Two companies promote two competing products. Currently, each product controls 50% of the market. Because of recent improvements in the two products, each company plans to launch an advertising campaign. If neither company advertises, equal market shares will continue. If either company launches a stronger campaign, the other company is certain to lose a proportional percentage of its customers. A survey of the market shows that 50% of potential customers can be reached through television, 30% through newspapers, and 20% through radio.

(a) Formulate the problem as a two-person zero-sum game, and determine the advertising media for each company.

(b) Determine a range for the value of the game. Can each company operate with a single pure strategy?