# Game Theory

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15. At a time when demand for ready-to-eat cereal was stagnant, a spokesperson for the cereal maker Kellogg's was quoted as saying, "... for the past several years, our individual company growth has come out of the other fellow's hide." Kellogg's has been producing cereal since 1906 and continues to implement strategies that make it a leader in the cereal industry. Suppose that when Kellogg's and its largest rival advertise, each company earns $0 billion in profits. When neither company advertises, each company earns profits of $8 billion. If one company advertises and the other does not, the company that advertises earns $48 billion and the company that does not advertise loses $1 billion. Under what conditions could trigger strategies be used by these firms to support the collusive level of advertising?

16. You are the manager of GearNet and must decide how many Internet hubs to produce to maximize your firm's profit. GearNet and its only rival (NetWorks) sell dual speed Internet hubs that are identical from consumer's perspectives. The market price for hubs depends on the total quantity produced by the two firms. A survey reveals that the market price of hubs depends on total market output as follows:

Combined Hub Protection of GearNet and NetWorks Market Price of Hubs (Per Unit)

500 units $120

750 units 100

1000 units 90

GearNet and NetWorks each use labor, materials, and machines to produce output. Gear Net purchases labor and materials on an as-needed basis; its machines were purchased three years ago and are being depreciated according to the straight-line method. GearNet's accounting department has provided the following data about its unit production costs: GearNet's Unit Cost for an Output of:

Item 250 units 500 units

Direct Labor $40 $40

Direct materials 30 30

Depreciation charge 80 40

Reports from industry experts suggest that NetWork's cost structure is similar to GearNet's cost structure and that technological constraints require each firm to produce either 250 hubs or 500 hubs. Identify the costs that are relevant for your decision, and then determine whether Gear Net should produce 250 hubs or 500 hubs.

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Answers questions on game theory.

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The answer is in excel file where formating is preserved

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<br>15. At a time when demand for ready-to-eat cereal was stagnant, a spokesperson for the cereal maker Kellogg's was quoted as saying, "... for the past several years, our individual company growth has come out of the other fellow's hide." Kellogg's has been producing cereal since 1906 and continues to implement strategies that make it a leader in the cereal industry. Suppose that when Kellogg's and its largest rival advertise, each company earns $0 billion in profits. When neither company advertises, each company earns profits of $8 billion. If one company advertises and the other does not, the company that advertises earns $48 billion and the company that does not advertise loses $1 billion. Under what conditions could trigger strategies be used by these firms to support the collusive level of advertising?

<br><br>We construct a payoff matrix in terms of Profit by Kellog

<br><br>If Kellog advertises and competitor advertises/does not advertise Kellog earns 0/48

<br><br>If Kellog does not advertises and competitor advertises/does not advertise Kellog earns -1/8

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<br><br> Strategy by competitor

<br><br> Strategy by Kellog Advertise Do not advertise Row minimum Maximin

<br><br> Advertise 0 48 0 0

<br><br> Do not advertise -1 8 -1

<br><br> Column ...

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