approach?

C. Company B will select the strategy that minimizes the maximum payoff, thereby employing the Minimax approach to the game. Which strategy will Company B select based on this approach?

D. If a game is a mixed strategy solution, the players select their strategy based on a probability distribution. Let P(AB) = the probability that company A boosts advertising = 1/4 Let P(AF) = the probability that company A offers a free gift with purchase = 1/4 Let P(AD) = the probability that company A offers discounted price = 1/2 Calculate the Expected Gain in market share for company A across all 3 company B strategies. E(BB) = E(BF) = E(BD) =

2. Suppose 2 companies are competing for a percentage of the market share, and the table below represents the market share change for company B as well as three strategies that companies A and B might emplov Company B Free gift with purchase Company A Boost advertising Free gift with p Discount price for repeat Boost advertising Discount price for repeat -1 -2 A. IkCompany A offers a discount price and Company B offers a free gift with purchase, what will be the change in market share for company B? B. Company A will want to maximize the minimum payoff, thereby employing the Maximin approach to the game. Which strategy will Company A select based on the Maximin approach? C. Company B will select the strategy that minimizes the maximum payoff, thereby employing the Minimax approach to the game. Which strategy will Company B select based on this approach? D. If a game is a mixed strategy solution, the players select their strategy based on a probability distribution. Let P(AB) the probability that company A boosts advertising Let P(AF) the probability that company A offers a free gift with purchase Let P(AD)- the probability that company A offers discounted price2 Calculate the Expected Gain in market share for company A across all 3.company B strategies E(BF)

Answer 1

Answer:

Since there are two company in the market so Market share change in B is equal to negative of change in market share of A.

So change in market share of A

Table 1

	Change in market Share of B
	Company B
Company A	boost Advertising	Free gift	Discount price
boost Advertising	3	-4	2
Free gift	-1	3	-2
Discount price	5	4	1

A)

If company A chooses Discount price and Company B offers free gift then change in market share for B is 4% it means there is 4% increase in marker share for B.

B)

For Maximin Approach

We need to find the minimum payoff for each strategy and we need to find the maximum payout from these strategy.

From Table 1

So Minimum Payout for Boost Advertising =-4

Minimum Payout for Free gift =-2

Minimum Payout for discount price =1

So maximum payoff from above three maximum payoff is 1 which for discount price.

So Company A will choose Discount price strategy for maximin approach.

C)

For Minimax Approach

We need to find the maximum payoff for each strategy and we need to find the minimum payoff from these strategy.

From Table 1

So Maximum Payout for Boost Advertising =5

Maximum Payout for Free gift =4

Maximum Payout for discount price =2

So maximum payoff from above three minimum payoff is 2 which for discount price.

So Company B will choose Discount price strategy for Minimax approach.

D)

Expected gain = {P(AB)*Payoff for company A to boost advertising+P(AF)*payoff for company A to free gift+P(AD)*payoff for company A to discount price}

E(BB)={1/4*(3)+1/4*(-1)+1/2*(5)}=3

E(BF)={1/4*(-4)+1/4*(3)+1/2*(4)}=1.75

E(BD)={1/4*(2)+1/4*(-2)+1/2*(1)}=0.5