Suppose that two Japanese companies, Hitachi and Toshiba, are the sole producers (i.e., duopolists) of a microprocessor chip used in a number of different brands of personal computers. Assume that total demand for the chips is fixed and that each firm charges the same price for the chips. Each firm’s market share and profits are a function of the magnitude of the promotional campaign used to promote its version of the chip. Also assume that only two strategies are available to each firm: a limited promotional campaign (budget) and an extensive promotional campaign (budget). If the two firms engage in a limited promotional campaign, each firm will earn a quarterly profit of $7.5 million. If the two firms undertake an extensive promotional campaign, each firm will earn a quarterly profit of $5.0 million. With this strategy combination, market share and total sales will be the same as for a limited promotional campaign, but promotional costs will be higher and hence profits will be lower. If either firm engages in a limited promotional campaign and the other firm undertakes an extensive promotional campaign, then the firm that adopts the extensive campaign will increase its market share and earn a profit of $9.0 million, whereas the firm that chooses the limited campaign will earn a profit of only $4.0 million.
a. Develop a payoff matrix for this decision-making problem.
b. In the absence of a binding and enforceable agreement, determine the dominant advertising strategy and minimum payoff for Hitachi.
c. Determine the dominant advertising strategy and minimum payoff for Toshiba.
d. Explain why the firms may choose not to play their dominant strategies whenever this game is repeated over multiple decision-making periods.