# game theory and two companies

Assume two high-tech companies, X and Y, are the only producers of a new

product that is used my numerous computer manufacturers. The total demand for the new product is fixed and the price is set. Each firm's market share and profits are a function of the size of its advertising and promotional campaigns.

If the two firms engage in limited campaigns, each will earn an annual profit of $10 million. If the two firms undertake extensive advertising campaigns, each will earn annual profits of $5 million. In both of the above outcomes, each firm will capture half of the market. If one firm engages in a limited campaign and the other in an extensive campaign, the firm with the extensive campaign will have the larger market share and earn an annual profit of $9 million and the other firm will earn a profit of $3 million.

a. Assuming a simultaneous move, non-repeated interaction game, identify the

Nash equilibrium or multiple equilibrium, assuming there is one.

b. Does either of the players have a dominant strategy. If so, what is it?

c. Is this an example of prisoner's dilemma? Explain your answer.

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#### Solution Preview

See the attached file. We can determine whether equilibrium exists by noting each firm's choices in each situation. If Firm 2 has a limited campaign, firm 1 will want a limited one as well. However, if firm 2 has an extensive campaign, firm 1 will want to have an extensive one as well. The same holds for firm ...

#### Solution Summary

Use of strategy in determining campaigns for high tech companies