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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.

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

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