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Two firms in a duopoly each have the option of advertising or not advertising. Assume that for both firms their respective products and brands are

Two firms in a duopoly each have the option of advertising or not advertising. Assume that for both firms their respective products and brands are well known (e.g. soft drink brands) so advertising is not essential. Also advertising costs money. However, the risk is if one firm decides not to advertise but the other does, then the rival who advertises dominates the market for that year. The profit payoffs for each in millions of dollars of the choice combinations are shown in the decision matrix in the Figure below.

Firm B

Firm B advertise

Firm B does NOT advertise

Firm A

Firm A advertises

Firm B earns $70 M profit.

Firm A earns $80 M profit.

Firm B earns $40 M profit.

Firm A earns $120 M profit.

Firm A does NOT advertise

Firm B earns $100M profit.

Firm A earns $50 M profit.

Firm B earns $80 M profit.

Firm A earns $90 M profit.

  1. What is the dominant strategy (i.e. a Nash equilibrium) for the two firms? Explain briefly.
  2. Now assume that Firm A decides to pay Firm B not to advertise. (Let us just assume it is legal.) How much does Firm A have to pay Firm B for Firm B to not advertise? Briefly explain why you chose that amount.

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