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 the 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 $11 million. If the two firms undertake an extensive promotional campaign, each firm will earn a quarterly profit of $8 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 $16 million, whereas the firm that chooses the limited campaign will earn a profit of only $4 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 the minimum payoff for Hitachi.
c. Determine the dominant advertising strategy and the minimum payoff for Toshiba

However, if one firm engages in an extensive campaign and the other firm engages in a limited one, the firm engaging in a limited campaign earns $4 million while the one engaging in an extensive campaign earns $16 million.

I have attached a photo to show the payoff matrix as a table.

b) In the absence of a binding and enforceable agreement, that is to say that if both firms are not colluding, Hitachi's dominant strategy would be to engage in an EXTENSIVE PROMOTIONAL CAMPAIGN.

A Firm's dominant strategy in absence of an agreement is that strategy that a firm can go on and make a maximum amount of profit regardless of what the other firm does.

Should Hitachi engage in an Extensive Campaign, they will make $16 million in quarterly profit if Toshiba engages in a Limited Campaign. Should Toshiba also decide to engage in an Extensive Campaign, then Hitachi makes a profit of $8 million. This is therefore their best alternative as opposed to embarking on a limited Campaign where there is a chance that they will make $4 million.

With the Extensive Campaign, Hitachi's Minimum Payoff is $8 million.

c) The game is the same for both players so the best option for Hitachi, is the best option for Toshiba as well. This means that Toshiba's dominant Strategy is an EXTENSIVE PROMOTIONAL CAMPAIGN and their minimum payoff is $8 million as well.