Two companies promote two competing products. Currently, Product A controls 60% of the market and Product B controls 40% of the market. Because of recent improvements in the two products, each company is preparing to launch an advertising campaign. If neither company advertises, the same market shares will continue. If the two companies launch different campaigns, each product is certain to lose a proportional percentage of its customers. Otherwise, they maintain their current market shares. A survey of the market shows that 50% of potential customers can be reached through television, 30% through newspapers, and 20% through radio. (Assume that either company are not allowed to mix the medium used in their campaigns).
Formulate the problem as a zero-sum game and prepare the payoff matrix. Answer the succeeding questions.
1. What is the value of the game? %
2. What is the corresponding payoff if company A chooses a newspaper campaign while company B chooses a TV campaign?
3. What is the corresponding payoff if company A chooses a TV campaign while company B chooses a radio campaign?
4. What is the corresponding payoff if company A chooses a newspaper campaign while company B chooses a radio campaign?
Please show complete solution, matrix, and explanation.