Suppose 2 companies are competing for a percentage of the market share, and the

Question

Suppose 2 companies are competing for a percentage of the market share, and the table below represents the market share change A as well as three strategies that companies A and B might employ. If Company A opens more locations and Company B offers a free gift with purchase, what will be the change in market share for company B? Company A will want to maximize the minimum payoff. Which strategy will Company A select based on the Maximum approach? Company B will select the strategy that minimizes the maximum payoff. Which strategy will Company B select based on this approach? 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 boost advertising = 1/2 Let P(AF) = the probability that company A offers a free gift with purchase = 1/4 Let P(AO) = the probability that company A opens more locations = 1/4 Calculate the Expected Gain in market share for company A across all 3 company B strategies. E(BB) =__E(BF) =___E(BO) =__.

Explanation / Answer

5.

A) If company A open more locations and company B offers a free gift with purchasethen comapny B will gain the market share by 2% as per the Game theory concepts of decision making.

B) Company A can be guaranteed a decrease in market share by 1% by selecting boost advertising option, decrease in market share by 1% by selecting free gift option and decrease in market share by 2% by selecting open more location option. As per Maximin approach,company A selects that provides the maximum of the row minimum values.Thus company can select any of the strategy between boost advertising and  free gift options

C) Company B can be guaranteed a decrease in market share by 4% by selecting boost advertising option, decrease in market share by 2% by selecting free gift option and decrease in market share by 2% by selecting open more location option.Thus ,to minimize the maximum payoff company B will select either of the two options Free Gift or Open more location. Company B has guaranteed that company A cannot gain more than 2% of market share.

D) E (BB) = 4*P(AB) + 2* P(AF) + 3 * P(AO)

= 4*(1/2) + 2*(1/4) + 3 * (1/4)

= 3.25 % Expected Gain in market share for Company A

E (BO) = 2*P(AB) - 1* P(AF) + 2 * P(AO)

= 2*(1/2) - 1*(1/4) + 2 * (1/4)

= 1.25 % Expected increase in market share for Company A

E (BF) = -1*P(AB) + 2* P(AF) - 2 * P(AO)

= 4*(1/2) + 2*(1/4) - 2 * (1/4)

= -0.5 % Expected decrease in market share for Company A

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